Sample records for lagrangian-eulerian finite element

  1. CELFE: Coupled Eulerian-Lagrangian Finite Element program for high velocity impact. Part 1: Theory and formulation. [hydroelasto-viscoplastic model

    NASA Technical Reports Server (NTRS)

    Lee, C. H.

    1978-01-01

    A 3-D finite element program capable of simulating the dynamic behavior in the vicinity of the impact point, together with predicting the dynamic response in the remaining part of the structural component subjected to high velocity impact is discussed. The finite algorithm is formulated in a general moving coordinate system. In the vicinity of the impact point contained by a moving failure front, the relative velocity of the coordinate system will approach the material particle velocity. The dynamic behavior inside the region is described by Eulerian formulation based on a hydroelasto-viscoplastic model. The failure front which can be regarded as the boundary of the impact zone is described by a transition layer. The layer changes the representation from the Eulerian mode to the Lagrangian mode outside the failure front by varying the relative velocity of the coordinate system to zero. The dynamic response in the remaining part of the structure described by the Lagrangian formulation is treated using advanced structural analysis. An interfacing algorithm for coupling CELFE with NASTRAN is constructed to provide computational capabilities for large structures.

  2. Eulerian-Lagrangian Simulations of Transonic Flutter Instabilities

    NASA Technical Reports Server (NTRS)

    Bendiksen, Oddvar O.

    1994-01-01

    This paper presents an overview of recent applications of Eulerian-Lagrangian computational schemes in simulating transonic flutter instabilities. This approach, the fluid-structure system is treated as a single continuum dynamics problem, by switching from an Eulerian to a Lagrangian formulation at the fluid-structure boundary. This computational approach effectively eliminates the phase integration errors associated with previous methods, where the fluid and structure are integrated sequentially using different schemes. The formulation is based on Hamilton's Principle in mixed coordinates, and both finite volume and finite element discretization schemes are considered. Results from numerical simulations of transonic flutter instabilities are presented for isolated wings, thin panels, and turbomachinery blades. The results suggest that the method is capable of reproducing the energy exchange between the fluid and the structure with significantly less error than existing methods. Localized flutter modes and panel flutter modes involving traveling waves can also be simulated effectively with no a priori knowledge of the type of instability involved.

  3. An Eulerian/Lagrangian coupling procedure for three-dimensional vortical flows

    NASA Technical Reports Server (NTRS)

    Felici, Helene M.; Drela, Mark

    1993-01-01

    A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of 3D vortical flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method, added to the Eulerian time-marching procedure, provides a correction of the Eulerian solution. In turn, the Eulerian solution is used to integrate the Lagrangian state-vector along the particles trajectories. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers describe accurately the convection properties and enhance the vorticity and entropy capturing capabilities of the Eulerian solver. The Eulerian/Lagrangian coupling strategies are discussed and the combined scheme is tested on a constant stagnation pressure flow in a 90 deg bend and on a swirling pipe flow. As the numerical diffusion is reduced when using the Lagrangian correction, a vorticity gradient augmentation is identified as a basic problem of this inviscid calculation.

  4. A finite-volume Eulerian-Lagrangian Localized Adjoint Method for solution of the advection-dispersion equation

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1993-01-01

    A new mass-conservative method for solution of the one-dimensional advection-dispersion equation is derived and discussed. Test results demonstrate that the finite-volume Eulerian-Lagrangian localized adjoint method (FVELLAM) outperforms standard finite-difference methods, in terms of accuracy and efficiency, for solute transport problems that are dominated by advection. For dispersion-dominated problems, the performance of the method is similar to that of standard methods. Like previous ELLAM formulations, FVELLAM systematically conserves mass globally with all types of boundary conditions. FVELLAM differs from other ELLAM approaches in that integrated finite differences, instead of finite elements, are used to approximate the governing equation. This approach, in conjunction with a forward tracking scheme, greatly facilitates mass conservation. The mass storage integral is numerically evaluated at the current time level, and quadrature points are then tracked forward in time to the next level. Forward tracking permits straightforward treatment of inflow boundaries, thus avoiding the inherent problem in backtracking, as used by most characteristic methods, of characteristic lines intersecting inflow boundaries. FVELLAM extends previous ELLAM results by obtaining mass conservation locally on Lagrangian space-time elements. Details of the integration, tracking, and boundary algorithms are presented. Test results are given for problems in Cartesian and radial coordinates.

  5. Dynamic analysis of a needle insertion for soft materials: Arbitrary Lagrangian-Eulerian-based three-dimensional finite element analysis.

    PubMed

    Yamaguchi, Satoshi; Tsutsui, Kihei; Satake, Koji; Morikawa, Shigehiro; Shirai, Yoshiaki; Tanaka, Hiromi T

    2014-10-01

    Our goal was to develop a three-dimensional finite element model that enables dynamic analysis of needle insertion for soft materials. To demonstrate large deformation and fracture, we used the arbitrary Lagrangian-Eulerian (ALE) method for fluid analysis. We performed ALE-based finite element analysis for 3% agar gel and three types of copper needle with bevel tips. To evaluate simulation results, we compared the needle deflection and insertion force with corresponding experimental results acquired with a uniaxial manipulator. We studied the shear stress distribution of agar gel on various time scales. For 30°, 45°, and 60°, differences in deflections of each needle between both sets of results were 2.424, 2.981, and 3.737mm, respectively. For the insertion force, there was no significant difference for mismatching area error (p<0.05) between simulation and experimental results. Our results have the potential to be a stepping stone to develop pre-operative surgical planning to estimate an optimal needle insertion path for MR image-guided microwave coagulation therapy and for analyzing large deformation and fracture in biological tissues. Copyright © 2014 Elsevier Ltd. All rights reserved.

  6. ALE3D: An Arbitrary Lagrangian-Eulerian Multi-Physics Code

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Noble, Charles R.; Anderson, Andrew T.; Barton, Nathan R.

    ALE3D is a multi-physics numerical simulation software tool utilizing arbitrary-Lagrangian- Eulerian (ALE) techniques. The code is written to address both two-dimensional (2D plane and axisymmetric) and three-dimensional (3D) physics and engineering problems using a hybrid finite element and finite volume formulation to model fluid and elastic-plastic response of materials on an unstructured grid. As shown in Figure 1, ALE3D is a single code that integrates many physical phenomena.

  7. A coupled Eulerian/Lagrangian method for the solution of three-dimensional vortical flows

    NASA Technical Reports Server (NTRS)

    Felici, Helene Marie

    1992-01-01

    A coupled Eulerian/Lagrangian method is presented for the reduction of numerical diffusion observed in solutions of three-dimensional rotational flows using standard Eulerian finite-volume time-marching procedures. A Lagrangian particle tracking method using particle markers is added to the Eulerian time-marching procedure and provides a correction of the Eulerian solution. In turn, the Eulerian solutions is used to integrate the Lagrangian state-vector along the particles trajectories. The Lagrangian correction technique does not require any a-priori information on the structure or position of the vortical regions. While the Eulerian solution ensures the conservation of mass and sets the pressure field, the particle markers, used as 'accuracy boosters,' take advantage of the accurate convection description of the Lagrangian solution and enhance the vorticity and entropy capturing capabilities of standard Eulerian finite-volume methods. The combined solution procedures is tested in several applications. The convection of a Lamb vortex in a straight channel is used as an unsteady compressible flow preservation test case. The other test cases concern steady incompressible flow calculations and include the preservation of turbulent inlet velocity profile, the swirling flow in a pipe, and the constant stagnation pressure flow and secondary flow calculations in bends. The last application deals with the external flow past a wing with emphasis on the trailing vortex solution. The improvement due to the addition of the Lagrangian correction technique is measured by comparison with analytical solutions when available or with Eulerian solutions on finer grids. The use of the combined Eulerian/Lagrangian scheme results in substantially lower grid resolution requirements than the standard Eulerian scheme for a given solution accuracy.

  8. Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary Lagrangian-Eulerian Approach

    NASA Astrophysics Data System (ADS)

    Melis, Matthew E.

    2003-01-01

    Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.

  9. Finite Element Simulation of a Space Shuttle Solid Rocket Booster Aft Skirt Splashdown Using an Arbitrary Lagrangian-eulerian Approach

    NASA Technical Reports Server (NTRS)

    Melis, Matthew E.

    2003-01-01

    Explicit finite element techniques employing an Arbitrary Lagrangian-Eulerian (ALE) methodology, within the transient dynamic code LS-DYNA, are used to predict splashdown loads on a proposed replacement/upgrade of the hydrazine tanks on the thrust vector control system housed within the aft skirt of a Space Shuttle Solid Rocket Booster. Two preliminary studies are performed prior to the full aft skirt analysis: An analysis of the proposed tank impacting water without supporting aft skirt structure, and an analysis of space capsule water drop tests conducted at NASA's Langley Research Center. Results from the preliminary studies provide confidence that useful predictions can be made by applying the ALE methodology to a detailed analysis of a 26-degree section of the skirt with proposed tank attached. Results for all three studies are presented and compared to limited experimental data. The challenges of using the LS-DYNA ALE capability for this type of analysis are discussed.

  10. Hybrid finite difference/finite element immersed boundary method.

    PubMed

    E Griffith, Boyce; Luo, Xiaoyu

    2017-12-01

    The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International  Journal  for  Numerical  Methods  in  Biomedical  Engineering Published by John Wiley & Sons Ltd.

  11. Reduction of numerical diffusion in three-dimensional vortical flows using a coupled Eulerian/Lagrangian solution procedure

    NASA Technical Reports Server (NTRS)

    Felici, Helene M.; Drela, Mark

    1993-01-01

    A new approach based on the coupling of an Eulerian and a Lagrangian solver, aimed at reducing the numerical diffusion errors of standard Eulerian time-marching finite-volume solvers, is presented. The approach is applied to the computation of the secondary flow in two bent pipes and the flow around a 3D wing. Using convective point markers the Lagrangian approach provides a correction of the basic Eulerian solution. The Eulerian flow in turn integrates in time the Lagrangian state-vector. A comparison of coarse and fine grid Eulerian solutions makes it possible to identify numerical diffusion. It is shown that the Eulerian/Lagrangian approach is an effective method for reducing numerical diffusion errors.

  12. Higher-Order Advection-Based Remap of Magnetic Fields in an Arbitrary Lagrangian-Eulerian Code

    NASA Astrophysics Data System (ADS)

    Cornille, Brian; White, Dan

    2017-10-01

    We will present methods formulated for the Eulerian advection stage of an arbitrary Lagrangian-Eulerian code for the new addition of magnetohydrodynamic (MHD) effects. The various physical fields are advanced in time using a Lagrangian formulation of the system. When this Lagrangian motion produces substantial distortion of the mesh, it can be difficult or impossible to progress the simulation forward. This is overcome by relaxation of the mesh while the physical fields are frozen. The code has already successfully been extended to include evolution of magnetic field diffusion during the Lagrangian motion stage. This magnetic field is discretized using an H(div) compatible finite element basis. The advantage of this basis is that the divergence-free constraint of magnetic fields is maintained exactly during the Lagrangian motion evolution. Our goal is to preserve this property during Eulerian advection as well. We will demonstrate this property and the importance of MHD effects in several numerical experiments. In pulsed-power experiments magnetic fields may be imposed or spontaneously generated. When these magnetic fields are present, the evolution of the experiment may differ from a comparable configuration without magnetic fields. Prepared by LLNL under Contract DE-AC52-07NA27344. Supported by DOE CSGF under Grant Number DE-FG02-97ER25308.

  13. Comparison of updated Lagrangian FEM with arbitrary Lagrangian Eulerian method for 3D thermo-mechanical extrusion of a tube profile

    NASA Astrophysics Data System (ADS)

    Kronsteiner, J.; Horwatitsch, D.; Zeman, K.

    2017-10-01

    Thermo-mechanical numerical modelling and simulation of extrusion processes faces several serious challenges. Large plastic deformations in combination with a strong coupling of thermal with mechanical effects leads to a high numerical demand for the solution as well as for the handling of mesh distortions. The two numerical methods presented in this paper also reflect two different ways to deal with mesh distortions. Lagrangian Finite Element Methods (FEM) tackle distorted elements by building a new mesh (called re-meshing) whereas Arbitrary Lagrangian Eulerian (ALE) methods use an "advection" step to remap the solution from the distorted to the undistorted mesh. Another difference between conventional Lagrangian and ALE methods is the separate treatment of material and mesh in ALE, allowing the definition of individual velocity fields. In theory, an ALE formulation contains the Eulerian formulation as a subset to the Lagrangian description of the material. The investigations presented in this paper were dealing with the direct extrusion of a tube profile using EN-AW 6082 aluminum alloy and a comparison of experimental with Lagrangian and ALE results. The numerical simulations cover the billet upsetting and last until one third of the billet length is extruded. A good qualitative correlation of experimental and numerical results could be found, however, major differences between Lagrangian and ALE methods concerning thermo-mechanical coupling lead to deviations in the thermal results.

  14. Adaptive reconnection-based arbitrary Lagrangian Eulerian method

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Bo, Wurigen; Shashkov, Mikhail

    We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

  15. Adaptive reconnection-based arbitrary Lagrangian Eulerian method

    DOE PAGES

    Bo, Wurigen; Shashkov, Mikhail

    2015-07-21

    We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less

  16. Bayesian Nonlinear Assimilation of Eulerian and Lagrangian Coastal Flow Data

    DTIC Science & Technology

    2015-09-30

    Lagrangian Coastal Flow Data Dr. Pierre F.J. Lermusiaux Department of Mechanical Engineering Center for Ocean Science and Engineering Massachusetts...Develop and apply theory, schemes and computational systems for rigorous Bayesian nonlinear assimilation of Eulerian and Lagrangian coastal flow data...coastal ocean fields, both in Eulerian and Lagrangian forms. - Further develop and implement our GMM-DO schemes for robust Bayesian nonlinear estimation

  17. Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in Flash

    NASA Technical Reports Server (NTRS)

    Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

    2012-01-01

    In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

  18. Imposing a Lagrangian Particle Framework on an Eulerian Hydrodynamics Infrastructure in FLASH

    NASA Astrophysics Data System (ADS)

    Dubey, A.; Daley, C.; ZuHone, J.; Ricker, P. M.; Weide, K.; Graziani, C.

    2012-08-01

    In many astrophysical simulations, both Eulerian and Lagrangian quantities are of interest. For example, in a galaxy cluster merger simulation, the intracluster gas can have Eulerian discretization, while dark matter can be modeled using particles. FLASH, a component-based scientific simulation code, superimposes a Lagrangian framework atop an adaptive mesh refinement Eulerian framework to enable such simulations. The discretization of the field variables is Eulerian, while the Lagrangian entities occur in many different forms including tracer particles, massive particles, charged particles in particle-in-cell mode, and Lagrangian markers to model fluid-structure interactions. These widely varying roles for Lagrangian entities are possible because of the highly modular, flexible, and extensible architecture of the Lagrangian framework. In this paper, we describe the Lagrangian framework in FLASH in the context of two very different applications, Type Ia supernovae and galaxy cluster mergers, which use the Lagrangian entities in fundamentally different ways.

  19. Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence

    NASA Technical Reports Server (NTRS)

    Squires, Kyle D.; Eaton, John K.

    1991-01-01

    Direct numerical simulation is used to study dispersion in decaying isotropic turbulence and homogeneous shear flow. Both Lagrangian and Eulerian data are presented allowing direct comparison, but at fairly low Reynolds number. The quantities presented include properties of the dispersion tensor, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The Lagrangian time microscale is found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame.

  20. Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

    USGS Publications Warehouse

    Casulli, V.; Cheng, R.T.

    1990-01-01

    In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

  1. a Marker-Based Eulerian-Lagrangian Method for Multiphase Flow with Supersonic Combustion Applications

    NASA Astrophysics Data System (ADS)

    Fan, Xiaofeng; Wang, Jiangfeng

    2016-06-01

    The atomization of liquid fuel is a kind of intricate dynamic process from continuous phase to discrete phase. Procedures of fuel spray in supersonic flow are modeled with an Eulerian-Lagrangian computational fluid dynamics methodology. The method combines two distinct techniques and develops an integrated numerical simulation method to simulate the atomization processes. The traditional finite volume method based on stationary (Eulerian) Cartesian grid is used to resolve the flow field, and multi-component Navier-Stokes equations are adopted in present work, with accounting for the mass exchange and heat transfer occupied by vaporization process. The marker-based moving (Lagrangian) grid is utilized to depict the behavior of atomized liquid sprays injected into a gaseous environment, and discrete droplet model 13 is adopted. To verify the current approach, the proposed method is applied to simulate processes of liquid atomization in supersonic cross flow. Three classic breakup models, TAB model, wave model and K-H/R-T hybrid model, are discussed. The numerical results are compared with multiple perspectives quantitatively, including spray penetration height and droplet size distribution. In addition, the complex flow field structures induced by the presence of liquid spray are illustrated and discussed. It is validated that the maker-based Eulerian-Lagrangian method is effective and reliable.

  2. Effects of Helicity on Lagrangian and Eulerian Time Correlations in Turbulence

    NASA Technical Reports Server (NTRS)

    Rubinstein, Robert; Zhou, Ye

    1998-01-01

    Taylor series expansions of turbulent time correlation functions are applied to show that helicity influences Eulerian time correlations more strongly than Lagrangian time correlations: to second order in time, the helicity effect on Lagrangian time correlations vanishes, but the helicity effect on Eulerian time correlations is nonzero. Fourier analysis shows that the helicity effect on Eulerian time correlations is confined to the largest inertial range scales. Some implications for sound radiation by swirling flows are discussed.

  3. Lagrangian continuum dynamics in ALEGRA.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Wong, Michael K. W.; Love, Edward

    Alegra is an ALE (Arbitrary Lagrangian-Eulerian) multi-material finite element code that emphasizes large deformations and strong shock physics. The Lagrangian continuum dynamics package in Alegra uses a Galerkin finite element spatial discretization and an explicit central-difference stepping method in time. The goal of this report is to describe in detail the characteristics of this algorithm, including the conservation and stability properties. The details provided should help both researchers and analysts understand the underlying theory and numerical implementation of the Alegra continuum hydrodynamics algorithm.

  4. Coupled Eulerian-Lagrangian transport of large debris by tsunamis

    NASA Astrophysics Data System (ADS)

    Conde, Daniel A. S.; Ferreira, Rui M. L.; Sousa Oliveira, Carlos

    2016-04-01

    Tsunamis are notorious for the large disruption they can cause on coastal environments, not only due to the imparted momentum of the incoming wave but also due to its capacity to transport large quantities of solid debris, either from natural or human-made sources, over great distances. A 2DH numerical model under development at CERIS-IST (Ferreira et al., 2009; Conde, 2013) - STAV2D - capable of simulating solid transport in both Eulerian and Lagrangian paradigms will be used to assess the relevance of Lagrangian-Eulerian coupling when modelling the transport of solid debris by tsunamis. The model has been previously validated and applied to tsunami scenarios (Conde, 2013), being well-suited for overland tsunami propagation and capable of handling morphodynamic changes in estuaries and seashores. The discretization scheme is an explicit Finite Volume technique employing flux-vector splitting and a reviewed Roe-Riemann solver. Source term formulations are employed in a semi-implicit way, including the two-way coupling of the Lagrangian and Eulerian solvers by means of conservative mass and momentum transfers between fluid and solid phases. The model was applied to Sines Port, a major commercial port in Portugal, where two tsunamigenic scenarios are considered: an 8.5 Mw scenario, consistent with the Great Lisbon Earthquake and Tsunami of the 1st November 1755 (Baptista, 2009), and an hypothetical 9.5 Mw worst-case scenario based on the same historical event. Open-ocean propagation of these scenarios were simulated with GeoClaw model from ClawPack (Leveque, 2011). Following previous efforts on the modelling of debris transport by tsunamis in seaports (Conde, 2015), this work discusses the sensitivity of the obtained results with respect to the phenomenological detail of the employed Eulerian-Lagrangian formulation and the resolution of the mesh used in the Eulerian solver. The results have shown that the fluid to debris mass ratio is the key parameter regarding the

  5. Seakeeping with the semi-Lagrangian particle finite element method

    NASA Astrophysics Data System (ADS)

    Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

    2017-07-01

    The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

  6. Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

    DOE PAGES

    Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.; ...

    2016-04-27

    We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

  7. Multi-Material Closure Model for High-Order Finite Element Lagrangian Hydrodynamics

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Dobrev, V. A.; Kolev, T. V.; Rieben, R. N.

    We present a new closure model for single fluid, multi-material Lagrangian hydrodynamics and its application to high-order finite element discretizations of these equations [1]. The model is general with respect to the number of materials, dimension and space and time discretizations. Knowledge about exact material interfaces is not required. Material indicator functions are evolved by a closure computation at each quadrature point of mixed cells, which can be viewed as a high-order variational generalization of the method of Tipton [2]. This computation is defined by the notion of partial non-instantaneous pressure equilibration, while the full pressure equilibration is achieved bymore » both the closure model and the hydrodynamic motion. Exchange of internal energy between materials is derived through entropy considerations, that is, every material produces positive entropy, and the total entropy production is maximized in compression and minimized in expansion. Results are presented for standard one-dimensional two-material problems, followed by two-dimensional and three-dimensional multi-material high-velocity impact arbitrary Lagrangian–Eulerian calculations. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.« less

  8. A direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume scheme on unstructured tetrahedral meshes for conservative and non-conservative hyperbolic systems in 3D

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael

    2014-10-01

    In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with

  9. Assimilating Eulerian and Lagrangian data in traffic-flow models

    NASA Astrophysics Data System (ADS)

    Xia, Chao; Cochrane, Courtney; DeGuire, Joseph; Fan, Gaoyang; Holmes, Emma; McGuirl, Melissa; Murphy, Patrick; Palmer, Jenna; Carter, Paul; Slivinski, Laura; Sandstede, Björn

    2017-05-01

    Data assimilation of traffic flow remains a challenging problem. One difficulty is that data come from different sources ranging from stationary sensors and camera data to GPS and cell phone data from moving cars. Sensors and cameras give information about traffic density, while GPS data provide information about the positions and velocities of individual cars. Previous methods for assimilating Lagrangian data collected from individual cars relied on specific properties of the underlying computational model or its reformulation in Lagrangian coordinates. These approaches make it hard to assimilate both Eulerian density and Lagrangian positional data simultaneously. In this paper, we propose an alternative approach that allows us to assimilate both Eulerian and Lagrangian data. We show that the proposed algorithm is accurate and works well in different traffic scenarios and regardless of whether ensemble Kalman or particle filters are used. We also show that the algorithm is capable of estimating parameters and assimilating real traffic observations and synthetic observations obtained from microscopic models.

  10. Solution of the advection-dispersion equation by a finite-volume eulerian-lagrangian local adjoint method

    USGS Publications Warehouse

    Healy, R.W.; Russell, T.F.

    1992-01-01

    A finite-volume Eulerian-Lagrangian local adjoint method for solution of the advection-dispersion equation is developed and discussed. The method is mass conservative and can solve advection-dominated ground-water solute-transport problems accurately and efficiently. An integrated finite-difference approach is used in the method. A key component of the method is that the integral representing the mass-storage term is evaluated numerically at the current time level. Integration points, and the mass associated with these points, are then forward tracked up to the next time level. The number of integration points required to reach a specified level of accuracy is problem dependent and increases as the sharpness of the simulated solute front increases. Integration points are generally equally spaced within each grid cell. For problems involving variable coefficients it has been found to be advantageous to include additional integration points at strategic locations in each well. These locations are determined by backtracking. Forward tracking of boundary fluxes by the method alleviates problems that are encountered in the backtracking approaches of most characteristic methods. A test problem is used to illustrate that the new method offers substantial advantages over other numerical methods for a wide range of problems.

  11. A Combined Eulerian-Lagrangian Data Representation for Large-Scale Applications.

    PubMed

    Sauer, Franz; Xie, Jinrong; Ma, Kwan-Liu

    2017-10-01

    The Eulerian and Lagrangian reference frames each provide a unique perspective when studying and visualizing results from scientific systems. As a result, many large-scale simulations produce data in both formats, and analysis tasks that simultaneously utilize information from both representations are becoming increasingly popular. However, due to their fundamentally different nature, drawing correlations between these data formats is a computationally difficult task, especially in a large-scale setting. In this work, we present a new data representation which combines both reference frames into a joint Eulerian-Lagrangian format. By reorganizing Lagrangian information according to the Eulerian simulation grid into a "unit cell" based approach, we can provide an efficient out-of-core means of sampling, querying, and operating with both representations simultaneously. We also extend this design to generate multi-resolution subsets of the full data to suit the viewer's needs and provide a fast flow-aware trajectory construction scheme. We demonstrate the effectiveness of our method using three large-scale real world scientific datasets and provide insight into the types of performance gains that can be achieved.

  12. Examination of Eulerian and Lagrangian Coordinate Systems.

    ERIC Educational Resources Information Center

    Remillard, Wilfred J.

    1978-01-01

    Studies the relationship between Eulerian and Lagrangian coordinate systems with the help of computer plots of variables such as density and particle displacement. Gives examples which illustrate the differences in the shape of a traveling wave as seen by observers in the two systems. (Author/GA)

  13. Arbitrary-Lagrangian-Eulerian Discontinuous Galerkin schemes with a posteriori subcell finite volume limiting on moving unstructured meshes

    NASA Astrophysics Data System (ADS)

    Boscheri, Walter; Dumbser, Michael

    2017-10-01

    We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total

  14. Simulating Space Capsule Water Landing with Explicit Finite Element Method

    NASA Technical Reports Server (NTRS)

    Wang, John T.; Lyle, Karen H.

    2007-01-01

    A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.

  15. Eulerian and Lagrangian Plasma Jet Modeling for the Plasma Liner Experiment

    NASA Astrophysics Data System (ADS)

    Hatcher, Richard; Cassibry, Jason; Stanic, Milos; Loverich, John; Hakim, Ammar

    2011-10-01

    The Plasma Liner Experiment (PLX) aims to demonstrate the feasibility of using spherically-convergent plasma jets to from an imploding plasma liner. Our group has modified two hydrodynamic simulation codes to include radiative loss, tabular equations of state (EOS), and thermal transport. Nautilus, created by TechX Corporation, is a finite-difference Eulerian code which solves the MHD equations formulated as systems of hyperbolic conservation laws. The other is SPHC, a smoothed particle hydrodynamics code produced by Stellingwerf Consulting. Use of the Lagrangian fluid particle approach of SPH is motivated by the ability to accurately track jet interfaces, the plasma vacuum boundary, and mixing of various layers, but Eulerian codes have been in development for much longer and have better shock capturing. We validate these codes against experimental measurements of jet propagation, expansion, and merging of two jets. Precursor jets are observed to form at the jet interface. Conditions that govern evolution of two and more merging jets are explored.

  16. Structure of sheared and rotating turbulence: Multiscale statistics of Lagrangian and Eulerian accelerations and passive scalar dynamics.

    PubMed

    Jacobitz, Frank G; Schneider, Kai; Bos, Wouter J T; Farge, Marie

    2016-01-01

    The acceleration statistics of sheared and rotating homogeneous turbulence are studied using direct numerical simulation results. The statistical properties of Lagrangian and Eulerian accelerations are considered together with the influence of the rotation to shear ratio, as well as the scale dependence of their statistics. The probability density functions (pdfs) of both Lagrangian and Eulerian accelerations show a strong and similar dependence on the rotation to shear ratio. The variance and flatness of both accelerations are analyzed and the extreme values of the Eulerian acceleration are observed to be above those of the Lagrangian acceleration. For strong rotation it is observed that flatness yields values close to three, corresponding to Gaussian-like behavior, and for moderate and vanishing rotation the flatness increases. Furthermore, the Lagrangian and Eulerian accelerations are shown to be strongly correlated for strong rotation due to a reduced nonlinear term in this case. A wavelet-based scale-dependent analysis shows that the flatness of both Eulerian and Lagrangian accelerations increases as scale decreases, which provides evidence for intermittent behavior. For strong rotation the Eulerian acceleration is even more intermittent than the Lagrangian acceleration, while the opposite result is obtained for moderate rotation. Moreover, the dynamics of a passive scalar with gradient production in the direction of the mean velocity gradient is analyzed and the influence of the rotation to shear ratio is studied. Concerning the concentration of a passive scalar spread by the flow, the pdf of its Eulerian time rate of change presents higher extreme values than those of its Lagrangian time rate of change. This suggests that the Eulerian time rate of change of scalar concentration is mainly due to advection, while its Lagrangian counterpart is only due to gradient production and viscous dissipation.

  17. Modeling and Numerical Challenges in Eulerian-Lagrangian Computations of Shock-driven Multiphase Flows

    NASA Astrophysics Data System (ADS)

    Diggs, Angela; Balachandar, Sivaramakrishnan

    2015-06-01

    The present work addresses the numerical methods required for particle-gas and particle-particle interactions in Eulerian-Lagrangian simulations of multiphase flow. Local volume fraction as seen by each particle is the quantity of foremost importance in modeling and evaluating such interactions. We consider a general multiphase flow with a distribution of particles inside a fluid flow discretized on an Eulerian grid. Particle volume fraction is needed both as a Lagrangian quantity associated with each particle and also as an Eulerian quantity associated with the flow. In Eulerian Projection (EP) methods, the volume fraction is first obtained within each cell as an Eulerian quantity and then interpolated to each particle. In Lagrangian Projection (LP) methods, the particle volume fraction is obtained at each particle and then projected onto the Eulerian grid. Traditionally, EP methods are used in multiphase flow, but sub-grid resolution can be obtained through use of LP methods. By evaluating the total error and its components we compare the performance of EP and LP methods. The standard von Neumann error analysis technique has been adapted for rigorous evaluation of rate of convergence. The methods presented can be extended to obtain accurate field representations of other Lagrangian quantities. Most importantly, we will show that such careful attention to numerical methodologies is needed in order to capture complex shock interaction with a bed of particles. Supported by U.S. Department of Defense SMART Program and the U.S. Department of Energy PSAAP-II program under Contract No. DE-NA0002378.

  18. Eulerian and Lagrangian approaches to multidimensional condensation and collection

    NASA Astrophysics Data System (ADS)

    Li, Xiang-Yu; Brandenburg, A.; Haugen, N. E. L.; Svensson, G.

    2017-06-01

    Turbulence is argued to play a crucial role in cloud droplet growth. The combined problem of turbulence and cloud droplet growth is numerically challenging. Here an Eulerian scheme based on the Smoluchowski equation is compared with two Lagrangian superparticle (or superdroplet) schemes in the presence of condensation and collection. The growth processes are studied either separately or in combination using either two-dimensional turbulence, a steady flow or just gravitational acceleration without gas flow. Good agreement between the different schemes for the time evolution of the size spectra is observed in the presence of gravity or turbulence. The Lagrangian superparticle schemes are found to be superior over the Eulerian one in terms of computational performance. However, it is shown that the use of interpolation schemes such as the cloud-in-cell algorithm is detrimental in connection with superparticle or superdroplet approaches. Furthermore, the use of symmetric over asymmetric collection schemes is shown to reduce the amount of scatter in the results. For the Eulerian scheme, gravitational collection is rather sensitive to the mass bin resolution, but not so in the case with turbulence.Plain Language SummaryThe bottleneck problem of cloud droplet growth is one of the most challenging problems in cloud physics. Cloud droplet growth is neither dominated by condensation nor gravitational collision in the size range of 15 μm ˜ 40 μm [1]. Turbulence-generated collection has been thought to be the mechanism to bridge the size gap, i.e., the bottleneck problem. This study compares the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> schemes in detail to tackle with the turbulence-generated collection.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70013978','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70013978"><span><span class="hlt">Eulerian-Lagrangian</span> solution of the convection-dispersion equation in natural coordinates</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.; Casulli, Vincenzo; Milford, S. Nevil</p> <p>1984-01-01</p> <p>The vast majority of numerical investigations of transport phenomena use an <span class="hlt">Eulerian</span> formulation for the convenience that the computational grids are fixed in space. An <span class="hlt">Eulerian-Lagrangian</span> method (ELM) of solution for the convection-dispersion equation is discussed and analyzed. The ELM uses the <span class="hlt">Lagrangian</span> concept in an <span class="hlt">Eulerian</span> computational grid system. The values of the dependent variable off the grid are calculated by interpolation. When a linear interpolation is used, the method is a slight improvement over the upwind difference method. At this level of approximation both the ELM and the upwind difference method suffer from large numerical dispersion. However, if second-order <span class="hlt">Lagrangian</span> polynomials are used in the interpolation, the ELM is proven to be free of artificial numerical dispersion for the convection-dispersion equation. The concept of the ELM is extended for treatment of anisotropic dispersion in natural coordinates. In this approach the anisotropic properties of dispersion can be conveniently related to the properties of the flow field. Several numerical examples are given to further substantiate the results of the present analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20030052220','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20030052220"><span>A Vertically <span class="hlt">Lagrangian</span> <span class="hlt">Finite</span>-Volume Dynamical Core for Global Models</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lin, Shian-Jiann</p> <p>2003-01-01</p> <p>A <span class="hlt">finite</span>-volume dynamical core with a terrain-following <span class="hlt">Lagrangian</span> control-volume discretization is described. The vertically <span class="hlt">Lagrangian</span> discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-<span class="hlt">Lagrangian</span>-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-<span class="hlt">Lagrangian</span> algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the <span class="hlt">Lagrangian</span> dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating <span class="hlt">Lagrangian</span> control-volume to an <span class="hlt">Eulerian</span> terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the <span class="hlt">Lagrangian</span> surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li class="active"><span>2</span></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_2 --> <div id="page_3" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="41"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDQ34007F"><span>Uncertainty quantification in <span class="hlt">Eulerian-Lagrangian</span> models for particle-laden flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fountoulakis, Vasileios; Jacobs, Gustaaf; Udaykumar, Hs</p> <p>2017-11-01</p> <p>A common approach to ameliorate the computational burden in simulations of particle-laden flows is to use a point-particle based <span class="hlt">Eulerian-Lagrangian</span> model, which traces individual particles in their <span class="hlt">Lagrangian</span> frame and models particles as mathematical points. The particle motion is determined by Stokes drag law, which is empirically corrected for Reynolds number, Mach number and other parameters. The empirical corrections are subject to uncertainty. Treating them as random variables renders the coupled system of PDEs and ODEs stochastic. An approach to quantify the propagation of this parametric uncertainty to the particle solution variables is proposed. The approach is based on averaging of the governing equations and allows for estimation of the first moments of the quantities of interest. We demonstrate the feasibility of our proposed methodology of uncertainty quantification of particle-laden flows on one-dimensional linear and nonlinear <span class="hlt">Eulerian-Lagrangian</span> systems. This research is supported by AFOSR under Grant FA9550-16-1-0008.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016OcMod..97...27F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016OcMod..97...27F"><span>A LES-based <span class="hlt">Eulerian-Lagrangian</span> approach to predict the dynamics of bubble plumes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fraga, Bruño; Stoesser, Thorsten; Lai, Chris C. K.; Socolofsky, Scott A.</p> <p>2016-01-01</p> <p>An approach for <span class="hlt">Eulerian-Lagrangian</span> large-eddy simulation of bubble plume dynamics is presented and its performance evaluated. The main numerical novelties consist in defining the gas-liquid coupling based on the bubble size to mesh resolution ratio (Dp/Δx) and the interpolation between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> frameworks through the use of delta functions. The model's performance is thoroughly validated for a bubble plume in a cubic tank in initially quiescent water using experimental data obtained from high-resolution ADV and PIV measurements. The predicted time-averaged velocities and second-order statistics show good agreement with the measurements, including the reproduction of the anisotropic nature of the plume's turbulence. Further, the predicted <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> velocity fields, second-order turbulence statistics and interfacial gas-liquid forces are quantified and discussed as well as the visualization of the time-averaged primary and secondary flow structure in the tank.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CPM.....1..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1..103G"><span>Evaluating the performance of the particle <span class="hlt">finite</span> <span class="hlt">element</span> method in parallel architectures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gimenez, Juan M.; Nigro, Norberto M.; Idelsohn, Sergio R.</p> <p>2014-05-01</p> <p>This paper presents a high performance implementation for the particle-mesh based method called particle <span class="hlt">finite</span> <span class="hlt">element</span> method two (PFEM-2). It consists of a material derivative based formulation of the equations with a hybrid spatial discretization which uses an <span class="hlt">Eulerian</span> mesh and <span class="hlt">Lagrangian</span> particles. The main aim of PFEM-2 is to solve transport equations as fast as possible keeping some level of accuracy. The method was found to be competitive with classical <span class="hlt">Eulerian</span> alternatives for these targets, even in their range of optimal application. To evaluate the goodness of the method with large simulations, it is imperative to use of parallel environments. Parallel strategies for <span class="hlt">Finite</span> <span class="hlt">Element</span> Method have been widely studied and many libraries can be used to solve <span class="hlt">Eulerian</span> stages of PFEM-2. However, <span class="hlt">Lagrangian</span> stages, such as streamline integration, must be developed considering the parallel strategy selected. The main drawback of PFEM-2 is the large amount of memory needed, which limits its application to large problems with only one computer. Therefore, a distributed-memory implementation is urgently needed. Unlike a shared-memory approach, using domain decomposition the memory is automatically isolated, thus avoiding race conditions; however new issues appear due to data distribution over the processes. Thus, a domain decomposition strategy for both particle and mesh is adopted, which minimizes the communication between processes. Finally, performance analysis running over multicore and multinode architectures are presented. The Courant-Friedrichs-Lewy number used influences the efficiency of the parallelization and, in some cases, a weighted partitioning can be used to improve the speed-up. However the total cputime for cases presented is lower than that obtained when using classical <span class="hlt">Eulerian</span> strategies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1194068-point-centered-arbitrary-lagrangian-eulerian-hydrodynamic-approach-tetrahedral-meshes"><span>A point-centered arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> hydrodynamic approach for tetrahedral meshes</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Morgan, Nathaniel R.; Waltz, Jacob I.; Burton, Donald E.; ...</p> <p>2015-02-24</p> <p>We present a three dimensional (3D) arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) hydrodynamic scheme suitable for modeling complex compressible flows on tetrahedral meshes. The new approach stores the conserved variables (mass, momentum, and total energy) at the nodes of the mesh and solves the conservation equations on a control volume surrounding the point. This type of an approach is termed a point-centered hydrodynamic (PCH) method. The conservation equations are discretized using an edge-based <span class="hlt">finite</span> <span class="hlt">element</span> (FE) approach with linear basis functions. All fluxes in the new approach are calculated at the center of each tetrahedron. A multidirectional Riemann-like problem is solved atmore » the center of the tetrahedron. The advective fluxes are calculated by solving a 1D Riemann problem on each face of the nodal control volume. A 2-stage Runge–Kutta method is used to evolve the solution forward in time, where the advective fluxes are part of the temporal integration. The mesh velocity is smoothed by solving a Laplacian equation. The details of the new ALE hydrodynamic scheme are discussed. Results from a range of numerical test problems are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70020645','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70020645"><span>Solution of the advection-dispersion equation in two dimensions by a <span class="hlt">finite</span>-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Healy, R.W.; Russell, T.F.</p> <p>1998-01-01</p> <p>We extend the <span class="hlt">finite</span>-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) for solution of the advection-dispersion equation to two dimensions. The method can conserve mass globally and is not limited by restrictions on the size of the grid Peclet or Courant number. Therefore, it is well suited for solution of advection-dominated ground-water solute transport problems. In test problem comparisons with standard <span class="hlt">finite</span> differences, FVELLAM is able to attain accurate solutions on much coarser space and time grids. On fine grids, the accuracy of the two methods is comparable. A critical aspect of FVELLAM (and all other ELLAMs) is evaluation of the mass storage integral from the preceding time level. In FVELLAM this may be accomplished with either a forward or backtracking approach. The forward tracking approach conserves mass globally and is the preferred approach. The backtracking approach is less computationally intensive, but not globally mass conservative. Boundary terms are systematically represented as integrals in space and time which are evaluated by a common integration scheme in conjunction with forward tracking through time. Unlike the one-dimensional case, local mass conservation cannot be guaranteed, so slight oscillations in concentration can develop, particularly in the vicinity of inflow or outflow boundaries. Published by Elsevier Science Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=128805&keyword=Herrera&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span>AN <span class="hlt">EULERIAN-LAGRANGIAN</span> LOCALIZED ADJOINT METHOD FOR THE ADVECTION-DIFFUSION EQUATION</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>Many numerical methods use characteristic analysis to accommodate the advective component of transport. Such characteristic methods include <span class="hlt">Eulerian-Lagrangian</span> methods (ELM), modified method of characteristics (MMOC), and operator splitting methods. A generalization of characteri...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016CG.....89..200T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016CG.....89..200T"><span>A majorized Newton-CG augmented <span class="hlt">Lagrangian</span>-based <span class="hlt">finite</span> <span class="hlt">element</span> method for 3D restoration of geological models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia</p> <p>2016-04-01</p> <p>In this paper, we propose a majorized Newton-CG augmented <span class="hlt">Lagrangian</span>-based <span class="hlt">finite</span> <span class="hlt">element</span> method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the <span class="hlt">finite</span> <span class="hlt">element</span> method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented <span class="hlt">Lagrangian</span> method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29051631','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29051631"><span>Acoustic streaming: an arbitrary <span class="hlt">Lagrangian-Eulerian</span> perspective.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco</p> <p>2017-08-25</p> <p>We analyse acoustic streaming flows using an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the <span class="hlt">Lagrangian</span> flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the <span class="hlt">Lagrangian</span> velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid-structure interaction problems in microacoustofluidic devices. After the formulation's exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CPM.....1...85O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CPM.....1...85O"><span><span class="hlt">Lagrangian</span> analysis of multiscale particulate flows with the particle <span class="hlt">finite</span> <span class="hlt">element</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Oñate, Eugenio; Celigueta, Miguel Angel; Latorre, Salvador; Casas, Guillermo; Rossi, Riccardo; Rojek, Jerzy</p> <p>2014-05-01</p> <p>We present a <span class="hlt">Lagrangian</span> numerical technique for the analysis of flows incorporating physical particles of different sizes. The numerical approach is based on the particle <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM) which blends concepts from particle-based techniques and the FEM. The basis of the <span class="hlt">Lagrangian</span> formulation for particulate flows and the procedure for modelling the motion of small and large particles that are submerged in the fluid are described in detail. The numerical technique for analysis of this type of multiscale particulate flows using a stabilized mixed velocity-pressure formulation and the PFEM is also presented. Examples of application of the PFEM to several particulate flows problems are given.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017WRR....53.9040S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017WRR....53.9040S"><span>A <span class="hlt">Lagrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial (LATERS) Markov Model for Prediction of Effective Bimolecular Reactive Transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sund, Nicole; Porta, Giovanni; Bolster, Diogo; Parashar, Rishi</p> <p>2017-11-01</p> <p>Prediction of effective transport for mixing-driven reactive systems at larger scales, requires accurate representation of mixing at small scales, which poses a significant upscaling challenge. Depending on the problem at hand, there can be benefits to using a <span class="hlt">Lagrangian</span> framework, while in others an <span class="hlt">Eulerian</span> might have advantages. Here we propose and test a novel hybrid model which attempts to leverage benefits of each. Specifically, our framework provides a <span class="hlt">Lagrangian</span> closure required for a volume-averaging procedure of the advection diffusion reaction equation. This hybrid model is a <span class="hlt">LAgrangian</span> Transport <span class="hlt">Eulerian</span> Reaction Spatial Markov model (LATERS Markov model), which extends previous implementations of the <span class="hlt">Lagrangian</span> Spatial Markov model and maps concentrations to an <span class="hlt">Eulerian</span> grid to quantify closure terms required to calculate the volume-averaged reaction terms. The advantage of this approach is that the Spatial Markov model is known to provide accurate predictions of transport, particularly at preasymptotic early times, when assumptions required by traditional volume-averaging closures are least likely to hold; likewise, the <span class="hlt">Eulerian</span> reaction method is efficient, because it does not require calculation of distances between particles. This manuscript introduces the LATERS Markov model and demonstrates by example its ability to accurately predict bimolecular reactive transport in a simple benchmark 2-D porous medium.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040031690','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040031690"><span>A <span class="hlt">Eulerian-Lagrangian</span> Model to Simulate Two-Phase/Particulate Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Apte, S. V.; Mahesh, K.; Lundgren, T.</p> <p>2003-01-01</p> <p>Figure 1 shows a snapshot of liquid fuel spray coming out of an injector nozzle in a realistic gas-turbine combustor. Here the spray atomization was simulated using a stochastic secondary breakup model (Apte et al. 2003a) with point-particle approximation for the droplets. Very close to the injector, it is observed that the spray density is large and the droplets cannot be treated as point-particles. The volume displaced by the liquid in this region is significant and can alter the gas-phase ow and spray evolution. In order to address this issue, one can compute the dense spray regime by an <span class="hlt">Eulerian-Lagrangian</span> technique using advanced interface tracking/level-set methods (Sussman et al. 1994; Tryggvason et al. 2001; Herrmann 2003). This, however, is computationally intensive and may not be viable in realistic complex configurations. We therefore plan to develop a methodology based on <span class="hlt">Eulerian-Lagrangian</span> technique which will allow us to capture the essential features of primary atomization using models to capture interactions between the fluid and droplets and which can be directly applied to the standard atomization models used in practice. The numerical scheme for unstructured grids developed by Mahesh et al. (2003) for incompressible flows is modified to take into account the droplet volume fraction. The numerical framework is directly applicable to realistic combustor geometries. Our main objectives in this work are: Develop a numerical formulation based on <span class="hlt">Eulerian-Lagrangian</span> techniques with models for interaction terms between the fluid and particles to capture the Kelvin- Helmholtz type instabilities observed during primary atomization. Validate this technique for various two-phase and particulate flows. Assess its applicability to capture primary atomization of liquid jets in conjunction with secondary atomization models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1429778-arbitrary-lagrangianeulerian-finite-element-formulation-poroelasticity-problem-stemming-from-mixture-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1429778-arbitrary-lagrangianeulerian-finite-element-formulation-poroelasticity-problem-stemming-from-mixture-theory"><span>An arbitrary Lagrangian–<span class="hlt">Eulerian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation for a poroelasticity problem stemming from mixture theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Costanzo, Francesco; Miller, Scott T.</p> <p>2017-05-22</p> <p>In this paper, a <span class="hlt">finite</span> <span class="hlt">element</span> formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1429778','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1429778"><span>An arbitrary Lagrangian–<span class="hlt">Eulerian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation for a poroelasticity problem stemming from mixture theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Costanzo, Francesco; Miller, Scott T.</p> <p></p> <p>In this paper, a <span class="hlt">finite</span> <span class="hlt">element</span> formulation is developed for a poroelastic medium consisting of an incompressible hyperelastic skeleton saturated by an incompressible fluid. The governing equations stem from mixture theory and the application is motivated by the study of interstitial fluid flow in brain tissue. The formulation is based on the adoption of an arbitrary Lagrangian–<span class="hlt">Eulerian</span> (ALE) perspective. We focus on a flow regime in which inertia forces are negligible. Finally, the stability and convergence of the formulation is discussed, and numerical results demonstrate agreement with the theory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CompM..50..805L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CompM..50..805L"><span>A coupled PFEM-<span class="hlt">Eulerian</span> approach for the solution of porous FSI problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Larese, A.; Rossi, R.; Oñate, E.; Idelsohn, S. R.</p> <p>2012-12-01</p> <p>This paper aims to present a coupled solution strategy for the problem of seepage through a rockfill dam taking into account the free-surface flow within the solid as well as in its vicinity. A combination of a <span class="hlt">Lagrangian</span> model for the structural behavior and an <span class="hlt">Eulerian</span> approach for the fluid is used. The particle <span class="hlt">finite</span> <span class="hlt">element</span> method is adopted for the evaluation of the structural response, whereas an <span class="hlt">Eulerian</span> fixed-mesh approach is employed for the fluid. The free surface is tracked by the use of a level set technique. The numerical results are validated with experiments on scale models rockfill dams.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.L2012Z"><span>Scalable Methods for <span class="hlt">Eulerian-Lagrangian</span> Simulation Applied to Compressible Multiphase Flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zwick, David; Hackl, Jason; Balachandar, S.</p> <p>2017-11-01</p> <p>Multiphase flows can be found in countless areas of physics and engineering. Many of these flows can be classified as dispersed two-phase flows, meaning that there are solid particles dispersed in a continuous fluid phase. A common technique for simulating such flow is the <span class="hlt">Eulerian-Lagrangian</span> method. While useful, this method can suffer from scaling issues on larger problem sizes that are typical of many realistic geometries. Here we present scalable techniques for <span class="hlt">Eulerian-Lagrangian</span> simulations and apply it to the simulation of a particle bed subjected to expansion waves in a shock tube. The results show that the methods presented here are viable for simulation of larger problems on modern supercomputers. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1315138. This work was supported in part by the U.S. Department of Energy under Contract No. DE-NA0002378.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/957621','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/957621"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling of the Deformation of a Thin Magnetoelastic Film Compared to a Membrane Model</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Barham, M; White, D; Steigmann, D</p> <p>2009-04-08</p> <p>Recently a new class of biocompatible elastic polymers loaded with small ferrous particles (magnetoelastomer) was developed at Lawrence Livermore National Laboratory. This new material was formed as a thin film using spin casting. The deformation of this material using a magnetic field has many possible applications to microfluidics. Two methods will be used to calculate the deformation of a circular magneto-elastomeric film subjected to a magnetic field. The first method is an arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) and the second is based on nonlinear continuum electromagnetism and continuum elasticity in the membrane limit. The comparison of these twomore » methods is used to test/validate the <span class="hlt">finite</span> <span class="hlt">element</span> method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26754057','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26754057"><span>Modified Mixed <span class="hlt">Lagrangian-Eulerian</span> Method Based on Numerical Framework of MT3DMS on Cauchy Boundary.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Suk, Heejun</p> <p>2016-07-01</p> <p>MT3DMS, a modular three-dimensional multispecies transport model, has long been a popular model in the groundwater field for simulating solute transport in the saturated zone. However, the method of characteristics (MOC), modified MOC (MMOC), and hybrid MOC (HMOC) included in MT3DMS did not treat Cauchy boundary conditions in a straightforward or rigorous manner, from a mathematical point of view. The MOC, MMOC, and HMOC regard the Cauchy boundary as a source condition. For the source, MOC, MMOC, and HMOC calculate the <span class="hlt">Lagrangian</span> concentration by setting it equal to the cell concentration at an old time level. However, the above calculation is an approximate method because it does not involve backward tracking in MMOC and HMOC or allow performing forward tracking at the source cell in MOC. To circumvent this problem, a new scheme is proposed that avoids direct calculation of the <span class="hlt">Lagrangian</span> concentration on the Cauchy boundary. The proposed method combines the numerical formulations of two different schemes, the <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) and the <span class="hlt">Eulerian-Lagrangian</span> method (ELM), into one global matrix equation. This study demonstrates the limitation of all MT3DMS schemes, including MOC, MMOC, HMOC, and a third-order total-variation-diminishing (TVD) scheme under Cauchy boundary conditions. By contrast, the proposed method always shows good agreement with the exact solution, regardless of the flow conditions. Finally, the successful application of the proposed method sheds light on the possible flexibility and capability of the MT3DMS to deal with the mass transport problems of all flow regimes. © 2016, National Ground Water Association.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930062646&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3DLagrangian"><span>Extension of rezoned <span class="hlt">Eulerian-Lagrangian</span> method to astrophysical plasma applications</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Song, M. T.; Wu, S. T.; Dryer, Murray</p> <p>1993-01-01</p> <p>The rezoned <span class="hlt">Eulerian-Lagrangian</span> procedure developed by Brackbill and Pracht (1973), which is limited to simple configurations of the magnetic fields, is modified in order to make it applicable to astrophysical plasma. For this purpose, two specific methods are introduced, which make it possible to determine the initial field topology for which no analytical expressions are available. Numerical examples illustrating these methods are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016GMD.....9..749B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016GMD.....9..749B"><span>Adjoint of the global <span class="hlt">Eulerian-Lagrangian</span> coupled atmospheric transport model (A-GELCA v1.0): development and validation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Belikov, Dmitry A.; Maksyutov, Shamil; Yaremchuk, Alexey; Ganshin, Alexander; Kaminski, Thomas; Blessing, Simon; Sasakawa, Motoki; Gomez-Pelaez, Angel J.; Starchenko, Alexander</p> <p>2016-02-01</p> <p>We present the development of the Adjoint of the Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric (A-GELCA) model that consists of the National Institute for Environmental Studies (NIES) model as an <span class="hlt">Eulerian</span> three-dimensional transport model (TM), and FLEXPART (FLEXible PARTicle dispersion model) as the <span class="hlt">Lagrangian</span> Particle Dispersion Model (LPDM). The forward tangent linear and adjoint components of the <span class="hlt">Eulerian</span> model were constructed directly from the original NIES TM code using an automatic differentiation tool known as TAF (Transformation of Algorithms in Fortran; http://www.FastOpt.com, with additional manual pre- and post-processing aimed at improving transparency and clarity of the code and optimizing the performance of the computing, including MPI (Message Passing Interface). The <span class="hlt">Lagrangian</span> component did not require any code modification, as LPDMs are self-adjoint and track a significant number of particles backward in time in order to calculate the sensitivity of the observations to the neighboring emission areas. The constructed <span class="hlt">Eulerian</span> adjoint was coupled with the <span class="hlt">Lagrangian</span> component at a time boundary in the global domain. The simulations presented in this work were performed using the A-GELCA model in forward and adjoint modes. The forward simulation shows that the coupled model improves reproduction of the seasonal cycle and short-term variability of CO2. Mean bias and standard deviation for five of the six Siberian sites considered decrease roughly by 1 ppm when using the coupled model. The adjoint of the <span class="hlt">Eulerian</span> model was shown, through several numerical tests, to be very accurate (within machine epsilon with mismatch around to ±6 e-14) compared to direct forward sensitivity calculations. The developed adjoint of the coupled model combines the flux conservation and stability of an <span class="hlt">Eulerian</span> discrete adjoint formulation with the flexibility, accuracy, and high resolution of a <span class="hlt">Lagrangian</span> backward trajectory formulation. A-GELCA will be incorporated</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900048341&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900048341&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>Modeling of confined turbulent fluid-particle flows using <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> schemes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Adeniji-Fashola, A.; Chen, C. P.</p> <p>1990-01-01</p> <p>Two important aspects of fluid-particulate interaction in dilute gas-particle turbulent flows (the turbulent particle dispersion and the turbulence modulation effects) are addressed, using the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> modeling approaches to describe the particulate phase. Gradient-diffusion approximations are employed in the <span class="hlt">Eulerian</span> formulation, while a stochastic procedure is utilized to simulate turbulent dispersion in the Lagrangina formulation. The k-epsilon turbulence model is used to characterize the time and length scales of the continuous phase turbulence. Models proposed for both schemes are used to predict turbulent fully-developed gas-solid vertical pipe flow with reasonable accuracy.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_1");'>1</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li class="active"><span>3</span></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_3 --> <div id="page_4" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="61"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA542504','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA542504"><span>Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Simulation of Steep and Breaking Waves and Surface Fluxes in High Winds</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2010-09-30</p> <p>simulating violent free - surface flows , and show the importance of wave breaking in energy transport...using <span class="hlt">Eulerian</span> simulation . 3 IMPACT/APPLICATION This project aims at developing an advanced simulation tool for multi-fluids free - surface flows that...several <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for free - surface turbulence and wave simulation . The WIND–SNOW is used to simulate 1 Report</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890001792','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890001792"><span>Modeling of combustion processes of stick propellants via combined <span class="hlt">Eulerian-Lagrangian</span> approach</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kuo, K. K.; Hsieh, K. C.; Athavale, M. M.</p> <p>1988-01-01</p> <p>This research is motivated by the improved ballistic performance of large-caliber guns using stick propellant charges. A comprehensive theoretical model for predicting the flame spreading, combustion, and grain deformation phenomena of long, unslotted stick propellants is presented. The formulation is based upon a combined <span class="hlt">Eulerian-Lagrangian</span> approach to simulate special characteristics of the two phase combustion process in a cartridge loaded with a bundle of sticks. The model considers five separate regions consisting of the internal perforation, the solid phase, the external interstitial gas phase, and two lumped parameter regions at either end of the stick bundle. For the external gas phase region, a set of transient one-dimensional fluid-dynamic equations using the <span class="hlt">Eulerian</span> approach is obtained; governing equations for the stick propellants are formulated using the <span class="hlt">Lagrangian</span> approach. The motion of a representative stick is derived by considering the forces acting on the entire propellant stick. The instantaneous temperature and stress fields in the stick propellant are modeled by considering the transient axisymmetric heat conduction equation and dynamic structural analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920064328&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>An <span class="hlt">Eulerian/Lagrangian</span> method for computing blade/vortex impingement</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Steinhoff, John; Senge, Heinrich; Yonghu, Wenren</p> <p>1991-01-01</p> <p>A combined <span class="hlt">Eulerian/Lagrangian</span> approach to calculating helicopter rotor flows with concentrated vortices is described. The method computes a general evolving vorticity distribution without any significant numerical diffusion. Concentrated vortices can be accurately propagated over long distances on relatively coarse grids with cores only several grid cells wide. The method is demonstrated for a blade/vortex impingement case in 2D and 3D where a vortex is cut by a rotor blade, and the results are compared to previous 2D calculations involving a fifth-order Navier-Stokes solver on a finer grid.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CMAME.333...55L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CMAME.333...55L"><span>A quasi-<span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> method for the Navier-Stokes equations in a time-dependent domain</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lozovskiy, Alexander; Olshanskii, Maxim A.; Vassilevski, Yuri V.</p> <p>2018-05-01</p> <p>The paper develops a <span class="hlt">finite</span> <span class="hlt">element</span> method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-<span class="hlt">Lagrangian</span> formulation of the problem. The paper provides stability and convergence analysis of the fully discrete (<span class="hlt">finite</span>-difference in time and <span class="hlt">finite-element</span> in space) method. The analysis does not assume any CFL time-step restriction, it rather needs mild conditions of the form $\\Delta t\\le C$, where $C$ depends only on problem data, and $h^{2m_u+2}\\le c\\,\\Delta t$, $m_u$ is polynomial degree of velocity <span class="hlt">finite</span> <span class="hlt">element</span> space. Both conditions result from a numerical treatment of practically important non-homogeneous boundary conditions. The theoretically predicted convergence rate is confirmed by a set of numerical experiments. Further we apply the method to simulate a flow in a simplified model of the left ventricle of a human heart, where the ventricle wall dynamics is reconstructed from a sequence of contrast enhanced Computed Tomography images.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016APS..DFDA12003S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016APS..DFDA12003S"><span>A <span class="hlt">Finite</span> <span class="hlt">Element</span> Method for Simulation of Compressible Cavitating Flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad</p> <p>2016-11-01</p> <p>This work focuses on a novel approach for <span class="hlt">finite</span> <span class="hlt">element</span> simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized <span class="hlt">finite</span> <span class="hlt">element</span> methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary <span class="hlt">Lagrangian-Eulerian</span> formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29060488','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29060488"><span>Serial fusion of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> approaches for accurate heart-rate estimation using face videos.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Gupta, Puneet; Bhowmick, Brojeshwar; Pal, Arpan</p> <p>2017-07-01</p> <p>Camera-equipped devices are ubiquitous and proliferating in the day-to-day life. Accurate heart rate (HR) estimation from the face videos acquired from the low cost cameras in a non-contact manner, can be used in many real-world scenarios and hence, require rigorous exploration. This paper has presented an accurate and near real-time HR estimation system using these face videos. It is based on the phenomenon that the color and motion variations in the face video are closely related to the heart beat. The variations also contain the noise due to facial expressions, respiration, eye blinking and environmental factors which are handled by the proposed system. Neither <span class="hlt">Eulerian</span> nor <span class="hlt">Lagrangian</span> temporal signals can provide accurate HR in all the cases. The cases where <span class="hlt">Eulerian</span> temporal signals perform spuriously are determined using a novel poorness measure and then both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> temporal signals are employed for better HR estimation. Such a fusion is referred as serial fusion. Experimental results reveal that the error introduced in the proposed algorithm is 1.8±3.6 which is significantly lower than the existing well known systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70033100','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70033100"><span><span class="hlt">Eulerian-Lagrangian</span> numerical scheme for simulating advection, dispersion, and transient storage in streams and a comparison of numerical methods</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cox, T.J.; Runkel, R.L.</p> <p>2008-01-01</p> <p>Past applications of one-dimensional advection, dispersion, and transient storage zone models have almost exclusively relied on a central differencing, <span class="hlt">Eulerian</span> numerical approximation to the nonconservative form of the fundamental equation. However, there are scenarios where this approach generates unacceptable error. A new numerical scheme for this type of modeling is presented here that is based on tracking <span class="hlt">Lagrangian</span> control volumes across a fixed (<span class="hlt">Eulerian</span>) grid. Numerical tests are used to provide a direct comparison of the new scheme versus nonconservative <span class="hlt">Eulerian</span> numerical methods, in terms of both accuracy and mass conservation. Key characteristics of systems for which the <span class="hlt">Lagrangian</span> scheme performs better than the <span class="hlt">Eulerian</span> scheme include: nonuniform flow fields, steep gradient plume fronts, and pulse and steady point source loadings in advection-dominated systems. A new analytical derivation is presented that provides insight into the loss of mass conservation in the nonconservative <span class="hlt">Eulerian</span> scheme. This derivation shows that loss of mass conservation in the vicinity of spatial flow changes is directly proportional to the lateral inflow rate and the change in stream concentration due to the inflow. While the nonconservative <span class="hlt">Eulerian</span> scheme has clearly worked well for past published applications, it is important for users to be aware of the scheme's limitations. ?? 2008 ASCE.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21428686','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21428686"><span>Coupled porohyperelastic mass transport (PHEXPT) <span class="hlt">finite</span> <span class="hlt">element</span> models for soft tissues using ABAQUS.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P</p> <p>2011-04-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) <span class="hlt">finite</span> <span class="hlt">element</span> approach developed using a commercially available ABAQUS <span class="hlt">finite</span> <span class="hlt">element</span> software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an <span class="hlt">Eulerian</span> PHE FEM is coupled to a <span class="hlt">Lagrangian</span> XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS <span class="hlt">finite</span> <span class="hlt">element</span> formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark <span class="hlt">finite</span> <span class="hlt">element</span> simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including <span class="hlt">finite</span> deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of <span class="hlt">finite</span> deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, <span class="hlt">finite</span> <span class="hlt">element</span> libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017StGM...39...27K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017StGM...39...27K"><span>Influence of Installation Effects on Pile Bearing Capacity in Cohesive Soils - Large Deformation Analysis Via <span class="hlt">Finite</span> <span class="hlt">Element</span> Method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Konkol, Jakub; Bałachowski, Lech</p> <p>2017-03-01</p> <p>In this paper, the whole process of pile construction and performance during loading is modelled via large deformation <span class="hlt">finite</span> <span class="hlt">element</span> methods such as Coupled <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> (CEL) and Updated <span class="hlt">Lagrangian</span> (UL). Numerical study consists of installation process, consolidation phase and following pile static load test (SLT). The Poznań site is chosen as the reference location for the numerical analysis, where series of pile SLTs have been performed in highly overconsolidated clay (OCR ≈ 12). The results of numerical analysis are compared with corresponding field tests and with so-called "wish-in-place" numerical model of pile, where no installation effects are taken into account. The advantages of using large deformation numerical analysis are presented and its application to the pile designing is shown.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1419712','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1419712"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Parameterization of the Oceanic Mixed Layer using Large Eddy Simulation and MPAS-Ocean</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Van Roekel, Luke</p> <p></p> <p>We have conducted a suite of Large Eddy Simulation (LES) to form the basis of a multi-model comparison (left). The results have led to proposed model improvements. We have verified that <span class="hlt">Eulerian-Lagrangian</span> effective diffusivity estimates of mesoscale mixing are consistent with traditional particle statistics metrics (right). LES and <span class="hlt">Lagrangian</span> particles will be utilized to better represent the movement of water into and out of the mixed layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MNRAS.477.2251G"><span>Well-balanced Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> <span class="hlt">finite</span> volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael</p> <p>2018-06-01</p> <p>In this work, we present a novel second-order accurate well-balanced arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) <span class="hlt">finite</span> volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative <span class="hlt">finite</span> volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..1511185C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..1511185C"><span>A <span class="hlt">lagrangian-eulerian</span> description of debris transport by a tsunami in the Lisbon waterfront</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Conde, Daniel; Canelas, Ricardo; Baptista, Maria Ana; João Telhado, Maria; Ferreira, Rui M. L.</p> <p>2013-04-01</p> <p>Several major tsunamis are known to have struck the Portuguese coast over the past millennia (Baptista and Miranda, 2009). The Tagus estuary has great exposure to tsunami occurrences and, being bordered by the largest metropolitan area in the country, is a particularly worrisome location in what concerns safety of populations and economic losses due to disruption of built infrastructures. The last major earthquake and tsunami combination known to have critically affected the Tagus estuary dates back to November 1st 1755. This catastrophe critically damaged Lisbon's infrastructures, led to numerous casualties and priceless heritage losses. The urban tissue of the present city still bears visible the effects of the catastrophe and of the ensuing protection measures. The objective of this work is to simulate the propagation of debris carried by a 1755-like tsunami along the present-day bathimetric and altimetric conditions of Lisbon waterfront. Particular emphasis was directed to the modeling of vehicles since the tsunami is likely to affect areas that are major traffic nodes such as Alcântara, with more than 1500 vehicles in road network of about 3 km. The simulation tool employed is based on a 2DH spatial (<span class="hlt">eulerian</span>) shallow-flow approach suited to complex and dynamic bottom boundaries. The discretization technique relies on a <span class="hlt">finite</span>-volume scheme, based on a flux-splitting technique incorporating a reviewed version of the Roe Riemann solver (Canelas et al. 2013). Two formulations were employed to model the advection of debris: a fully coupled continuum approach, where solid bodies are described by the concentration only and an uncoupled material (<span class="hlt">lagrangian</span>) formulation where solid bodies are tracked between two time-steps once the flow field is determined by the <span class="hlt">eulerian</span> solver. In the latter case, concentrations are updated after tracking the solid bodies thus correcting the mass and momentum balance to be used for the next time-step. The urban tissue was</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014EGUGA..1613316G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014EGUGA..1613316G"><span><span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method for solving the conservative solute transport in heterogeneous porous media</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gotovac, Hrvoje; Srzic, Veljko</p> <p>2014-05-01</p> <p>Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different <span class="hlt">Eulerian</span>, <span class="hlt">Lagrangian</span> and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACP....12.8979P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACP....12.8979P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p> <p>2012-10-01</p> <p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which two models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/15013474','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/15013474"><span>Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Method with Local Structured Adaptive Mesh Refinement for Modeling Shock Hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Anderson, R W; Pember, R B; Elliott, N S</p> <p>2001-10-22</p> <p>A new method that combines staggered grid Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid <span class="hlt">Lagrangian</span> integration method. The novel components of the method are mainly driven by the need to reconcile traditionalmore » AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by <span class="hlt">Lagrangian</span> methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012ACPD...12.1267P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012ACPD...12.1267P"><span>Comparing <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> models for CO2 transport - a step towards Bayesian inverse modeling using WRF/STILT-VPRM</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pillai, D.; Gerbig, C.; Kretschmer, R.; Beck, V.; Karstens, U.; Neininger, B.; Heimann, M.</p> <p>2012-01-01</p> <p>We present simulations of atmospheric CO2 concentrations provided by two modeling systems, run at high spatial resolution: the <span class="hlt">Eulerian</span>-based Weather Research Forecasting (WRF) model and the <span class="hlt">Lagrangian</span>-based Stochastic Time-Inverted <span class="hlt">Lagrangian</span> Transport (STILT) model, both of which are coupled to a diagnostic biospheric model, the Vegetation Photosynthesis and Respiration Model (VPRM). The consistency of the simulations is assessed with special attention paid to the details of horizontal as well as vertical transport and mixing of CO2 concentrations in the atmosphere. The dependence of model mismatch (<span class="hlt">Eulerian</span> vs. <span class="hlt">Lagrangian</span>) on models' spatial resolution is further investigated. A case study using airborne measurements during which both models showed large deviations from each other is analyzed in detail as an extreme case. Using aircraft observations and pulse release simulations, we identified differences in the representation of details in the interaction between turbulent mixing and advection through wind shear as the main cause of discrepancies between WRF and STILT transport at a spatial resolution such as 2 and 6 km. Based on observations and inter-model comparisons of atmospheric CO2 concentrations, we show that a refinement of the parameterization of turbulent velocity variance and <span class="hlt">Lagrangian</span> time-scale in STILT is needed to achieve a better match between the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> transport at such a high spatial resolution (e.g. 2 and 6 km). Nevertheless, the inter-model differences in simulated CO2 time series for a tall tower observatory at Ochsenkopf in Germany are about a factor of two smaller than the model-data mismatch and about a factor of three smaller than the mismatch between the current global model simulations and the data. Thus suggests that it is reasonable to use STILT as an adjoint model of WRF atmospheric transport.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JSV...414..299V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JSV...414..299V"><span>Non-material <span class="hlt">finite</span> <span class="hlt">element</span> modelling of large vibrations of axially moving strings and beams</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vetyukov, Yury</p> <p>2018-02-01</p> <p>We present a new mathematical model for the dynamics of a beam or a string, which moves in a given axial direction across a particular domain. Large in-plane vibrations are coupled with the gross axial motion, and a <span class="hlt">Lagrangian</span> (material) form of the equations of structural mechanics becomes inefficient. The proposed mixed <span class="hlt">Eulerian-Lagrangian</span> description features mechanical fields as functions of a spatial coordinate in the axial direction. The material travels across a <span class="hlt">finite</span> <span class="hlt">element</span> mesh, and the boundary conditions are applied in fixed nodes. Beginning with the variational equation of virtual work in its material form, we analytically derive the Lagrange's equations of motion of the second kind for the considered case of a discretized non-material control domain and for geometrically exact kinematics. The dynamic analysis is straightforward as soon as the strain and the kinetic energies of the control domain are available. In numerical simulations we demonstrate the rapid mesh convergence of the model, the effect of the bending stiffness and the dynamic instability when the axial velocity gets high. We also show correspondence to the results of fully <span class="hlt">Lagrangian</span> benchmark solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015OcDyn..65..679R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015OcDyn..65..679R"><span>Comparison of HF radar measurements with <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> surface currents</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Röhrs, Johannes; Sperrevik, Ann Kristin; Christensen, Kai Håkon; Broström, Göran; Breivik, Øyvind</p> <p>2015-05-01</p> <p>High-frequency (HF) radar-derived ocean currents are compared with in situ measurements to conclude if the radar observations include effects of surface waves that are of second order in the wave amplitude. <span class="hlt">Eulerian</span> current measurements from a high-resolution acoustic Doppler current profiler and <span class="hlt">Lagrangian</span> measurements from surface drifters are used as references. Directional wave spectra are obtained from a combination of pressure sensor data and a wave model. Our analysis shows that the wave-induced Stokes drift is not included in the HF radar-derived currents, that is, HF radars measure the <span class="hlt">Eulerian</span> current. A disputed nonlinear correction to the phase velocity of surface gravity waves, which may affect HF radar signals, has a magnitude of about half the Stokes drift at the surface. In our case, this contribution by nonlinear dispersion would be smaller than the accuracy of the HF radar currents, hence no conclusion can be made. Finally, the analysis confirms that the HF radar data represent an exponentially weighted vertical average where the decay scale is proportional to the wavelength of the transmitted signal.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26456304','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26456304"><span>The Trapping Index: How to integrate the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approach for the computation of the transport time scales of semi-enclosed basins.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cucco, Andrea; Umgiesser, Georg</p> <p>2015-09-15</p> <p>In this work, we investigated if the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> approaches for the computation of the Transport Time Scales (TTS) of semi-enclosed water bodies can be used univocally to define the spatial variability of basin flushing features. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> TTS were computed for both simplified test cases and a realistic domain: the Venice Lagoon. The results confirmed the two approaches cannot be adopted univocally and that the spatial variability of the water renewal capacity can be investigated only through the computation of both the TTS. A specific analysis, based on the computation of a so-called Trapping Index, was then suggested to integrate the information provided by the two different approaches. The obtained results proved the Trapping Index to be useful to avoid any misleading interpretation due to the evaluation of the basin renewal features just from an <span class="hlt">Eulerian</span> only or from a <span class="hlt">Lagrangian</span> only perspective. Copyright © 2015 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CTM....16..435J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CTM....16..435J"><span>Comparisons of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> PDF methods in simulations of non-premixed turbulent jet flames with moderate-to-strong turbulence-chemistry interactions</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jaishree, J.; Haworth, D. C.</p> <p>2012-06-01</p> <p>Transported probability density function (PDF) methods have been applied widely and effectively for modelling turbulent reacting flows. In most applications of PDF methods to date, <span class="hlt">Lagrangian</span> particle Monte Carlo algorithms have been used to solve a modelled PDF transport equation. However, <span class="hlt">Lagrangian</span> particle PDF methods are computationally intensive and are not readily integrated into conventional <span class="hlt">Eulerian</span> computational fluid dynamics (CFD) codes. <span class="hlt">Eulerian</span> field PDF methods have been proposed as an alternative. Here a systematic comparison is performed among three methods for solving the same underlying modelled composition PDF transport equation: a consistent hybrid <span class="hlt">Lagrangian</span> particle/<span class="hlt">Eulerian</span> mesh (LPEM) method, a stochastic <span class="hlt">Eulerian</span> field (SEF) method and a deterministic <span class="hlt">Eulerian</span> field method with a direct-quadrature-method-of-moments closure (a multi-environment PDF-MEPDF method). The comparisons have been made in simulations of a series of three non-premixed, piloted methane-air turbulent jet flames that exhibit progressively increasing levels of local extinction and turbulence-chemistry interactions: Sandia/TUD flames D, E and F. The three PDF methods have been implemented using the same underlying CFD solver, and results obtained using the three methods have been compared using (to the extent possible) equivalent physical models and numerical parameters. Reasonably converged mean and rms scalar profiles are obtained using 40 particles per cell for the LPEM method or 40 <span class="hlt">Eulerian</span> fields for the SEF method. Results from these stochastic methods are compared with results obtained using two- and three-environment MEPDF methods. The relative advantages and disadvantages of each method in terms of accuracy and computational requirements are explored and identified. In general, the results obtained from the two stochastic methods (LPEM and SEF) are very similar, and are in closer agreement with experimental measurements than those obtained using the MEPDF method</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_2");'>2</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li class="active"><span>4</span></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_4 --> <div id="page_5" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="81"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910015431','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910015431"><span>Parallel computing using a <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, May-Fun; Loh, Ching Yuen</p> <p>1991-01-01</p> <p>A new <span class="hlt">Lagrangian</span> formulation of the Euler equation is adopted for the calculation of 2-D supersonic steady flow. The <span class="hlt">Lagrangian</span> formulation represents the inherent parallelism of the flow field better than the common <span class="hlt">Eulerian</span> formulation and offers a competitive alternative on parallel computers. The implementation of the <span class="hlt">Lagrangian</span> formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a <span class="hlt">finite</span> volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, a better than six times speed-up was achieved on a 8192-processor CM-2 over a single processor of a CRAY-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950059889&hterms=fun&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfun','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950059889&hterms=fun&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfun"><span>Parallel computing using a <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, May-Fun; Loh, Ching-Yuen</p> <p>1992-01-01</p> <p>This paper adopts a new <span class="hlt">Lagrangian</span> formulation of the Euler equation for the calculation of two dimensional supersonic steady flow. The <span class="hlt">Lagrangian</span> formulation represents the inherent parallelism of the flow field better than the common <span class="hlt">Eulerian</span> formulation and offers a competitive alternative on parallel computers. The implementation of the <span class="hlt">Lagrangian</span> formulation on the Thinking Machines Corporation CM-2 Computer is described. The program uses a <span class="hlt">finite</span> volume, first-order Godunov scheme and exhibits high accuracy in dealing with multidimensional discontinuities (slip-line and shock). By using this formulation, we have achieved better than six times speed-up on a 8192-processor CM-2 over a single processor of a CRAY-2.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950017213','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950017213"><span>A Generalized <span class="hlt">Eulerian-Lagrangian</span> Analysis, with Application to Liquid Flows with Vapor Bubbles</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dejong, Frederik J.; Meyyappan, Meyya</p> <p>1993-01-01</p> <p>Under a NASA MSFC SBIR Phase 2 effort an analysis has been developed for liquid flows with vapor bubbles such as those in liquid rocket engine components. The analysis is based on a combined <span class="hlt">Eulerian-Lagrangian</span> technique, in which <span class="hlt">Eulerian</span> conservation equations are solved for the liquid phase, while <span class="hlt">Lagrangian</span> equations of motion are integrated in computational coordinates for the vapor phase. The novel aspect of the <span class="hlt">Lagrangian</span> analysis developed under this effort is that it combines features of the so-called particle distribution approach with those of the so-called particle trajectory approach and can, in fact, be considered as a generalization of both of those traditional methods. The result of this generalization is a reduction in CPU time and memory requirements. Particle time step (stability) limitations have been eliminated by semi-implicit integration of the particle equations of motion (and, for certain applications, the particle temperature equation), although practical limitations remain in effect for reasons of accuracy. The analysis has been applied to the simulation of cavitating flow through a single-bladed section of a labyrinth seal. Models for the simulation of bubble formation and growth have been included, as well as models for bubble drag and heat transfer. The results indicate that bubble formation is more or less 'explosive'. for a given flow field, the number density of bubble nucleation sites is very sensitive to the vapor properties and the surface tension. The bubble motion, on the other hand, is much less sensitive to the properties, but is affected strongly by the local pressure gradients in the flow field. In situations where either the material properties or the flow field are not known with sufficient accuracy, parametric studies can be carried out rapidly to assess the effect of the important variables. Future work will include application of the analysis to cavitation in inducer flow fields.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.A31C2183S"><span>Insights into the physico-chemical evolution of pyrogenic organic carbon emissions from biomass burning using coupled <span class="hlt">Lagrangian-Eulerian</span> simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Suciu, L. G.; Griffin, R. J.; Masiello, C. A.</p> <p>2017-12-01</p> <p>Wildfires and prescribed burning are important sources of particulate and gaseous pyrogenic organic carbon (PyOC) emissions to the atmosphere. These emissions impact atmospheric chemistry, air quality and climate, but the spatial and temporal variabilities of these impacts are poorly understood, primarily because small and fresh fire plumes are not well predicted by three-dimensional <span class="hlt">Eulerian</span> chemical transport models due to their coarser grid size. Generally, this results in underestimation of downwind deposition of PyOC, hydroxyl radical reactivity, secondary organic aerosol formation and ozone (O3) production. However, such models are very good for simulation of multiple atmospheric processes that could affect the lifetimes of PyOC emissions over large spatiotemporal scales. Finer resolution models, such as <span class="hlt">Lagrangian</span> reactive plumes models (or plume-in-grid), could be used to trace fresh emissions at the sub-grid level of the <span class="hlt">Eulerian</span> model. Moreover, <span class="hlt">Lagrangian</span> plume models need background chemistry predicted by the <span class="hlt">Eulerian</span> models to accurately simulate the interactions of the plume material with the background air during plume aging. Therefore, by coupling the two models, the physico-chemical evolution of the biomass burning plumes can be tracked from local to regional scales. In this study, we focus on the physico-chemical changes of PyOC emissions from sub-grid to grid levels using an existing chemical mechanism. We hypothesize that finer scale <span class="hlt">Lagrangian-Eulerian</span> simulations of several prescribed burns in the U.S. will allow more accurate downwind predictions (validated by airborne observations from smoke plumes) of PyOC emissions (i.e., submicron particulate matter, organic aerosols, refractory black carbon) as well as O3 and other trace gases. Simulation results could be used to optimize the implementation of additional PyOC speciation in the existing chemical mechanism.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFD.Q6008A"><span>Compressibility Effects on Particle-Fluid Interaction Force for <span class="hlt">Eulerian-Eulerian</span> Simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Akiki, Georges; Francois, Marianne; Zhang, Duan</p> <p>2017-11-01</p> <p>Particle-fluid interaction forces are essential in modeling multiphase flows. Several models can be found in the literature based on empirical, numerical, and experimental results from various simplified flow conditions. Some of these models also account for <span class="hlt">finite</span> Mach number effects. Using these models is relatively straightforward with <span class="hlt">Eulerian-Lagrangian</span> calculations if the model for the total force on particles is used. In <span class="hlt">Eulerian-Eulerian</span> simulations, however, there is the pressure gradient terms in the momentum equation for particles. For low Mach number flows, the pressure gradient force is negligible if the particle density is much greater than that of the fluid. For supersonic flows where a standing shock is present, even for a steady and uniform flow, it is unclear whether the significant pressure-gradient force should to be separated out from the particle force model. To answer this conceptual question, we perform single-sphere fully-resolved DNS simulations for a wide range of Mach numbers. We then examine whether the total force obtained from the DNS can be categorized into well-established models, such as the quasi-steady, added-mass, pressure-gradient, and history forces. Work sponsored by Advanced Simulation and Computing (ASC) program of NNSA and LDRD-CNLS of LANL.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf','USGSPUBS'); return false;" href="http://water.usgs.gov/nrp/gwsoftware/moc3d/doc/moc3dv3.5.pdf"><span>A three-dimensional <span class="hlt">finite</span>-volume <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) for solute-transport modeling</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.</p> <p>2000-01-01</p> <p>This report documents the U.S. Geological Survey <span class="hlt">Eulerian-Lagrangian</span> Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770023699','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770023699"><span>Development and application of a three dimensional numerical model for predicting pollutant and sediment transport using an <span class="hlt">Eulerian-Lagrangian</span> marker particle technique</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pavish, D. L.; Spaulding, M. L.</p> <p>1977-01-01</p> <p>A computer coded <span class="hlt">Lagrangian</span> marker particle in <span class="hlt">Eulerian</span> <span class="hlt">finite</span> difference cell solution to the three dimensional incompressible mass transport equation, Water Advective Particle in Cell Technique, WAPIC, was developed, verified against analytic solutions, and subsequently applied in the prediction of long term transport of a suspended sediment cloud resulting from an instantaneous dredge spoil release. Numerical results from WAPIC were verified against analytic solutions to the three dimensional incompressible mass transport equation for turbulent diffusion and advection of Gaussian dye releases in unbounded uniform and uniformly sheared uni-directional flow, and for steady-uniform plug channel flow. WAPIC was utilized to simulate an analytic solution for non-equilibrium sediment dropout from an initially vertically uniform particle distribution in one dimensional turbulent channel flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22482601','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22482601"><span><span class="hlt">Lagrangian</span> displacement tracking using a polar grid between endocardial and epicardial contours for cardiac strain imaging.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ma, Chi; Varghese, Tomy</p> <p>2012-04-01</p> <p>Accurate cardiac deformation analysis for cardiac displacement and strain imaging over time requires <span class="hlt">Lagrangian</span> description of deformation of myocardial tissue structures. Failure to couple the estimated displacement and strain information with the correct myocardial tissue structures will lead to erroneous result in the displacement and strain distribution over time. <span class="hlt">Lagrangian</span> based tracking in this paper divides the tissue structure into a fixed number of pixels whose deformation is tracked over the cardiac cycle. An algorithm that utilizes a polar-grid generated between the estimated endocardial and epicardial contours for cardiac short axis images is proposed to ensure <span class="hlt">Lagrangian</span> description of the pixels. Displacement estimates from consecutive radiofrequency frames were then mapped onto the polar grid to obtain a distribution of the actual displacement that is mapped to the polar grid over time. A <span class="hlt">finite</span> <span class="hlt">element</span> based canine heart model coupled with an ultrasound simulation program was used to verify this approach. Segmental analysis of the accumulated displacement and strain over a cardiac cycle demonstrate excellent agreement between the ideal result obtained directly from the <span class="hlt">finite</span> <span class="hlt">element</span> model and our <span class="hlt">Lagrangian</span> approach to strain estimation. Traditional <span class="hlt">Eulerian</span> based estimation results, on the other hand, show significant deviation from the ideal result. An in vivo comparison of the displacement and strain estimated using parasternal short axis views is also presented. <span class="hlt">Lagrangian</span> displacement tracking using a polar grid provides accurate tracking of myocardial deformation demonstrated using both <span class="hlt">finite</span> <span class="hlt">element</span> and in vivo radiofrequency data acquired on a volunteer. In addition to the cardiac application, this approach can also be utilized for transverse scans of arteries, where a polar grid can be generated between the contours delineating the outer and inner wall of the vessels from the blood flowing though the vessel.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AtmEn.184..304D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AtmEn.184..304D"><span><span class="hlt">Eulerian-Lagrangian</span> CFD modelling of pesticide dust emissions from maize planters</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Devarrewaere, Wouter; Foqué, Dieter; Nicolai, Bart; Nuyttens, David; Verboven, Pieter</p> <p>2018-07-01</p> <p>An <span class="hlt">Eulerian-Lagrangian</span> 3D computational fluid dynamics (CFD) model of pesticide dust drift from precision vacuum planters in field conditions was developed. Tractor and planter models were positioned in an atmospheric computational domain, representing the field and its edges. Physicochemical properties of dust abraded from maize seeds (particle size, shape, porosity, density, a.i. content), dust emission rates and exhaust air velocity values at the planter fan outlets were measured experimentally and implemented in the model. The wind profile, the airflow pattern around the machines and the dust dispersion were computed. Various maize sowing scenarios with different wind conditions, dust properties, planter designs and vacuum pressures were simulated. Dust particle trajectories were calculated by means of <span class="hlt">Lagrangian</span> particle tracking, considering nonspherical particle drag, gravity and turbulent dispersion. The dust dispersion model was previously validated with wind tunnel data. In this study, simulated pesticide concentrations in the air and on the soil in the different sowing scenarios were compared and discussed. The model predictions were similar to experimental literature data in terms of concentrations and drift distance. Pesticide exposure levels to bees during flight and foraging were estimated from the simulated concentrations. The proposed CFD model can be used in risk assessment studies and in the evaluation of dust drift mitigation measures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19830013121','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19830013121"><span><span class="hlt">Finite</span> <span class="hlt">element</span> modeling and analysis of tires</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, A. K.; Andersen, C. M.</p> <p>1983-01-01</p> <p>Predicting the response of tires under various loading conditions using <span class="hlt">finite</span> <span class="hlt">element</span> technology is addressed. Some of the recent advances in <span class="hlt">finite</span> <span class="hlt">element</span> technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed <span class="hlt">finite</span> <span class="hlt">element</span> models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total <span class="hlt">Lagrangian</span> description of the deformation are included.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016EGUGA..1818317B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016EGUGA..1818317B"><span><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> description of bed-load particle kinematics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ballio, Francesco; Sadabadi, Seyed Abbas Hosseini; Pokrajac, Dubravka; Radice, Alessio</p> <p>2016-04-01</p> <p>The motion of bed-load sediment particles transported by a flow can be analyzed within a <span class="hlt">Lagrangian</span> or an <span class="hlt">Eulerian</span> framework. In the former case, we consider the particles as individual objects in motion and we study their kinematic properties. The latter approach is instead referred to suitably chosen control volumes. Quantities describing sediment motion in the two frameworks are different, and the relationships among the two approaches are not straightforward. In this work, we intend to discuss the kinematic properties of sediment transport: first, a set of quantities is univocally defined; then, relationships among different representations are explored. Proof-of-concept results presented in the study are from a recent experiment involving weak bed-load sediment transport, where the moving particles were released over a fixed rough bed. The bulk flow velocity was 1.4 times the critical value for incipient particle motion, and particles were mostly moving by rolling and sliding, with limited saltation. The particle motion was filmed from the top and the measurements were conducted by image-based methods, obtaining extensive samples of virtually-instantaneous quantities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3462029"><span><span class="hlt">Lagrangian</span> transport properties of pulmonary interfacial flows</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Smith, Bradford J.; Lukens, Sarah; Yamaguchi, Eiichiro; Gaver, Donald P.</p> <p>2012-01-01</p> <p>Disease states characterized by airway fluid occlusion and pulmonary surfactant insufficiency, such as respiratory distress syndrome, have a high mortality rate. Understanding the mechanics of airway reopening, particularly involving surfactant transport, may provide an avenue to increase patient survival via optimized mechanical ventilation waveforms. We model the occluded airway as a liquid-filled rigid tube with the fluid phase displaced by a finger of air that propagates with both mean and sinusoidal velocity components. <span class="hlt">Finite</span>-time Lyapunov exponent (FTLE) fields are employed to analyse the convective transport characteristics, taking note of <span class="hlt">Lagrangian</span> coherent structures (LCSs) and their effects on transport. The <span class="hlt">Lagrangian</span> perspective of these techniques reveals flow characteristics that are not readily apparent by observing <span class="hlt">Eulerian</span> measures. These analysis techniques are applied to surfactant-free velocity fields determined computationally, with the boundary <span class="hlt">element</span> method, and measured experimentally with micro particle image velocimetry (μ-PIV). We find that the LCS divides the fluid into two regimes, one advected upstream (into the thin residual film) and the other downstream ahead of the advancing bubble. At higher oscillatory frequencies particles originating immediately inside the LCS experience long residence times at the air–liquid interface, which may be conducive to surfactant transport. At high frequencies a well-mixed attractor region is identified; this volume of fluid cyclically travels along the interface and into the bulk fluid. The <span class="hlt">Lagrangian</span> analysis is applied to velocity data measured with 0.01 mg ml−1 of the clinical pulmonary surfactant Infasurf in the bulk fluid, demonstrating flow field modifications with respect to the surfactant-free system that were not visible in the <span class="hlt">Eulerian</span> frame. PMID:23049141</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035994&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. II - The spinning sphere</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Van Dommelen, Leon L.</p> <p>1990-01-01</p> <p>A theory to explain the initial stages of unsteady separation was proposed by Van Dommelen and Cowley (1989). This theory is verified for the separation process that occurs at the equatorial plane of a sphere or a spheroid which is impulsively spun around an axis of symmetry. A <span class="hlt">Lagrangian</span> numerical scheme is developed which gives results in good agreement with <span class="hlt">Eulerian</span> computations, but which is significantly more accurate. This increased accuracy, and a simpler structure to the solution, also allows verification of the <span class="hlt">Eulerian</span> structure, including the presence of logarithmic terms. Further, while the <span class="hlt">Eulerian</span> computations broke down at the first occurrence of separation, it is found that the <span class="hlt">Lagrangian</span> computation can be continued. It is argued that this separated solution does provide useful insight into the further evolution of the separated flow. A remarkable conclusion is that an unseparated vorticity layer at the wall, a familiar feature in unsteady separation processes, disappears in <span class="hlt">finite</span> time.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/12779582','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/12779582"><span><span class="hlt">Lagrangian</span> averages, averaged <span class="hlt">Lagrangians</span>, and the mean effects of fluctuations in fluid dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Holm, Darryl D.</p> <p>2002-06-01</p> <p>We begin by placing the generalized <span class="hlt">Lagrangian</span> mean (GLM) equations for a compressible adiabatic fluid into the Euler-Poincare (EP) variational framework of fluid dynamics, for an averaged <span class="hlt">Lagrangian</span>. This is the <span class="hlt">Lagrangian</span> averaged Euler-Poincare (LAEP) theorem. Next, we derive a set of approximate small amplitude GLM equations (glm equations) at second order in the fluctuating displacement of a <span class="hlt">Lagrangian</span> trajectory from its mean position. These equations express the linear and nonlinear back-reaction effects on the <span class="hlt">Eulerian</span> mean fluid quantities by the fluctuating displacements of the <span class="hlt">Lagrangian</span> trajectories in terms of their <span class="hlt">Eulerian</span> second moments. The derivation of the glm equations uses the linearized relations between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> fluctuations, in the tradition of <span class="hlt">Lagrangian</span> stability analysis for fluids. The glm derivation also uses the method of averaged <span class="hlt">Lagrangians</span>, in the tradition of wave, mean flow interaction. Next, the new glm EP motion equations for incompressible ideal fluids are compared with the Euler-alpha turbulence closure equations. An alpha model is a GLM (or glm) fluid theory with a Taylor hypothesis closure. Such closures are based on the linearized fluctuation relations that determine the dynamics of the <span class="hlt">Lagrangian</span> statistical quantities in the Euler-alpha equations. Thus, by using the LAEP theorem, we bridge between the GLM equations and the Euler-alpha closure equations, through the small-amplitude glm approximation in the EP variational framework. We conclude by highlighting a new application of the GLM, glm, and alpha-model results for <span class="hlt">Lagrangian</span> averaged ideal magnetohydrodynamics. (c) 2002 American Institute of Physics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164425','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164425"><span>On tide-induced <span class="hlt">Lagrangian</span> residual current and residual transport: 1. <span class="hlt">Lagrangian</span> residual current</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Feng, Shizuo; Cheng, Ralph T.; Pangen, Xi</p> <p>1986-01-01</p> <p>Residual currents in tidal estuaries and coastal embayments have been recognized as fundamental factors which affect the long-term transport processes. It has been pointed out by previous studies that it is more relevant to use a <span class="hlt">Lagrangian</span> mean velocity than an <span class="hlt">Eulerian</span> mean velocity to determine the movements of water masses. Under weakly nonlinear approximation, the parameter k, which is the ratio of the net displacement of a labeled water mass in one tidal cycle to the tidal excursion, is assumed to be small. Solutions for tides, tidal current, and residual current have been considered for two-dimensional, barotropic estuaries and coastal seas. Particular attention has been paid to the distinction between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents. When k is small, the first-order <span class="hlt">Lagrangian</span> residual is shown to be the sum of the <span class="hlt">Eulerian</span> residual current and the Stokes drift. The <span class="hlt">Lagrangian</span> residual drift velocity or the second-order <span class="hlt">Lagrangian</span> residual current has been shown to be dependent on the phase of tidal current. The <span class="hlt">Lagrangian</span> drift velocity is induced by nonlinear interactions between tides, tidal currents, and the first-order residual currents, and it takes the form of an ellipse on a hodograph plane. Several examples are given to further demonstrate the unique properties of the <span class="hlt">Lagrangian</span> residual current.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70164423','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70164423"><span>On <span class="hlt">Lagrangian</span> residual currents with applications in south San Francisco Bay, California</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.; Casulli, Vincenzo</p> <p>1982-01-01</p> <p>The <span class="hlt">Lagrangian</span> residual circulation has often been introduced as the sum of the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift. Unfortunately, this definition of the <span class="hlt">Lagrangian</span> residual circulation is conceptually incorrect because both the <span class="hlt">Eulerian</span> residual circulation and the Stokes' drift are <span class="hlt">Eulerian</span> variables. In this paper a classification of various residual variables are reviewed and properly defined. The <span class="hlt">Lagrangian</span> residual circulation is then studied by means of a two-stage formulation of a computer model. The tidal circulation is first computed in a conventional <span class="hlt">Eulerian</span> way, and then the <span class="hlt">Lagrangian</span> residual circulation is determined by a method patterned after the method of markers and cells. To demonstrate properties of the <span class="hlt">Lagrangian</span> residual circulation, application of this approach in South San Francisco Bay, California, is considered. With the aid of the model results, properties of the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residual circulation are examined. It can be concluded that estimation of the <span class="hlt">Lagrangian</span> residual circulation from <span class="hlt">Eulerian</span> data may lead to unacceptable error, particularly in a tidal estuary where the tidal excursion is of the same order of magnitude as the length scale of the basin. A direction calculation of the <span class="hlt">Lagrangian</span> residual circulation must be made and has been shown to be feasible.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDD37005K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDD37005K"><span>Investigation of erosion behavior in different pipe-fitting using <span class="hlt">Eulerian-Lagrangian</span> approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kulkarni, Harshwardhan; Khadamkar, Hrushikesh; Mathpati, Channamallikarjun</p> <p>2017-11-01</p> <p>Erosion is a wear mechanism of piping system in which wall thinning occurs because of turbulent flow along with along with impact of solid particle on the pipe wall, because of this pipe ruptures causes costly repair of plant and personal injuries. In this study two way coupled <span class="hlt">Eulerian-Lagrangian</span> approach is used to solve the liquid solid (water-ferrous suspension) flow in the different pipe fitting namely elbow, t-junction, reducer, orifice and 50% open gate valve. Simulations carried out using incomressible transient solver in OpenFOAM for different Reynolds's number (10k, 25k, 50k) and using WenYu drag model to find out possible higher erosion region in pipe fitting. Used transient solver is a hybrid in nature which is combination of <span class="hlt">Lagrangian</span> library and pimpleFoam. Result obtained from simulation shows that exit region of elbow specially downstream of straight, extradose of the bend section more affected by erosion. Centrifugal force on solid particle at bend affect the erosion behavior. In case of t-junction erosion occurs below the locus of the projection of branch pipe on the wall. For the case of reducer, orifice and a gate valve reduction area as well as downstream is getting more affected by erosion because of increase in velocities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://files.eric.ed.gov/fulltext/ED119999.pdf','ERIC'); return false;" href="http://files.eric.ed.gov/fulltext/ED119999.pdf"><span>The Case for Including <span class="hlt">Eulerian</span> Kinematics in Undergraduate Dynamics.</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Uram, Earl M.</p> <p></p> <p>A <span class="hlt">Eulerian</span> framework is proposed as an alternative to the <span class="hlt">Lagrangian</span> framework usually used in undergraduate dynamics courses. An attempt to introduce <span class="hlt">Eulerian</span> kinematics into a dynamics course is discussed. (LMH)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70011338','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70011338"><span>Euler-<span class="hlt">Lagrangian</span> computation for estuarine hydrodynamics</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cheng, Ralph T.</p> <p>1983-01-01</p> <p>The transport of conservative and suspended matter in fluid flows is a phenomenon of <span class="hlt">Lagrangian</span> nature because the process is usually convection dominant. Nearly all numerical investigations of such problems use an <span class="hlt">Eulerian</span> formulation for the convenience that the computational grids are fixed in space and because the vast majority of field data are collected in an <span class="hlt">Eulerian</span> reference frame. Several examples are given in this paper to illustrate a modeling approach which combines the advantages of both the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> computational techniques.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016PhFl...28f1901S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016PhFl...28f1901S"><span>An unstructured mesh arbitrary <span class="hlt">Lagrangian-Eulerian</span> unsteady incompressible flow solver and its application to insect flight aerodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Su, Xiaohui; Cao, Yuanwei; Zhao, Yong</p> <p>2016-06-01</p> <p>In this paper, an unstructured mesh Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) incompressible flow solver is developed to investigate the aerodynamics of insect hovering flight. The proposed <span class="hlt">finite</span>-volume ALE Navier-Stokes solver is based on the artificial compressibility method (ACM) with a high-resolution method of characteristics-based scheme on unstructured grids. The present ALE model is validated and assessed through flow passing over an oscillating cylinder. Good agreements with experimental results and other numerical solutions are obtained, which demonstrates the accuracy and the capability of the present model. The lift generation mechanisms of 2D wing in hovering motion, including wake capture, delayed stall, rapid pitch, as well as clap and fling are then studied and illustrated using the current ALE model. Moreover, the optimized angular amplitude in symmetry model, 45°, is firstly reported in details using averaged lift and the energy power method. Besides, the lift generation of complete cyclic clap and fling motion, which is simulated by few researchers using the ALE method due to large deformation, is studied and clarified for the first time. The present ALE model is found to be a useful tool to investigate lift force generation mechanism for insect wing flight.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_3");'>3</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li class="active"><span>5</span></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_5 --> <div id="page_6" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="101"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1304832-finite-element-ale-method-using-approximate-riemann-solution','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1304832-finite-element-ale-method-using-approximate-riemann-solution"><span>A 3D <span class="hlt">finite</span> <span class="hlt">element</span> ALE method using an approximate Riemann solution</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Chiravalle, V. P.; Morgan, N. R.</p> <p>2016-08-09</p> <p>Arbitrary Lagrangian–<span class="hlt">Eulerian</span> <span class="hlt">finite</span> volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D <span class="hlt">finite</span> <span class="hlt">element</span> arbitrary Lagrangian–<span class="hlt">Eulerian</span> SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1304832','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1304832"><span>A 3D <span class="hlt">finite</span> <span class="hlt">element</span> ALE method using an approximate Riemann solution</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Chiravalle, V. P.; Morgan, N. R.</p> <p></p> <p>Arbitrary Lagrangian–<span class="hlt">Eulerian</span> <span class="hlt">finite</span> volume methods that solve a multidimensional Riemann-like problem at the cell center in a staggered grid hydrodynamic (SGH) arrangement have been proposed. This research proposes a new 3D <span class="hlt">finite</span> <span class="hlt">element</span> arbitrary Lagrangian–<span class="hlt">Eulerian</span> SGH method that incorporates a multidimensional Riemann-like problem. Here, two different Riemann jump relations are investigated. A new limiting method that greatly improves the accuracy of the SGH method on isentropic flows is investigated. A remap method that improves upon a well-known mesh relaxation and remapping technique in order to ensure total energy conservation during the remap is also presented. Numerical details and test problemmore » results are presented.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.338..339Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.338..339Y"><span>Vertical discretization with <span class="hlt">finite</span> <span class="hlt">elements</span> for a global hydrostatic model on the cubed sphere</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yi, Tae-Hyeong; Park, Ja-Rin</p> <p>2017-06-01</p> <p>A formulation of Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global <span class="hlt">Eulerian</span> hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral <span class="hlt">elements</span> on a cubed sphere grid. This replaces the vertical discretization of conventional central <span class="hlt">finite</span> difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin <span class="hlt">finite</span> <span class="hlt">elements</span> for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since <span class="hlt">Eulerian</span> advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical <span class="hlt">finite</span> <span class="hlt">element</span> with the cubic basis-spline function is more accurate and stable than that of the vertical <span class="hlt">finite</span> difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical <span class="hlt">finite</span> <span class="hlt">element</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1399708-eulerian-formulation-interacting-particle-representation-model-homogeneous-turbulence','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1399708-eulerian-formulation-interacting-particle-representation-model-homogeneous-turbulence"><span><span class="hlt">Eulerian</span> formulation of the interacting particle representation model of homogeneous turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca</p> <p>2016-10-21</p> <p>The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a <span class="hlt">Lagrangian</span> setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an <span class="hlt">Eulerian</span> framework and evolution equations are developed for the marginal PDFs. <span class="hlt">Eulerian</span> methods avoid the issues associated with statistical estimators used by <span class="hlt">Lagrangian</span> approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with <span class="hlt">Eulerian</span> simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new <span class="hlt">Eulerian</span> solution method are thoroughly analyzed. The sensitivity of the <span class="hlt">Eulerian</span> simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new <span class="hlt">Eulerian</span> solution method and the original <span class="hlt">Lagrangian</span> approach.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015APS..DFDG26009K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015APS..DFDG26009K"><span>A musculo-mechanical model of esophageal transport based on an immersed boundary-<span class="hlt">finite</span> <span class="hlt">element</span> approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kou, Wenjun; Griffith, Boyce E.; Pandolfino, John E.; Kahrilas, Peter J.; Patankar, Neelesh A.</p> <p>2015-11-01</p> <p>This work extends a fiber-based immersed boundary (IB) model of esophageal transport by incorporating a continuum model of the deformable esophageal wall. The continuum-based esophagus model adopts <span class="hlt">finite</span> <span class="hlt">element</span> approach that is capable of describing more complex and realistic material properties and geometries. The leakage from mismatch between <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> meshes resulting from large deformations of the esophageal wall is avoided by careful choice of interaction points. The esophagus model, which is described as a multi-layered, fiber-reinforced nonlinear elastic material, is coupled to bolus and muscle-activation models using the IB approach to form the esophageal transport model. Cases of esophageal transport with different esophagus models are studied. Results on the transport characteristics, including pressure field and esophageal wall kinematics and stress, are analyzed and compared. Support from NIH grant R01 DK56033 and R01 DK079902 is gratefully acknowledged. BEG is supported by NSF award ACI 1460334.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CMAME.336..533B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CMAME.336..533B"><span>The aggregated unfitted <span class="hlt">finite</span> <span class="hlt">element</span> method for elliptic problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.</p> <p>2018-07-01</p> <p>Unfitted <span class="hlt">finite</span> <span class="hlt">element</span> techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to severe ill conditioning problems that obstruct the efficient use of iterative Krylov methods and, in consequence, hinders the practical usage of unfitted methods for realistic large scale applications. In this work, we present a technique that addresses such conditioning problems by constructing enhanced <span class="hlt">finite</span> <span class="hlt">element</span> spaces based on a cell aggregation technique. The presented method, called aggregated unfitted <span class="hlt">finite</span> <span class="hlt">element</span> method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard <span class="hlt">finite</span> <span class="hlt">elements</span> for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal <span class="hlt">finite</span> <span class="hlt">element</span> convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MMTB...48.1248L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MMTB...48.1248L"><span>Modeling of Quasi-Four-Phase Flow in Continuous Casting Mold Using Hybrid <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Zhongqiu; Sun, Zhenbang; Li, Baokuan</p> <p>2017-04-01</p> <p><span class="hlt">Lagrangian</span> tracking model combined with <span class="hlt">Eulerian</span> multi-phase model is employed to predict the time-dependent argon-steel-slag-air quasi-four-phase flow inside a slab continuous casting mold. The <span class="hlt">Eulerian</span> approach is used for the description of three phases (molten steel, liquid slag, and air at the top of liquid slag layer). The dispersed argon bubble injected from the SEN is treated in the <span class="hlt">Lagrangian</span> way. The complex interfacial momentum transfers between various phases are considered. Validation is supported by the measurement data of cold model experiments and industrial practice. Close agreements were achieved for the gas volume fraction, liquid flow pattern, level fluctuation, and exposed slag eye phenomena. Many known phenomena and new predictions were successfully reproduced using this model. The vortex slag entrapment phenomenon at the slag-steel interface was obtained using this model, some small slag drops are sucked deep into the liquid pool of molten steel. Varying gas flow rates have a large effect on the steel flow pattern in the upper recirculation zone. Three typical flow patterns inside the mold with different argon gas flow rates have been obtained: double roll, three roll, and single roll. Effects of argon gas flow rate, casting speed, and slag layer thickness on the exposed slag eye and level fluctuation at the slag-steel interface were studied. A dimensionless value of H ave/ h was proposed to describe the time-averaged level fluctuation of slag-steel interface. The exposed slag eye near the SEN would be formed when the value of H ave/ h is larger than 0.4.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JGRC..122.5445S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JGRC..122.5445S"><span>Impact of data assimilation on <span class="hlt">Eulerian</span> versus <span class="hlt">Lagrangian</span> estimates of upper ocean transport</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sperrevik, Ann Kristin; Röhrs, Johannes; Christensen, Kai Hâkon</p> <p>2017-07-01</p> <p>Using four-dimensional variational analysis, we produce an estimate of the state of a coastal region in Northern Norway during the late winter and spring in 1984. We use satellite sea surface temperature and in situ observations from a series of intensive field campaigns, and obtain a more realistic distribution of water masses both in the horizontal and the vertical than a pure downscaling approach can achieve. Although the distribution of <span class="hlt">Eulerian</span> surface current speeds are similar, we find that they are more variable and less dependent on model bathymetry in our reanalysis compared to a hindcast produced using the same modeling system. <span class="hlt">Lagrangian</span> drift currents on the other hand are significantly changed, with overall higher kinetic energy levels in the reanalysis than in the hindcast, particularly in the superinertial frequency band.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19940033879&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DLagrangian"><span>The piecewise-linear predictor-corrector code - A <span class="hlt">Lagrangian</span>-remap method for astrophysical flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lufkin, Eric A.; Hawley, John F.</p> <p>1993-01-01</p> <p>We describe a time-explicit <span class="hlt">finite</span>-difference algorithm for solving the nonlinear fluid equations. The method is similar to existing <span class="hlt">Eulerian</span> schemes in its use of operator-splitting and artificial viscosity, except that we solve the <span class="hlt">Lagrangian</span> equations of motion with a predictor-corrector and then remap onto a fixed <span class="hlt">Eulerian</span> grid. The remap is formulated to eliminate errors associated with coordinate singularities, with a general prescription for remaps of arbitrary order. We perform a comprehensive series of tests on standard problems. Self-convergence tests show that the code has a second-order rate of convergence in smooth, two-dimensional flow, with pressure forces, gravity, and curvilinear geometry included. While not as accurate on idealized problems as high-order Riemann-solving schemes, the predictor-corrector <span class="hlt">Lagrangian</span>-remap code has great flexibility for application to a variety of astrophysical problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDA37008R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDA37008R"><span>GPU acceleration of <span class="hlt">Eulerian-Lagrangian</span> particle-laden turbulent flow simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Richter, David; Sweet, James; Thain, Douglas</p> <p>2017-11-01</p> <p>The <span class="hlt">Lagrangian</span> point-particle approximation is a popular numerical technique for representing dispersed phases whose properties can substantially deviate from the local fluid. In many cases, particularly in the limit of one-way coupled systems, large numbers of particles are desired; this may be either because many physical particles are present (e.g. LES of an entire cloud), or because the use of many particles increases statistical convergence (e.g. high-order statistics). Solving the trajectories of very large numbers of particles can be problematic in traditional MPI implementations, however, and this study reports the benefits of using graphical processing units (GPUs) to integrate the particle equations of motion while preserving the original MPI version of the <span class="hlt">Eulerian</span> flow solver. It is found that GPU acceleration becomes cost effective around one million particles, and performance enhancements of up to 15x can be achieved when O(108) particles are computed on the GPU rather than the CPU cluster. Optimizations and limitations will be discussed, as will prospects for expanding to two- and four-way coupled systems. ONR Grant No. N00014-16-1-2472.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26611112','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26611112"><span>Updated <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulations of various biological soft tissue non-linear material models: a comprehensive procedure and review.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Townsend, Molly T; Sarigul-Klijn, Nesrin</p> <p>2016-01-01</p> <p>Simplified material models are commonly used in computational simulation of biological soft tissue as an approximation of the complicated material response and to minimize computational resources. However, the simulation of complex loadings, such as long-duration tissue swelling, necessitates complex models that are not easy to formulate. This paper strives to offer the updated <span class="hlt">Lagrangian</span> formulation comprehensive procedure of various non-linear material models for the application of <span class="hlt">finite</span> <span class="hlt">element</span> analysis of biological soft tissues including a definition of the Cauchy stress and the spatial tangential stiffness. The relationships between water content, osmotic pressure, ionic concentration and the pore pressure stress of the tissue are discussed with the merits of these models and their applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20130010995','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20130010995"><span>Ice Accretion Modeling using an <span class="hlt">Eulerian</span> Approach for Droplet Impingement</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kim, Joe Woong; Garza, Dennis P.; Sankar, Lakshmi N.; Kreeger, Richard E.</p> <p>2012-01-01</p> <p>A three-dimensional <span class="hlt">Eulerian</span> analysis has been developed for modeling droplet impingement on lifting bodes. The <span class="hlt">Eulerian</span> model solves the conservation equations of mass and momentum to obtain the droplet flow field properties on the same mesh used in CFD simulations. For complex configurations such as a full rotorcraft, the <span class="hlt">Eulerian</span> approach is more efficient because the <span class="hlt">Lagrangian</span> approach would require a significant amount of seeding for accurate estimates of collection efficiency. Simulations are done for various benchmark cases such as NACA0012 airfoil, MS317 airfoil and oscillating SC2110 airfoil to illustrate its use. The present results are compared with results from the <span class="hlt">Lagrangian</span> approach used in an industry standard analysis called LEWICE.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhCS.753h2031F"><span>Wake modeling in complex terrain using a hybrid <span class="hlt">Eulerian-Lagrangian</span> Split Solver</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fuchs, Franz G.; Rasheed, Adil; Tabib, Mandar; Fonn, Eivind</p> <p>2016-09-01</p> <p>Wake vortices (WVs) generated by aircraft are a source of risk to the following aircraft. The probability of WV related accidents increases in the vicinity of airport runways due to the shorter time of recovery after a WV encounter. Hence, solutions that can reduce the risk of WV encounters are needed to ensure increased flight safety. In this work we propose an interesting approach to model such wake vortices in real time using a hybrid <span class="hlt">Eulerian</span>- <span class="hlt">Lagrangian</span> approach. We derive an appropriate mathematical model, and show a comparison of the different types of solvers. We will conclude with a real life application of the methodology by simulating how wake vortices left behind by an aircraft at the Vffirnes airport in Norway get transported and decay under the influence of a background wind and turbulence field. Although the work demonstrates the application in an aviation context the same approach can be used in a wind energy context.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/19029589','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/19029589"><span>Simulation of atmospheric dispersion of radionuclides using an <span class="hlt">Eulerian-Lagrangian</span> modelling system.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Basit, Abdul; Espinosa, Francisco; Avila, Ruben; Raza, S; Irfan, N</p> <p>2008-12-01</p> <p>In this paper we present an atmospheric dispersion scenario for a proposed nuclear power plant in Pakistan involving the hypothetical accidental release of radionuclides. For this, a concept involving a <span class="hlt">Lagrangian</span> stochastic particle model (LSPM) coupled with an <span class="hlt">Eulerian</span> regional atmospheric modelling system (RAMS) is used. The atmospheric turbulent dispersion of radionuclides (represented by non-buoyant particles/neutral traces) in the LSPM is modelled by applying non-homogeneous turbulence conditions. The mean wind velocities governed by the topography of the region and the surface fluxes of momentum and heat are calculated by the RAMS code. A moving least squares (MLS) technique is introduced to calculate the concentration of radionuclides at ground level. The numerically calculated vertical profiles of wind velocity and temperature are compared with observed data. The results obtained demonstrate that in regions of complex terrain it is not sufficient to model the atmospheric dispersion of particles using a straight-line Gaussian plume model, and that by utilising a <span class="hlt">Lagrangian</span> stochastic particle model and regional atmospheric modelling system a much more realistic estimation of the dispersion in such a hypothetical scenario was ascertained. The particle dispersion results for a 12 h ground release show that a triangular area of about 400 km(2) situated in the north-west quadrant of release is under radiological threat. The particle distribution shows that the use of a Gaussian plume model (GPM) in such situations will yield quite misleading results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1360930-modeling-shockwaves-impact-phenomena-eulerian-peridynamics"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.; ...</p> <p>2017-05-09</p> <p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> formulation, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1360930','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1360930"><span>Modeling shockwaves and impact phenomena with <span class="hlt">Eulerian</span> peridynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Silling, Stewart A.; Parks, Michael L.; Kamm, James R.</p> <p></p> <p>Most previous development of the peridynamic theory has assumed a <span class="hlt">Lagrangian</span> formulation, in which the material model refers to an undeformed reference configuration. Here, an <span class="hlt">Eulerian</span> form of material modeling is developed, in which bond forces depend only on the positions of material points in the deformed configuration. The formulation is consistent with the thermodynamic form of the peridynamic model and is derivable from a suitable expression for the free energy of a material. We show that the resulting formulation of peridynamic material models can be used to simulate strong shock waves and fluid response in which very large deformationsmore » make the <span class="hlt">Lagrangian</span> form unsuitable. The <span class="hlt">Eulerian</span> capability is demonstrated in numerical simulations of ejecta from a wavy free surface on a metal subjected to strong shock wave loading. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> contributions to bond force can be combined in a single material model, allowing strength and fracture under tensile or shear loading to be modeled consistently with high compressive stresses. Furthermore, we demonstrate this capability in numerical simulation of bird strike against an aircraft, in which both tensile fracture and high pressure response are important.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1412853-computing-eddy-driven-effective-diffusivity-using-lagrangian-particles"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Wolfram, Phillip J.; Ringler, Todd D.</p> <p>2017-08-14</p> <p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1412853','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1412853"><span>Computing eddy-driven effective diffusivity using <span class="hlt">Lagrangian</span> particles</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wolfram, Phillip J.; Ringler, Todd D.</p> <p></p> <p>A novel method to derive effective diffusivity from <span class="hlt">Lagrangian</span> particle trajectory data sets is developed and then analyzed relative to particle-derived meridional diffusivity for eddy-driven mixing in an idealized circumpolar current. Quantitative standard dispersion- and transport-based mixing diagnostics are defined, compared and contrasted to motivate the computation and use of effective diffusivity derived from <span class="hlt">Lagrangian</span> particles. We compute the effective diffusivity by first performing scalar transport on <span class="hlt">Lagrangian</span> control areas using stored trajectories computed from online <span class="hlt">Lagrangian</span> In-situ Global High-performance particle Tracking (LIGHT) using the Model for Prediction Across Scales Ocean (MPAS-O). Furthermore, the <span class="hlt">Lagrangian</span> scalar transport scheme is comparedmore » against an <span class="hlt">Eulerian</span> scalar transport scheme. Spatially-variable effective diffusivities are computed from resulting time-varying cumulative concentrations that vary as a function of cumulative area. The transport-based <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivity diagnostics are found to be qualitatively consistent with the dispersion-based diffusivity. All diffusivity estimates show a region of increased subsurface diffusivity within the core of an idealized circumpolar current and results are within a factor of two of each other. The <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> effective diffusivities are most similar; smaller and more spatially diffused values are obtained with the dispersion-based diffusivity computed with particle clusters.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996PhRvE..54.1530N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996PhRvE..54.1530N"><span>Sufficient condition for a <span class="hlt">finite</span>-time singularity in a high-symmetry Euler flow: Analysis and statistics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ng, C. S.; Bhattacharjee, A.</p> <p>1996-08-01</p> <p>A sufficient condition is obtained for the development of a <span class="hlt">finite</span>-time singularity in a highly symmetric Euler flow, first proposed by Kida [J. Phys. Soc. Jpn. 54, 2132 (1995)] and recently simulated by Boratav and Pelz [Phys. Fluids 6, 2757 (1994)]. It is shown that if the second-order spatial derivative of the pressure (pxx) is positive following a <span class="hlt">Lagrangian</span> <span class="hlt">element</span> (on the x axis), then a <span class="hlt">finite</span>-time singularity must occur. Under some assumptions, this <span class="hlt">Lagrangian</span> sufficient condition can be reduced to an <span class="hlt">Eulerian</span> sufficient condition which requires that the fourth-order spatial derivative of the pressure (pxxxx) at the origin be positive for all times leading up to the singularity. Analytical as well as direct numerical evaluation over a large ensemble of initial conditions demonstrate that for fixed total energy, pxxxx is predominantly positive with the average value growing with the numbers of modes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1047333-reissner-mindlin-legendre-spectral-finite-elements-mixed-reduced-quadrature','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1047333-reissner-mindlin-legendre-spectral-finite-elements-mixed-reduced-quadrature"><span>Reissner-Mindlin Legendre Spectral <span class="hlt">Finite</span> <span class="hlt">Elements</span> with Mixed Reduced Quadrature</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Brito, K. D.; Sprague, M. A.</p> <p>2012-10-01</p> <p>Legendre spectral <span class="hlt">finite</span> <span class="hlt">elements</span> (LSFEs) are examined through numerical experiments for static and dynamic Reissner-Mindlin plate bending and a mixed-quadrature scheme is proposed. LSFEs are high-order <span class="hlt">Lagrangian</span>-interpolant <span class="hlt">finite</span> <span class="hlt">elements</span> with nodes located at the Gauss-Lobatto-Legendre quadrature points. Solutions on unstructured meshes are examined in terms of accuracy as a function of the number of model nodes and total operations. While nodal-quadrature LSFEs have been shown elsewhere to be free of shear locking on structured grids, locking is demonstrated here on unstructured grids. LSFEs with mixed quadrature are, however, locking free and are significantly more accurate than low-order <span class="hlt">finite-elements</span> for amore » given model size or total computation time.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_4");'>4</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li class="active"><span>6</span></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_6 --> <div id="page_7" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="121"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998NucFu..38..776B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998NucFu..38..776B"><span>BOOK REVIEW: Nonlinear Continuum Mechanics for <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Bialek, James M.</p> <p>1998-05-01</p> <p>Nonlinear continuum mechanics of solids is a fascinating subject. All the assumptions inherited from an overexposure to linear behaviour and analysis must be re-examined. The standard definitions of strain designed for small deformation linear problems may be totally misleading when <span class="hlt">finite</span> motion or large deformations are considered. Nonlinear behaviour includes phenomena like `snap-through', where bifurcation theory is applied to engineering design. Capabilities in this field are growing at a fantastic speed; for example, modern automobiles are presently being designed to crumple in the most energy absorbing manner in order to protect the occupants. The combination of nonlinear mechanics and the <span class="hlt">finite</span> <span class="hlt">element</span> method is a very important field. Most engineering designs encountered in the fusion effort are strictly limited to small deformation linear theory. In fact, fusion devices are usually kept in the low stress, long life regime that avoids large deformations, nonlinearity and any plastic behaviour. The only aspect of nonlinear continuum solid mechanics about which the fusion community now worries is that rare case where details of the metal forming process must be considered. This text is divided into nine sections: introduction, mathematical preliminaries, kinematics, stress and equilibrium, hyperelasticity, linearized equilibrium equations, discretization and solution, computer implementation and an appendix covering an introduction to large inelastic deformations. The authors have decided to use vector and tensor notation almost exclusively. This means that the usual maze of indicial equations is avoided, but most readers will therefore be stretched considerably to follow the presentation, which quickly proceeds to the heart of nonlinear behaviour in solids. With great speed the reader is led through the material (<span class="hlt">Lagrangian</span>) and spatial (<span class="hlt">Eulerian</span>) co-ordinates, the deformation gradient tensor (an example of a two point tensor), the right and left Cauchy</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AdWR..113..141E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AdWR..113..141E"><span>Shear and shearless <span class="hlt">Lagrangian</span> structures in compound channels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Enrile, F.; Besio, G.; Stocchino, A.</p> <p>2018-03-01</p> <p>Transport processes in a physical model of a natural stream with a composite cross-section (compound channel) are investigated by means of a <span class="hlt">Lagrangian</span> analysis based on nonlinear dynamical system theory. Two-dimensional free surface <span class="hlt">Eulerian</span> experimental velocity fields of a uniform flow in a compound channel form the basis for the identification of the so-called <span class="hlt">Lagrangian</span> Coherent Structures. <span class="hlt">Lagrangian</span> structures are recognized as the key features that govern particle trajectories. We seek for two particular class of <span class="hlt">Lagrangian</span> structures: Shear and shearless structures. The former are generated whenever the shear dominates the flow whereas the latter behave as jet-cores. These two type of structures are detected as ridges and trenches of the <span class="hlt">Finite</span>-Time Lyapunov Exponents fields, respectively. Besides, shearlines computed applying the geodesic theory of transport barriers mark Shear <span class="hlt">Lagrangian</span> Coherent Structures. So far, the detection of these structures in real experimental flows has not been deeply investigated. Indeed, the present results obtained in a wide range of the controlling parameters clearly show a different behaviour depending on the shallowness of the flow. Shear and Shearless <span class="hlt">Lagrangian</span> Structures detected from laboratory experiments clearly appear as the flow develops in shallow conditions. The presence of these <span class="hlt">Lagrangian</span> Structures tends to fade in deep flow conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EGUGA..15.9576D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EGUGA..15.9576D"><span>Deformation of two-phase aggregates using standard numerical methods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.</p> <p>2013-04-01</p> <p>Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the <span class="hlt">finite</span> difference and <span class="hlt">finite</span> <span class="hlt">element</span> methods for solving viscous flow problems. On one hand, we implemented <span class="hlt">finite</span> difference method coupled with a <span class="hlt">Lagrangian</span> marker-in-cell technique to represent the deforming fluid. Thanks to it <span class="hlt">Eulerian</span> nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the <span class="hlt">finite</span> difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> results which are considered as reference solution. The comparison is then used to establish up to which strain can <span class="hlt">finite</span> difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the <span class="hlt">Eulerian</span> mesh.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1996dmu..conf..543B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1996dmu..conf..543B"><span><span class="hlt">Lagrangian</span> Perturbation Approach to the Formation of Large-scale Structure</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Buchert, Thomas</p> <p></p> <p>The present lecture notes address three columns on which the <span class="hlt">Lagrangian</span> perturbation approach to cosmological dynamics is based: 1. the formulation of a <span class="hlt">Lagrangian</span> theory of self-gravitating flows in which the dynamics is described in terms of a single field variable; 2. the procedure, how to obtain the dynamics of <span class="hlt">Eulerian</span> fields from the <span class="hlt">Lagrangian</span> picture, and 3. a precise definition of a Newtonian cosmology framework in which <span class="hlt">Lagrangian</span> perturbation solutions can be studied. While the first is a discussion of the basic equations obtained by transforming the <span class="hlt">Eulerian</span> evolution and field equations to the <span class="hlt">Lagrangian</span> picture, the second exemplifies how the <span class="hlt">Lagrangian</span> theory determines the evolution of <span class="hlt">Eulerian</span> fields including kinematical variables like expansion, vorticity, as well as the shear and tidal tensors. The third column is based on a specification of initial and boundary conditions, and in particular on the identification of the average flow of an inhomogeneous cosmology with a `Hubble-flow'. Here, we also look at the limits of the <span class="hlt">Lagrangian</span> perturbation approach as inferred from comparisons with N-body simulations and illustrate some striking properties of the solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMNG23A..04D"><span>Bayesian <span class="hlt">Lagrangian</span> Data Assimilation and Drifter Deployment Strategies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dutt, A.; Lermusiaux, P. F. J.</p> <p>2017-12-01</p> <p>Ocean currents transport a variety of natural (e.g. water masses, phytoplankton, zooplankton, sediments, etc.) and man-made materials and other objects (e.g. pollutants, floating debris, search and rescue, etc.). <span class="hlt">Lagrangian</span> Coherent Structures (LCSs) or the most influential/persistent material lines in a flow, provide a robust approach to characterize such <span class="hlt">Lagrangian</span> transports and organize classic trajectories. Using the flow-map stochastic advection and a dynamically-orthogonal decomposition, we develop uncertainty prediction schemes for both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> variables. We then extend our Bayesian Gaussian Mixture Model (GMM)-DO filter to a joint <span class="hlt">Eulerian-Lagrangian</span> Bayesian data assimilation scheme. The resulting nonlinear filter allows the simultaneous non-Gaussian estimation of <span class="hlt">Eulerian</span> variables (e.g. velocity, temperature, salinity, etc.) and <span class="hlt">Lagrangian</span> variables (e.g. drifter/float positions, trajectories, LCSs, etc.). Its results are showcased using a double-gyre flow with a random frequency, a stochastic flow past a cylinder, and realistic ocean examples. We further show how our Bayesian mutual information and adaptive sampling equations provide a rigorous efficient methodology to plan optimal drifter deployment strategies and predict the optimal times, locations, and types of measurements to be collected.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017BoLMe.165..251D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017BoLMe.165..251D"><span>Water-Channel Estimation of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> Time Scales of the Turbulence in Idealized Two-Dimensional Urban Canopies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Di Bernardino, Annalisa; Monti, Paolo; Leuzzi, Giovanni; Querzoli, Giorgio</p> <p>2017-11-01</p> <p><span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> statistics are obtained from a water-channel experiment of an idealized two-dimensional urban canopy flow in neutral conditions. The objective is to quantify the <span class="hlt">Eulerian</span> (TE) and <span class="hlt">Lagrangian</span> (TL) time scales of the turbulence above the canopy layer as well as to investigate their dependence on the aspect ratio of the canopy, AR, as the latter is the ratio of the width ( W) to the height ( H) of the canyon. Experiments are also conducted for the case of flat terrain, which can be thought of as equivalent to a classical one-directional shear flow. The values found for the <span class="hlt">Eulerian</span> time scales on flat terrain are in agreement with previous numerical results found in the literature. It is found that both the streamwise and vertical components of the <span class="hlt">Lagrangian</span> time scale, T_u^L and T_w^L , follow Raupach's linear law within the constant-flux layer. The same holds true for T_w^L in both the canopies analyzed (AR= 1 and AR= 2) and also for T_u^L when AR = 1. In contrast, for AR = 2, T_u^L follows Raupach's law only above z=2H. Below that level, T_u^L is nearly constant with height, showing at z=H a value approximately one order of magnitude greater than that found for AR = 1. It is shown that the assumption usually adopted for flat terrain, that β =TL/TE is proportional to the inverse of the turbulence intensity, also holds true even for the canopy flow in the constant-flux layer. In particular, γ /i_u fits well β _u =T_u^L /T_u^E in both the configurations by choosing γ to be 0.35 (here, i_u =σ _u / \\bar{u} , where \\bar{u} and σ _u are the mean and the root-mean-square of the streamwise velocity component, respectively). On the other hand, β _w =T_w^L /T_w^E follows approximately γ /i_w =0.65/( {σ _w /\\bar{u} } ) for z > 2H, irrespective of the AR value. The second main objective is to estimate other parameters of interest in dispersion studies, such as the eddy diffusivity of momentum (KT) and the Kolmogorov constant (C_0). It is</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19760014504','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19760014504"><span>Three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> analysis for high velocity impact. [of projectiles from space debris</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chan, S. T. K.; Lee, C. H.; Brashears, M. R.</p> <p>1975-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the <span class="hlt">Eulerian</span> hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent <span class="hlt">finite</span> <span class="hlt">element</span> analysis utilizing three-dimensional isoparametric <span class="hlt">elements</span>, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014JCoPh.268..154K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014JCoPh.268..154K"><span>Compatible, total energy conserving and symmetry preserving arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in 2D rz - Cylindrical coordinates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kenamond, Mack; Bement, Matthew; Shashkov, Mikhail</p> <p>2014-07-01</p> <p>We present a new discretization for 2D arbitrary <span class="hlt">Lagrangian-Eulerian</span> hydrodynamics in rz geometry (cylindrical coordinates) that is compatible, total energy conserving and symmetry preserving. In the first part of the paper, we describe the discretization of the basic <span class="hlt">Lagrangian</span> hydrodynamics equations in axisymmetric 2D rz geometry on general polygonal meshes. It exactly preserves planar, cylindrical and spherical symmetry of the flow on meshes aligned with the flow. In particular, spherical symmetry is preserved on polar equiangular meshes. The discretization conserves total energy exactly up to machine round-off on any mesh. It has a consistent definition of kinetic energy in the zone that is exact for a velocity field with constant magnitude. The method for discretization of the <span class="hlt">Lagrangian</span> equations is based on ideas presented in [2,3,7], where the authors use a special procedure to distribute zonal mass to corners of the zone (subzonal masses). The momentum equation is discretized in its “Cartesian” form with a special definition of “planar” masses (area-weighted). The principal contributions of this part of the paper are as follows: a definition of “planar” subzonal mass for nodes on the z axis (r=0) that does not require a special procedure for movement of these nodes; proof of conservation of the total energy; formulated for general polygonal meshes. We present numerical examples that demonstrate the robustness of the new method for <span class="hlt">Lagrangian</span> equations on a variety of grids and test problems including polygonal meshes. In particular, we demonstrate the importance of conservation of total energy for correctly modeling shock waves. In the second part of the paper we describe the remapping stage of the arbitrary <span class="hlt">Lagrangian-Eulerian</span> algorithm. The general idea is based on the following papers [25-28], where it was described for Cartesian coordinates. We describe a distribution-based algorithm for the definition of remapped subzonal densities and a</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.1476M"><span>An <span class="hlt">Eulerian-Lagrangian</span> description for fluvial coarse sediment transport: theory and verification with low-cost inertial sensors.</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Maniatis, Georgios</p> <p>2017-04-01</p> <p>Fluvial sediment transport is controlled by hydraulics, sediment properties and arrangement, and flow history across a range of time scales. One reference frame descriptions (<span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span>) yield useful results but restrict the theoretical understanding of the process as differences between the two phases (liquid and solid) are not explicitly accounted. Recently, affordable Inertial Measurement Units (IMUs) that can be embedded in coarse (100 mm diameter scale) natural or artificial particles became available. These sensors are subjected to technical limitations when deployed for natural sediment transport. However, they give us the ability to measure for the first time the inertial dynamics (acceleration and angular velocity) of moving sediment grains under fluvial transport. Theoretically, the assumption of an ideal (IMU), rigidly attached at the centre of the mass of a sediment particle can simplify greatly the derivation of a general <span class="hlt">Eulerian-Lagrangian</span> (E-L) model. This approach accounts for inertial characteristics of particles in a <span class="hlt">Lagrangian</span> (particle fixed) frame, and for the hydrodynamics in an independent <span class="hlt">Eulerian</span> frame. Simplified versions of the E-L model have been evaluated in laboratory experiments using real-IMUs [Maniatis et. al 2015]. Here, experimental results are presented relevant to the evaluation of the complete E-L model. Artificial particles were deployed in a series of laboratory and field experiments. The particles are equipped with an IMU capable of recording acceleration at ± 400 g and angular velocities at ± 1200 rads/sec ranges. The sampling frequency ranges from 50 to 200 Hz for the total IMU measurement. Two sets of laboratory experiments were conducted in a 0.9m wide laboratory flume. The first is a set of entrainment threshold experiments using two artificial particles: a spherical of D=90mm (A) and an ellipsoid with axes of 100, 70 and 30 mm (B). For the second set of experiments, a spherical artificial enclosure of D</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.350...84S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.350...84S"><span>Parallel implementation of a <span class="hlt">Lagrangian</span>-based model on an adaptive mesh in C++: Application to sea-ice</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Samaké, Abdoulaye; Rampal, Pierre; Bouillon, Sylvain; Ólason, Einar</p> <p>2017-12-01</p> <p>We present a parallel implementation framework for a new dynamic/thermodynamic sea-ice model, called neXtSIM, based on the Elasto-Brittle rheology and using an adaptive mesh. The spatial discretisation of the model is done using the <span class="hlt">finite-element</span> method. The temporal discretisation is semi-implicit and the advection is achieved using either a pure <span class="hlt">Lagrangian</span> scheme or an Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> scheme (ALE). The parallel implementation presented here focuses on the distributed-memory approach using the message-passing library MPI. The efficiency and the scalability of the parallel algorithms are illustrated by the numerical experiments performed using up to 500 processor cores of a cluster computing system. The performance obtained by the proposed parallel implementation of the neXtSIM code is shown being sufficient to perform simulations for state-of-the-art sea ice forecasting and geophysical process studies over geographical domain of several millions squared kilometers like the Arctic region.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26578642','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26578642"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p> <p>2016-11-01</p> <p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a <span class="hlt">finite-element</span> analysis-based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. © The Author(s) 2015.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4868801"><span>Segmental Analysis of Cardiac Short-Axis Views Using <span class="hlt">Lagrangian</span> Radial and Circumferential Strain</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Ma, Chi; Wang, Xiao; Varghese, Tomy</p> <p>2016-01-01</p> <p>Accurate description of myocardial deformation in the left ventricle is a three-dimensional problem, requiring three normal strain components along its natural axis, that is, longitudinal, radial, and circumferential strains. Although longitudinal strains are best estimated from long-axis views, radial and circumferential strains are best depicted in short-axis views. An algorithm that utilizes a polar grid for short-axis views previously developed in our laboratory for a <span class="hlt">Lagrangian</span> description of tissue deformation is utilized for radial and circumferential displacement and strain estimation. Deformation of the myocardial wall, utilizing numerical simulations with ANSYS, and a <span class="hlt">finite-element</span> analysis–based canine heart model were adapted as the input to a frequency-domain ultrasound simulation program to generate radiofrequency echo signals. Clinical in vivo data were also acquired from a healthy volunteer. Local displacements estimated along and perpendicular to the ultrasound beam propagation direction are then transformed into radial and circumferential displacements and strains using the polar grid based on a pre-determined centroid location. <span class="hlt">Lagrangian</span> strain variations demonstrate good agreement with the ideal strain when compared with <span class="hlt">Eulerian</span> results. <span class="hlt">Lagrangian</span> radial and circumferential strain estimation results are also demonstrated for experimental data on a healthy volunteer. <span class="hlt">Lagrangian</span> radial and circumferential strain tracking provide accurate results with the assistance of the polar grid, as demonstrated using both numerical simulations and in vivo study. PMID:26578642</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JCoPh.237..251S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JCoPh.237..251S"><span>A cell-centered <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> volume approach for computing elasto-plastic response of solids in cylindrical axisymmetric geometries</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sambasivan, Shiv Kumar; Shashkov, Mikhail J.; Burton, Donald E.</p> <p>2013-03-01</p> <p>A <span class="hlt">finite</span> volume cell-centered <span class="hlt">Lagrangian</span> formulation is presented for solving large deformation problems in cylindrical axisymmetric geometries. Since solid materials can sustain significant shear deformation, evolution equations for stress and strain fields are solved in addition to mass, momentum and energy conservation laws. The total strain-rate realized in the material is split into an elastic and plastic response. The elastic and plastic components in turn are modeled using hypo-elastic theory. In accordance with the hypo-elastic model, a predictor-corrector algorithm is employed for evolving the deviatoric component of the stress tensor. A trial elastic deviatoric stress state is obtained by integrating a rate equation, cast in the form of an objective (Jaumann) derivative, based on Hooke's law. The dilatational response of the material is modeled using an equation of state of the Mie-Grüneisen form. The plastic deformation is accounted for via an iterative radial return algorithm constructed from the J2 von Mises yield condition. Several benchmark example problems with non-linear strain hardening and thermal softening yield models are presented. Extensive comparisons with representative <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> hydrocodes in addition to analytical and experimental results are made to validate the current approach.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......102P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......102P"><span>Implementing a Loosely Coupled Fluid Structure Interaction <span class="hlt">Finite</span> <span class="hlt">Element</span> Model in PHASTA</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pope, David</p> <p></p> <p>Fluid Structure Interaction problems are an important multi-physics phenomenon in the design of aerospace vehicles and other engineering applications. A variety of computational fluid dynamics solvers capable of resolving the fluid dynamics exist. PHASTA is one such computational fluid dynamics solver. Enhancing the capability of PHASTA to resolve Fluid-Structure Interaction first requires implementing a structural dynamics solver. The implementation also requires a correction of the mesh used to solve the fluid equations to account for the deformation of the structure. This results in mesh motion and causes the need for an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification to the fluid dynamics equations currently implemented in PHASTA. With the implementation of both structural dynamics physics, mesh correction, and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> modification of the fluid dynamics equations, PHASTA is made capable of solving Fluid-Structure Interaction problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009EGUGA..11.5268B"><span><span class="hlt">Eulerian</span> velocity reconstruction in ideal atmospheric dynamics using potential vorticity and potential temperature</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Blender, R.</p> <p>2009-04-01</p> <p>An approach for the reconstruction of atmospheric flow is presented which uses space- and time-dependent fields of density ?, potential vorticity Q and potential temperature Î& cedil;[J. Phys. A, 38, 6419 (2005)]. The method is based on the fundamental equations without approximation. The basic idea is to consider the time-dependent continuity equation as a condition for zero divergence of momentum in four dimensions (time and space, with unit velocity in time). This continuity equation is solved by an ansatz for the four-dimensional momentum using three conserved stream functions, the potential vorticity, potential temperature and a third field, denoted as ?-potential. In zonal flows, the ?-potential identifies the initial longitude of particles, whereas potential vorticity and potential temperature identify mainly meridional and vertical positions. Since the <span class="hlt">Lagrangian</span> tracers Q, Î&,cedil; and ? determine the <span class="hlt">Eulerian</span> velocity field, the reconstruction combines the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> view of hydrodynamics. In stationary flows, the ?-potential is related to the Bernoulli function. The approach requires that the gradients of the potential vorticity and potential temperature do not vanish when the velocity remains <span class="hlt">finite</span>. This behavior indicates a possible interrelation with stability conditions. Examples with analytical solutions are presented for a Rossby wave and zonal and rotational shear flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22482465-lagrangian-flows-within-reflecting-internal-waves-horizontal-free-slip-surface"><span><span class="hlt">Lagrangian</span> flows within reflecting internal waves at a horizontal free-slip surface</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Zhou, Qi, E-mail: q.zhou@damtp.cam.ac.uk; Diamessis, Peter J.</p> <p></p> <p>In this paper sequel to Zhou and Diamessis [“Reflection of an internal gravity wave beam off a horizontal free-slip surface,” Phys. Fluids 25, 036601 (2013)], we consider <span class="hlt">Lagrangian</span> flows within nonlinear internal waves (IWs) reflecting off a horizontal free-slip rigid lid, the latter being a model of the ocean surface. The problem is approached both analytically using small-amplitude approximations and numerically by tracking <span class="hlt">Lagrangian</span> fluid particles in direct numerical simulation (DNS) datasets of the <span class="hlt">Eulerian</span> flow. Inviscid small-amplitude analyses for both plane IWs and IW beams (IWBs) show that <span class="hlt">Eulerian</span> mean flow due to wave-wave interaction and wave-induced Stokes driftmore » cancels each other out completely at the second order in wave steepness A, i.e., O(A{sup 2}), implying zero <span class="hlt">Lagrangian</span> mean flow up to that order. However, high-accuracy particle tracking in <span class="hlt">finite</span>-Reynolds-number fully nonlinear DNS datasets from the work of Zhou and Diamessis suggests that the Euler-Stokes cancelation on O(A{sup 2}) is not complete. This partial cancelation significantly weakens the mean <span class="hlt">Lagrangian</span> flows but does not entirely eliminate them. As a result, reflecting nonlinear IWBs produce mean <span class="hlt">Lagrangian</span> drifts on O(A{sup 2}) and thus particle dispersion on O(A{sup 4}). The above findings can be relevant to predicting IW-driven mass transport in the oceanic surface and subsurface region which bears important observational and environmental implications, under circumstances where the effect of Earth rotation can be ignored.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDG18003H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDG18003H"><span><span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> methods for vortex tracking in 2D and 3D flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Huang, Yangzi; Green, Melissa</p> <p>2014-11-01</p> <p>Coherent structures are a key component of unsteady flows in shear layers. Improvement of experimental techniques has led to larger amounts of data and requires of automated procedures for vortex tracking. Many vortex criteria are <span class="hlt">Eulerian</span>, and identify the structures by an instantaneous local swirling motion in the field, which are indicated by closed or spiral streamlines or pathlines in a reference frame. Alternatively, a <span class="hlt">Lagrangian</span> Coherent Structures (LCS) analysis is a <span class="hlt">Lagrangian</span> method based on the quantities calculated along fluid particle trajectories. In the current work, vortex detection is demonstrated on data from the simulation of two cases: a 2D flow with a flat plate undergoing a 45 ° pitch-up maneuver and a 3D wall-bounded turbulence channel flow. Vortices are visualized and tracked by their centers and boundaries using Γ1, the Q criterion, and LCS saddle points. In the cases of 2D flow, saddle points trace showed a rapid acceleration of the structure which indicates the shedding from the plate. For channel flow, saddle points trace shows that average structure convection speed exhibits a similar trend as a function of wall-normal distance as the mean velocity profile, and leads to statistical quantities of vortex dynamics. Dr. Jeff Eldredge and his research group at UCLA are gratefully acknowledged for sharing the database of simulation for the current research. This work was supported by the Air Force Office of Scientific Research under AFOSR Award No. FA9550-14-1-0210.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDKP1092C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDKP1092C"><span>Unstructured <span class="hlt">Finite</span> <span class="hlt">Elements</span> and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark</p> <p>2017-11-01</p> <p>Multi-phase processes involving phase change at interfaces, such as evaporation of a liquid or combustion of a solid, represent an interesting class of problems with varied applications. Large density ratio across phases, discontinuous fields at the interface and rapidly evolving geometries are some of the inherent challenges which influence the numerical modeling of multi-phase phase change problems. In this work, a mathematically consistent and robust computational approach to address these issues is presented. We use stabilized <span class="hlt">finite</span> <span class="hlt">element</span> methods on mixed topology unstructured grids for solving the compressible Navier-Stokes equations. Appropriate jump conditions derived from conservations laws across the interface are handled by using discontinuous interpolations, while the continuity of temperature and tangential velocity is enforced using a penalty parameter. The arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) technique is utilized to explicitly track the interface motion. Mesh at the interface is constrained to move with the interface while elsewhere it is moved using the linear elasticity analogy. Repositioning is applied to the layered mesh that maintains its structure and normal resolution. In addition, mesh modification is used to preserve the quality of the volumetric mesh. This work is supported by the U.S. Army Grants W911NF1410301 and W911NF16C0117.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDM31008C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDM31008C"><span>Evaluation of particle-based flow characteristics using novel <span class="hlt">Eulerian</span> indices</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cho, Youngmoon; Kang, Seongwon</p> <p>2017-11-01</p> <p>The main objective of this study is to evaluate flow characteristics in complex particle-laden flows efficiently using novel <span class="hlt">Eulerian</span> indices. For flows with a large number of particles, a <span class="hlt">Lagrangian</span> approach leads to accurate yet inefficient prediction in many engineering problems. We propose a technique based on <span class="hlt">Eulerian</span> transport equation and ensemble-averaged particle properties, which enables efficient evaluation of various particle-based flow characteristics such as the residence time, accumulated travel distance, mean radial force, etc. As a verification study, we compare the developed <span class="hlt">Eulerian</span> indices with those using <span class="hlt">Lagrangian</span> approaches for laminar flows with and without a swirling motion and density ratio. The results show satisfactory agreement between two approaches. The accumulated travel distance is modified to analyze flow motions inside IC engines and, when applied to flow bench cases, it can predict swirling and tumbling motions successfully. For flows inside a cyclone separator, the mean radial force is applied to predict the separation of particles and is shown to have a high correlation to the separation efficiency for various working conditions. In conclusion, the proposed <span class="hlt">Eulerian</span> indices are shown to be useful tools to analyze complex particle-based flow characteristics. Corresponding author.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AGUOSEC14C1023C"><span>On modeling heterogeneous coastal sediment transport - A numerical study using multiphase <span class="hlt">Eulerian</span> and Euler-<span class="hlt">Lagrangian</span> approaches</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cheng, Z.; Yu, X.; Hsu, T. J.; Calantoni, J.; Chauchat, J.</p> <p>2016-02-01</p> <p>Regional scale coastal evolution models do not explicitly resolve wave-driven sediment transport and must rely on bedload/suspended modules that utilize empirical assumptions. Under extreme wave events or in regions of high sediment heterogeneity, these empirical bedload/suspended load modules may need to be reevaluated with detailed observation and more sophisticated small-scale models. In the past decade, significant research efforts have been devoted to modeling sediment transport using multiphase <span class="hlt">Eulerian</span> or Euler-<span class="hlt">Lagrangian</span> approaches. Recently, an open-source multi-dimensional Reynolds-averaged two-phase sediment transport model, SedFOAM is developed by the authors and it has been adopted by many researchers to study momentary bed failure, granular rheology in sheet flow and scour around structures. In this abstract, we further report our recent progress made in extending the model with 3D turbulence-resolving capability and to model the sediment phase with the Discrete <span class="hlt">Element</span> method (DEM). Adopting the large-eddy simulation methodology, we validate the 3D model with measured fine sediment transport is oscillatory sheet flow and demonstrate that the model is able to resolve sediment burst events during flow reversals. To better resolve the intergranular interactions and to model heterogeneous properties of sediment (e.g., mixed grain sizes and grain shape), we use an Euler-<span class="hlt">Lagrangian</span> solver called CFDEM, which couples OpenFOAM for the fluid phase and LIGGGHTS for the particle phase. We improve the model by better enforcing conservation of mass in the pressure solver. The modified CFDEM solver is validated with measured oscillatory sheet flow data for coarse sand and we demonstrated that the model can reproduce the well-known armoring effects. We show that under Stokes second-order wave forcing, the armoring effect is more significant during the energetic positive peak, and hence the net onshore transport is reduced. Preliminary results modeling the shape</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_5");'>5</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li class="active"><span>7</span></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_7 --> <div id="page_8" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="141"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CompM.tmp..267R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CompM.tmp..267R"><span>Heat transfer model and <span class="hlt">finite</span> <span class="hlt">element</span> formulation for simulation of selective laser melting</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.</p> <p>2017-10-01</p> <p>A novel approach and <span class="hlt">finite</span> <span class="hlt">element</span> formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The <span class="hlt">finite</span> <span class="hlt">element</span> model is implemented into a general-purpose parallel <span class="hlt">finite</span> <span class="hlt">element</span> solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018CompM.tmp..250R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018CompM.tmp..250R"><span>Rigid body formulation in a <span class="hlt">finite</span> <span class="hlt">element</span> context with contact interaction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Refachinho de Campos, Paulo R.; Gay Neto, Alfredo</p> <p>2018-03-01</p> <p>The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body <span class="hlt">element</span>. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a <span class="hlt">finite</span> <span class="hlt">element</span> environment. Rodrigues rotation parameters are used to describe <span class="hlt">finite</span> rotations, by an updated <span class="hlt">Lagrangian</span> description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body <span class="hlt">element</span> and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/10145858-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Crowley, W.P.</p> <p>1992-06-17</p> <p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode`s and pde`s. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh <span class="hlt">elements</span>. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/6551547-quality-factors-local-adaption-applications-eulerian-hydrodynamics"><span>Quality factors and local adaption (with applications in <span class="hlt">Eulerian</span> hydrodynamics)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Crowley, W.P.</p> <p>1992-06-17</p> <p>Adapting the mesh to suit the solution is a technique commonly used for solving both ode's and pde's. For <span class="hlt">Lagrangian</span> hydrodynamics, ALE and Free-Lagrange are examples of structured and unstructured adaptive methods. For <span class="hlt">Eulerian</span> hydrodynamics the two basic approaches are the macro-unstructuring technique pioneered by Oliger and Berger and the micro-structuring technique due to Lohner and others. Here we will describe a new micro-unstructuring technique, LAM, (for Local Adaptive Mesh) as applied to <span class="hlt">Eulerian</span> hydrodynamics. The LAM technique consists of two independent parts: (1) the time advance scheme is a variation on the artificial viscosity method; (2) the adaption schememore » uses a micro-unstructured mesh with quadrilateral mesh <span class="hlt">elements</span>. The adaption scheme makes use of quality factors and the relation between these and truncation errors is discussed. The time advance scheme; the adaption strategy; and the effect of different adaption parameters on numerical solutions are described.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900013699','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900013699"><span>Nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> formulation for the large displacement analysis in multibody system dynamics</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Rismantab-Sany, J.; Chang, B.; Shabana, A. A.</p> <p>1989-01-01</p> <p>A total <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation for the deformable bodies in multibody mechanical systems that undergo <span class="hlt">finite</span> relative rotations is developed. The deformable bodies are discretized using <span class="hlt">finite</span> <span class="hlt">element</span> methods. The shape functions that are used to describe the displacement field are required to include the rigid body modes that describe only large translational displacements. This does not impose any limitations on the technique because most commonly used shape functions satisfy this requirement. The configuration of an <span class="hlt">element</span> is defined using four sets of coordinate systems: Body, <span class="hlt">Element</span>, Intermediate <span class="hlt">element</span>, Global. The body coordinate system serves as a unique standard for the assembly of the <span class="hlt">elements</span> forming the deformable body. The <span class="hlt">element</span> coordinate system is rigidly attached to the <span class="hlt">element</span> and therefore it translates and rotates with the <span class="hlt">element</span>. The intermediate <span class="hlt">element</span> coordinate system, whose axes are initially parallel to the <span class="hlt">element</span> axes, has an origin which is rigidly attached to the origin of the body coordinate system and is used to conveniently describe the configuration of the <span class="hlt">element</span> in undeformed state with respect to the body coordinate system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2003PhRvA..67a6101L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2003PhRvA..67a6101L"><span>Comment on ``Canonical formalism for <span class="hlt">Lagrangians</span> with nonlocality of <span class="hlt">finite</span> extent''</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Llosa, Josep</p> <p>2003-01-01</p> <p>The paper by Woodward [Phys. Rev. A 62, 052105 (2000)] claimed to have proved that <span class="hlt">Lagrangian</span> theories with a nonlocality of <span class="hlt">finite</span> extent are necessarily unstable. In this Comment we propose that this conclusion is false.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JCoPh.351..422P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JCoPh.351..422P"><span>An adaptive reconstruction for <span class="hlt">Lagrangian</span>, direct-forcing, immersed-boundary methods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Posa, Antonio; Vanella, Marcos; Balaras, Elias</p> <p>2017-12-01</p> <p><span class="hlt">Lagrangian</span>, direct-forcing, immersed boundary (IB) methods have been receiving increased attention due to their robustness in complex fluid-structure interaction problems. They are very sensitive, however, on the selection of the <span class="hlt">Lagrangian</span> grid, which is typically used to define a solid or flexible body immersed in a fluid flow. In the present work we propose a cost-efficient solution to this problem without compromising accuracy. Central to our approach is the use of isoparametric mapping to bridge the relative resolution requirements of <span class="hlt">Lagrangian</span> IB, and <span class="hlt">Eulerian</span> grids. With this approach, the density of surface <span class="hlt">Lagrangian</span> markers, which is essential to properly enforce boundary conditions, is adapted dynamically based on the characteristics of the underlying <span class="hlt">Eulerian</span> grid. The markers are not stored and the <span class="hlt">Lagrangian</span> data-structure is not modified. The proposed scheme is implemented in the framework of a moving least squares reconstruction formulation, but it can be adapted to any <span class="hlt">Lagrangian</span>, direct-forcing formulation. The accuracy and robustness of the approach is demonstrated in a variety of test cases of increasing complexity.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013MS%26E...52a2003M"><span>A cavitation model based on <span class="hlt">Eulerian</span> stochastic fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Magagnato, F.; Dumond, J.</p> <p>2013-12-01</p> <p>Non-linear phenomena can often be described using probability density functions (pdf) and pdf transport models. Traditionally the simulation of pdf transport requires Monte-Carlo codes based on <span class="hlt">Lagrangian</span> "particles" or prescribed pdf assumptions including binning techniques. Recently, in the field of combustion, a novel formulation called the stochastic-field method solving pdf transport based on <span class="hlt">Eulerian</span> fields has been proposed which eliminates the necessity to mix <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> techniques or prescribed pdf assumptions. In the present work, for the first time the stochastic-field method is applied to multi-phase flow and in particular to cavitating flow. To validate the proposed stochastic-field cavitation model, two applications are considered. Firstly, sheet cavitation is simulated in a Venturi-type nozzle. The second application is an innovative fluidic diode which exhibits coolant flashing. Agreement with experimental results is obtained for both applications with a fixed set of model constants. The stochastic-field cavitation model captures the wide range of pdf shapes present at different locations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1423820-evaluation-eulerian-multi-material-mixture-formulation-based-single-inverse-deformation-gradient-tensor-field"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture formulation based on a single inverse deformation gradient tensor field</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.; ...</p> <p>2017-12-31</p> <p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1423820','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1423820"><span>Evaluation of an <span class="hlt">Eulerian</span> multi-material mixture formulation based on a single inverse deformation gradient tensor field</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ghaisas, N. S.; Subramaniam, A.; Lele, S. K.</p> <p></p> <p>We report high energy-density solids undergoing elastic-plastic deformations coupled to compressible fluids are a common occurrence in engineering applications. Examples include problems involving high-velocity impact and penetration, cavitation, and several manufacturing processes, such as cold forming. Numerical simulations of such phenomena require the ability to handle the interaction of shock waves with multi-material interfaces that can undergo large deformations and severe distortions. As opposed to <span class="hlt">Lagrangian</span> (Benson 1992) and arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) methods (Donea et al. 2004), fully <span class="hlt">Eulerian</span> methods use grids that do not change in time. Consequently, <span class="hlt">Eulerian</span> methods do not suffer from difficulties on account of meshmore » entanglement, and do not require periodic, expensive, remap operations.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930011730','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930011730"><span>Nonlinear probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> models of laminated composite shells</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Engelstad, S. P.; Reddy, J. N.</p> <p>1993-01-01</p> <p>A probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> analysis procedure for laminated composite shells has been developed. A total <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4851392"><span>Fluid-Structure Interaction Simulation of Prosthetic Aortic Valves: Comparison between Immersed Boundary and Arbitrary <span class="hlt">Lagrangian-Eulerian</span> Techniques for the Mesh Representation</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Iannaccone, Francesco; Degroote, Joris; Vierendeels, Jan; Segers, Patrick</p> <p>2016-01-01</p> <p>In recent years the role of FSI (fluid-structure interaction) simulations in the analysis of the fluid-mechanics of heart valves is becoming more and more important, being able to capture the interaction between the blood and both the surrounding biological tissues and the valve itself. When setting up an FSI simulation, several choices have to be made to select the most suitable approach for the case of interest: in particular, to simulate flexible leaflet cardiac valves, the type of discretization of the fluid domain is crucial, which can be described with an ALE (Arbitrary <span class="hlt">Lagrangian-Eulerian</span>) or an <span class="hlt">Eulerian</span> formulation. The majority of the reported 3D heart valve FSI simulations are performed with the <span class="hlt">Eulerian</span> formulation, allowing for large deformations of the domains without compromising the quality of the fluid grid. Nevertheless, it is known that the ALE-FSI approach guarantees more accurate results at the interface between the solid and the fluid. The goal of this paper is to describe the same aortic valve model in the two cases, comparing the performances of an ALE-based FSI solution and an <span class="hlt">Eulerian</span>-based FSI approach. After a first simplified 2D case, the aortic geometry was considered in a full 3D set-up. The model was kept as similar as possible in the two settings, to better compare the simulations’ outcomes. Although for the 2D case the differences were unsubstantial, in our experience the performance of a full 3D ALE-FSI simulation was significantly limited by the technical problems and requirements inherent to the ALE formulation, mainly related to the mesh motion and deformation of the fluid domain. As a secondary outcome of this work, it is important to point out that the choice of the solver also influenced the reliability of the final results. PMID:27128798</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26317686','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26317686"><span>Particle transport in the human respiratory tract: formulation of a nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> transport and implementation of the Wind-Kessel algorithm for an oral delivery.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kannan, Ravishekar; Guo, Peng; Przekwas, Andrzej</p> <p>2016-06-01</p> <p>This paper is the first in a series wherein efficient computational methods are developed and implemented to accurately quantify the transport, deposition, and clearance of the microsized particles (range of interest: 2 to 10 µm) in the human respiratory tract. In particular, this paper (part I) deals with (i) development of a detailed 3D computational <span class="hlt">finite</span> volume mesh comprising of the NOPL (nasal, oral, pharyngeal and larynx), trachea and several airway generations; (ii) use of CFD Research Corporation's <span class="hlt">finite</span> volume Computational Biology (CoBi) flow solver to obtain the flow physics for an oral inhalation simulation; (iii) implement a novel and accurate nodal inverse distance weighted <span class="hlt">Eulerian-Lagrangian</span> formulation to accurately obtain the deposition, and (iv) development of Wind-Kessel boundary condition algorithm. This new Wind-Kessel boundary condition algorithm allows the 'escaped' particles to reenter the airway through the outlets, thereby to an extent accounting for the drawbacks of having a <span class="hlt">finite</span> number of lung generations in the computational mesh. The deposition rates in the NOPL, trachea, the first and second bifurcation were computed, and they were in reasonable accord with the Typical Path Length model. The quantitatively validated results indicate that these developments will be useful for (i) obtaining depositions in diseased lungs (because of asthma and COPD), for which there are no empirical models, and (ii) obtaining the secondary clearance (mucociliary clearance) of the deposited particles. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo; ...</p> <p>2017-09-01</p> <p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1409363-verification-eulerian-eulerian-eulerian-lagrangian-simulations-turbulent-fluid-particle-flows"><span>Verification of <span class="hlt">Eulerian-Eulerian</span> and <span class="hlt">Eulerian-Lagrangian</span> simulations for turbulent fluid-particle flows</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Patel, Ravi G.; Desjardins, Olivier; Kong, Bo</p> <p></p> <p>Here, we present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posingmore » fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent <span class="hlt">Eulerian</span> statistics remains a challenge for all methods.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910001565','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910001565"><span>A combined <span class="hlt">Eulerian-Lagrangian</span> two-phase analysis of the SSME HPOTP nozzle plug trajectories</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Garcia, Robert; Mcconnaughey, P. K.; Dejong, F. J.; Sabnis, J. S.; Pribik, D.</p> <p>1989-01-01</p> <p>As a result of high cycle fatigue, hydrogen embrittlement, and extended engine use, it was observed in testing that the trailing edge on the first stage nozzle plug in the High Pressure Oxygen Turbopump (HPOTP) could detach. The objective was to predict the trajectories followed by particles exiting the turbine. Experiments had shown that the heat exchanger soils, which lie downstream of the turbine, would be ruptured by particles traveling in the order of 360 ft/sec. An axisymmetric solution of the flow was obtained from the work of Lin et. al., who used INS3D to obtain the solution. The particle trajectories were obtained using the method of de Jong et. al., which employs <span class="hlt">Lagrangian</span> tracking of the particle through the <span class="hlt">Eulerian</span> flow field. The collision parameters were obtained from experiments conducted by Rocketdyne using problem specific alloys, speeds, and projectile geometries. A complete 3-D analysis using the most likely collision parameters shows maximum particle velocities of 200 ft/sec. in the heat exchanger region. Subsequent to this analysis, an engine level test was conducted in which seven particles passed through the turbine but no damage was observed on the heat exchanger coils.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1270630','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1270630"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p> <p></p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22525478-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro, E-mail: zvlah@stanford.edu, E-mail: mwhite@berkeley.edu, E-mail: aviles@berkeley.edu</p> <p></p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The 'new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. All the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1270630-lagrangian-effective-field-theory"><span>A <span class="hlt">Lagrangian</span> effective field theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Vlah, Zvonimir; White, Martin; Aviles, Alejandro</p> <p>2015-09-02</p> <p>We have continued the development of <span class="hlt">Lagrangian</span>, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all ofmore » our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the <span class="hlt">Lagrangian</span> model fares as well as EFT in its <span class="hlt">Eulerian</span> formulation, but at higher z the <span class="hlt">Eulerian</span> EFT fits the data to smaller scales than resummed, <span class="hlt">Lagrangian</span> EFT. Furthermore, all the perturbative models fare better than linear theory.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015WRR....51.1916W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015WRR....51.1916W"><span>Variational <span class="hlt">Lagrangian</span> data assimilation in open channel networks</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wu, Qingfang; Tinka, Andrew; Weekly, Kevin; Beard, Jonathan; Bayen, Alexandre M.</p> <p>2015-04-01</p> <p>This article presents a data assimilation method in a tidal system, where data from both <span class="hlt">Lagrangian</span> drifters and <span class="hlt">Eulerian</span> flow sensors were fused to estimate water velocity. The system is modeled by first-order, hyperbolic partial differential equations subject to periodic forcing. The estimation problem can then be formulated as the minimization of the difference between the observed variables and model outputs, and eventually provide the velocity and water stage of the hydrodynamic system. The governing equations are linearized and discretized using an implicit discretization scheme, resulting in linear equality constraints in the optimization program. Thus, the flow estimation can be formed as an optimization problem and efficiently solved. The effectiveness of the proposed method was substantiated by a large-scale field experiment in the Sacramento-San Joaquin River Delta in California. A fleet of 100 sensors developed at the University of California, Berkeley, were deployed in Walnut Grove, CA, to collect a set of <span class="hlt">Lagrangian</span> data, a time series of positions as the sensors moved through the water. Measurements were also taken from <span class="hlt">Eulerian</span> sensors in the region, provided by the United States Geological Survey. It is shown that the proposed method can effectively integrate <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> measurement data, resulting in a suited estimation of the flow variables within the hydraulic system.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_6");'>6</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li class="active"><span>8</span></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_8 --> <div id="page_9" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="161"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790021662','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790021662"><span>CELFE: Coupled <span class="hlt">Eulerian-Lagrangian</span> <span class="hlt">Finite</span> <span class="hlt">Element</span> program for high velocity impact. Part 2: Program user's manual</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lee, C. H.</p> <p>1978-01-01</p> <p>The CELFE computer program and user's manual, together with the execution of the CELFE/NASTRAN system, are described. The execution procedure and the transfer of data between the CELFE and NASTRAN programs are controlled through the use of DATA files in the Univac 1100 system. Five data files are used to control the runstream and data transfer, and three files are used to hold the programs. These files are contained on a single tape. Changes in NASTRAN routines required by the present analysis are also discussed in this report. All the program listings, except the last two files (where the absolute and relocatable <span class="hlt">elements</span> are stored), are included in the appendixes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790007154','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790007154"><span>CELFE/NASTRAN Code for the Analysis of Structures Subjected to High Velocity Impact</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chamis, C. C.</p> <p>1978-01-01</p> <p>CELFE (Coupled <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> <span class="hlt">Finite</span> <span class="hlt">Element</span>)/NASTRAN Code three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> code has the capability for analyzing of structures subjected to high velocity impact. The local response is predicted by CELFE and, for large problems, the far-field impact response is predicted by NASTRAN. The coupling of the CELFE code with NASTRAN (CELFE/NASTRAN code) and the application of the code to selected three-dimensional high velocity impact problems are described.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AGUFMOS42A..05T"><span>Modeling possible spreadings of a buoyant surface plume with <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> approaches at different resolutions using flow syntheses from 1992-2007 - a Gulf of Mexico study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tulloch, R.; Hill, C. N.; Jahn, O.</p> <p>2010-12-01</p> <p>We present results from an ensemble of BP oil spill simulations. The oil spill slick is modeled as a buoyant surface plume that is transported by ocean currents modulated, in some experiments, by surface winds. Ocean currents are taken from ECCO2 project (see http://ecco2.org ) observationally constrained state estimates spanning 1992-2007. In this work we (i) explore the role of increased resolution of ocean eddies, (ii) compare inferences from particle based, <span class="hlt">lagrangian</span>, approaches with <span class="hlt">eulerian</span>, field based, approaches and (ii) examine the impact of differential response of oil particles and water to normal and extreme, hurricane derived, wind stress. We focus on three main questions. Is the simulated response to an oil spill markedly different for different years, depending on ocean circulation and wind forcing? Does the simulated response depend heavily on resolution and are <span class="hlt">lagrangian</span> and <span class="hlt">eulerian</span> estimates comparable? We start from two regional configurations of the MIT General Circulation Model (MITgcm - see http://mitgcm.org ) at 16km and 4km resolutions respectively, both covering the Gulf of Mexico and western North Atlantic regions. The simulations are driven at open boundaries with momentum and hydrographic fields from ECCO2 observationally constrained global circulation estimates. The time dependent surface flow fields from these simulations are used to transport a dye that can optionally decay over time (approximating biological breakdown) and to transport <span class="hlt">lagrangian</span> particles. Using these experiments we examine the robustness of conclusions regarding the fate of a buoyant slick, injected at a single point. In conclusion we discuss how future drilling operations could use similar approaches to better anticipate outcomes of accidents both in this region and elsewhere.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JGRC..123..759C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JGRC..123..759C"><span>Nitrate Sources, Supply, and Phytoplankton Growth in the Great Australian Bight: An <span class="hlt">Eulerian-Lagrangian</span> Modeling Approach</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Cetina-Heredia, Paulina; van Sebille, Erik; Matear, Richard J.; Roughan, Moninya</p> <p>2018-02-01</p> <p>The Great Australian Bight (GAB), a coastal sea bordered by the Pacific, Southern, and Indian Oceans, sustains one of the largest fisheries in Australia but the geographical origin of nutrients that maintain its productivity is not fully known. We use 12 years of modeled data from a coupled hydrodynamic and biogeochemical model and an <span class="hlt">Eulerian-Lagrangian</span> approach to quantify nitrate supply to the GAB and the region between the GAB and the Subantarctic Australian Front (GAB-SAFn), identify phytoplankton growth within the GAB, and ascertain the source of nitrate that fuels it. We find that nitrate concentrations have a decorrelation timescale of ˜60 days; since most of the water from surrounding oceans takes longer than 60 days to reach the GAB, 23% and 75% of nitrate used by phytoplankton to grow are sourced within the GAB and from the GAB-SAFn, respectively. Thus, most of the nitrate is recycled locally. Although nitrate concentrations and fluxes into the GAB are greater below 100 m than above, 79% of the nitrate fueling phytoplankton growth is sourced from above 100 m. Our findings suggest that topographical uplift and stratification erosion are key mechanisms delivering nutrients from below the nutricline into the euphotic zone and triggering large phytoplankton growth. We find annual and semiannual periodicities in phytoplankton growth, peaking in the austral spring and autumn when the mixed layer deepens leading to a subsurface maximum of phytoplankton growth. This study highlights the importance of examining phytoplankton growth at depth and the utility of <span class="hlt">Lagrangian</span> approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AtmEn..45..839O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AtmEn..45..839O"><span>Development and evaluation of GRAL-C dispersion model, a hybrid <span class="hlt">Eulerian-Lagrangian</span> approach capturing NO-NO 2-O 3 chemistry</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Oettl, Dietmar; Uhrner, Ulrich</p> <p>2011-02-01</p> <p>Based on two recent publications using <span class="hlt">Lagrangian</span> dispersion models to simulate NO-NO 2-O 3 chemistry for industrial plumes, a similar modified approach was implemented using GRAL-C ( Graz <span class="hlt">Lagrangian</span> Model with Chemistry) and tested on two urban applications. In the hybrid dispersion model GRAL-C, the transport and turbulent diffusion of primary species such as NO and NO 2 are treated in a <span class="hlt">Lagrangian</span> framework while those of O 3 are treated in an <span class="hlt">Eulerian</span> framework. GRAL-C was employed on a one year street canyon simulation in Berlin and on a four-day simulation during a winter season in Graz, the second biggest city in Austria. In contrast to Middleton D.R., Jones A.R., Redington A.L., Thomson D.J., Sokhi R.S., Luhana L., Fisher B.E.A. (2008. <span class="hlt">Lagrangian</span> modelling of plume chemistry for secondary pollutants in large industrial plumes. Atmospheric Environment 42, 415-427) and Alessandrini S., Ferrero E. (2008. A <span class="hlt">Lagrangian</span> model with chemical reactions: application in real atmosphere. Proceedings of the 12th Int. Conf. on Harmonization within atmospheric dispersion modelling for regulatory purposes. Croatian Meteorological Journal, 43, ISSN: 1330-0083, 235-239) the treatment of ozone was modified in order to facilitate urban scale simulations encompassing dense road networks. For the street canyon application, modelled daily mean NO x/NO 2 concentrations deviated by +0.4%/-15% from observations, while the correlations for NO x and NO 2 were 0.67 and 0.76 respectively. NO 2 concentrations were underestimated in summer, but were captured well for other seasons. In Graz a fair agreement for NO x and NO 2 was obtained between observed and modelled values for NO x and NO 2. Simulated diurnal cycles of NO 2 and O 3 matched observations reasonably well, although O 3 was underestimated during the day. A possible explanation here might lie in the non-consideration of volatile organic compounds (VOCs) chemistry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1214912-modeling-high-speed-friction-stir-spot-welding-using-lagrangian-finite-element-approach','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1214912-modeling-high-speed-friction-stir-spot-welding-using-lagrangian-finite-element-approach"><span>MODELING OF HIGH SPEED FRICTION STIR SPOT WELDING USING A <span class="hlt">LAGRANGIAN</span> <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> APPROACH</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Miles, Michael; Karki, U.; Woodward, C.</p> <p>2013-09-03</p> <p>Friction stir spot welding (FSSW) has been shown to be capable of joining steels of very high strength, while also being very flexible in terms of controlling the heat of welding and the resulting microstructure of the joint. This makes FSSW a potential alternative to resistance spot welding (RSW) if tool life is sufficiently high, and if machine spindle loads are sufficiently low so that the process can be implemented on an industrial robot. Robots for spot welding can typically sustain vertical loads of about 8kN, but FSSW at tool speeds of less than 3000 rpm cause loads that aremore » too high, in the range of 11-14 kN. Therefore, in the current work tool speeds of 3000 rpm and higher were employed, in order to generate heat more quickly and to reduce welding loads to acceptable levels. The FSSW process was modeled using a <span class="hlt">finite</span> <span class="hlt">element</span> approach with the Forge® software package. An updated <span class="hlt">Lagrangian</span> scheme with explicit time integration was employed to model the flow of the sheet material, subjected to boundary conditions of a rotating tool and a fixed backing plate [3]. The modeling approach can be described as two-dimensional, axisymmetric, but with an aspect of three dimensions in terms of thermal boundary conditions. Material flow was calculated from a velocity field which was two dimensional, but heat generated by friction was computed using a virtual rotational velocity component from the tool surface. An isotropic, viscoplastic Norton-Hoff law was used to model the evolution of material flow stress as a function of strain, strain rate, and temperature. The model predicted welding temperatures and the movement of the joint interface with reasonable accuracy for the welding of a dual phase 980 steel.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22373526-lagrangian-eulerian-real-fourier-all-approaches-large-scale-structure-created-equal"><span><span class="hlt">Lagrangian</span> or <span class="hlt">Eulerian</span>; real or Fourier? Not all approaches to large-scale structure are created equal</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Tassev, Svetlin, E-mail: tassev@astro.princeton.edu</p> <p></p> <p>We present a pedagogical systematic investigation of the accuracy of <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theorymore » to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by <span class="hlt">Eulerian</span> Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1911392T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1911392T"><span>Mass and tracer transport within oceanic <span class="hlt">Lagrangian</span> coherent vortices as diagnosed in a global mesoscale eddying climate model</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tarshish, Nathaniel; Abernathey, Ryan; Dufour, Carolina; Frenger, Ivy; Griffies, Stephen</p> <p>2017-04-01</p> <p>Transient ocean mesoscale fluctuations play a central role in the global climate system, transporting climate relevant tracers such as heat and carbon. In satellite observations and numerical simulations, mesoscale vortices feature prominently as collectively rotating regions that remain visibly coherent. Prior studies on transport from ocean vortices typically rely on <span class="hlt">Eulerian</span> identification methods, in which vortices are identified by selecting closed contours of <span class="hlt">Eulerian</span> fields (e.g. sea surface height, or the Okubo-Weiss parameter) that satisfy geometric criteria and anomaly thresholds. In contrast, recent studies employ <span class="hlt">Lagrangian</span> analysis of virtual particle trajectories initialized within the selected <span class="hlt">Eulerian</span> contours, revealing significant discrepancies between the advection of the contour's material interior and the evolution of the <span class="hlt">Eulerian</span> field contour. This work investigates the global mass and tracer transport associated with materially coherent surface ocean vortices. Further, it addresses differences between <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> analyses for the detection of vortices. To do so, we use GFDL's CM2.6 coupled climate model with 5-10km horizontal grid spacing. We identify coherent vortices in CM2.6 by implementing the Rotationally Coherent <span class="hlt">Lagrangian</span> Vortex (RCLV) framework, which recently emerged from dynamical systems theory. This approach involves the numerical advection of millions of <span class="hlt">Lagrangian</span> particles and guarantees material coherence by construction. We compute the statistics, spatial distribution, and lifetimes of coherent vortices in addition to calculating the associated mass and tracer transports. We offer compelling evidence that <span class="hlt">Eulerian</span> vortex methods are poorly suited to answer questions of mass and tracer transport.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70020119','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70020119"><span>A robust, <span class="hlt">finite</span> <span class="hlt">element</span> model for hydrostatic surface water flows</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Walters, R.A.; Casulli, V.</p> <p>1998-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-<span class="hlt">Lagrangian</span> method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A <span class="hlt">finite</span> <span class="hlt">element</span> scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-<span class="hlt">Lagrangian</span> method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1413605S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1413605S"><span>An online-coupled NWP/ACT model with conserved <span class="hlt">Lagrangian</span> levels</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sørensen, B.; Kaas, E.; Lauritzen, P. H.</p> <p>2012-04-01</p> <p>Numerical weather and climate modelling is under constant development. Semi-implicit semi-<span class="hlt">Lagrangian</span> (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-<span class="hlt">Lagrangian</span> schemes with quasi-<span class="hlt">Lagrangian</span> vertical coordinates the <span class="hlt">Lagrangian</span> levels are remapped to <span class="hlt">Eulerian</span> model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-<span class="hlt">Lagrangian</span> advection method is introduced, it combines an inherently mass conserving 2D semi-<span class="hlt">Lagrangian</span> scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully <span class="hlt">Lagrangian</span> vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the <span class="hlt">Lagrangian</span> levels suffer from traditional <span class="hlt">Lagrangian</span> limitations caused by the convergence and divergence of the flow, remappings to the <span class="hlt">Eulerian</span> model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AtmEn.170....1P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AtmEn.170....1P"><span>Improved quantification of CO2 emission at Campi Flegrei by combined <span class="hlt">Lagrangian</span> Stochastic and <span class="hlt">Eulerian</span> dispersion modelling</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pedone, Maria; Granieri, Domenico; Moretti, Roberto; Fedele, Alessandro; Troise, Claudia; Somma, Renato; De Natale, Giuseppe</p> <p>2017-12-01</p> <p>This study investigates fumarolic CO2 emissions at Campi Flegrei (Southern Italy) and their dispersion in the lowest atmospheric boundary layer. We innovatively utilize a <span class="hlt">Lagrangian</span> Stochastic dispersion model (WindTrax) combined with an <span class="hlt">Eulerian</span> model (DISGAS) to diagnose the dispersion of diluted gas plumes over large and complex topographic domains. New measurements of CO2 concentrations acquired in February and October 2014 in the area of Pisciarelli and Solfatara, the two major fumarolic fields of Campi Flegrei caldera, and simultaneous measurements of meteorological parameters are used to: 1) test the ability of WindTrax to calculate the fumarolic CO2 flux from the investigated sources, and 2) perform predictive numerical simulations to resolve the mutual interference between the CO2 emissions of the two adjacent areas. This novel approach allows us to a) better quantify the CO2 emission of the fumarolic source, b) discriminate ;true; CO2 contributions for each source, and c) understand the potential impact of the composite CO2 plume (Pisciarelli ;plus; Solfatara) on the highly populated areas inside the Campi Flegrei caldera.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970001872','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970001872"><span>An Extended <span class="hlt">Lagrangian</span> Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1995-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method,' is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. The present method and the Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) method have a similarity in spirit-eliminating the cross-streamline numerical diffusion. For this purpose, we suggest a simple grid constraint condition and utilize an accurate discretization procedure. This grid constraint is only applied to the transverse cell face parallel to the local stream velocity, and hence our method for the steady state problems naturally reduces to the streamline-curvature method, without explicitly solving the steady stream-coordinate equations formulated a priori. Unlike the <span class="hlt">Lagrangian</span> method proposed by Loh and Hui which is valid only for steady supersonic flows, the present method is general and capable of treating subsonic flows and supersonic flows as well as unsteady flows, simply by invoking in the same code an appropriate grid constraint suggested in this paper. The approach is found to be robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1013698','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1013698"><span>Near-Surface Monsoonal Circulation of the Vietnam East Sea from <span class="hlt">Lagrangian</span> Drifters</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2015-09-30</p> <p>Sea from <span class="hlt">Lagrangian</span> Drifters Luca Centurioni Scripps Institution of Oceanography 9500 Gilman Drive Mail Code 0213 La Jolla, California 92103...Contribute to the study of coastal and open ocean current systems in sparsely sampled regions such us the South China Sea (SCS), using a <span class="hlt">Lagrangian</span> ...We intend to make new <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> observations to measure the seasonal circulation 1) in the coastal waters of Vietnam and 2) in the SCS</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770007853','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770007853"><span>The Relation of <span class="hlt">Finite</span> <span class="hlt">Element</span> and <span class="hlt">Finite</span> Difference Methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vinokur, M.</p> <p>1976-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> and <span class="hlt">finite</span> difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that <span class="hlt">finite</span> difference methods emphasize the discretization of independent variable, while <span class="hlt">finite</span> <span class="hlt">element</span> methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that <span class="hlt">finite</span> <span class="hlt">element</span> methods use global piecewise functional approximations, while <span class="hlt">finite</span> difference methods normally use local functional approximations. A general conclusion is that <span class="hlt">finite</span> <span class="hlt">element</span> methods are best designed to handle complex boundaries, while <span class="hlt">finite</span> difference methods are superior for complex equations. It is also shown that <span class="hlt">finite</span> volume difference methods possess many of the advantages attributed to <span class="hlt">finite</span> <span class="hlt">element</span> methods.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930017014','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930017014"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1992-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. Unlike the <span class="hlt">Lagrangian</span> method previously imposed which is valid only for supersonic flows, the present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multi-dimensional discontinuities with a high level of accuracy, similar to that found in one-dimensional problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CompM..60..905A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CompM..60..905A"><span>Fiber-reinforced materials: <span class="hlt">finite</span> <span class="hlt">elements</span> for the treatment of the inextensibility constraint</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter</p> <p>2017-12-01</p> <p>The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed <span class="hlt">finite</span> <span class="hlt">elements</span> based on the Lagrange multiplier, perturbed <span class="hlt">Lagrangian</span>, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed <span class="hlt">finite</span> <span class="hlt">elements</span> and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980236869','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980236869"><span>The Role of Multiphysics Simulation in Multidisciplinary Analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Rifai, Steven M.; Ferencz, Robert M.; Wang, Wen-Ping; Spyropoulos, Evangelos T.; Lawrence, Charles; Melis, Matthew E.</p> <p>1998-01-01</p> <p>This article describes the applications of the Spectrum(Tm) Solver in Multidisciplinary Analysis (MDA). Spectrum, a multiphysics simulation software based on the <span class="hlt">finite</span> <span class="hlt">element</span> method, addresses compressible and incompressible fluid flow, structural, and thermal modeling as well as the interaction between these disciplines. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena. Interaction constraints are enforced in a fully-coupled manner using the augmented-<span class="hlt">Lagrangian</span> method. Within the multiphysics framework, the <span class="hlt">finite</span> <span class="hlt">element</span> treatment of fluids is based on Galerkin-Least-Squares (GLS) method with discontinuity capturing operators. The arbitrary-<span class="hlt">Lagrangian-Eulerian</span> method is utilized to account for deformable fluid domains. The <span class="hlt">finite</span> <span class="hlt">element</span> treatment of solids and structures is based on the Hu-Washizu variational principle. The multiphysics architecture lends itself naturally to high-performance parallel computing. Aeroelastic, propulsion, thermal management and manufacturing applications are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..1913844L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..1913844L"><span>Estimating <span class="hlt">Eulerian</span> spectra from pairs of drifters</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>LaCasce, Joe</p> <p>2017-04-01</p> <p>GPS-tracked surface drifters offer the possibility of sampling energetic variations at the ocean surface on scales of only 10s of meters, much less than that resolved by satellite. Here we investigate whether velocity differences between pairs of drifters can be used to estimate kinetic energy spectra. Theoretical relations between the spectrum and the second-order longitudinal structure function for 2D non-divergent flow are derived. The structure function is a natural statistic for particle pairs and is easily calculated. However it integrates contributions across wavenumber, and this tends to obscure the spectral dependencies when turbulent inertial ranges are of <span class="hlt">finite</span> extent. Nevertheless, the transform from spectrum to structure function is robust, as illustrated with <span class="hlt">Eulerian</span> data collected from aircraft. The inverse transform, from structure function to spectrum, is much less robust, yielding poor results in particular at large wavenumbers. This occurs because the transform involves a filter function which magnifies contributions from large pair separations, which tend to be noisy. Fitting the structure function to a polynomial improves the spectral estimate, but not sufficiently to distinguish correct inertial range dependencies. Thus with <span class="hlt">Lagrangian</span> data, it is appears preferable to focus on structure functions, despite their shortcomings.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900001315','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900001315"><span>A high-order <span class="hlt">Lagrangian</span>-decoupling method for the incompressible Navier-Stokes equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ho, Lee-Wing; Maday, Yvon; Patera, Anthony T.; Ronquist, Einar M.</p> <p>1989-01-01</p> <p>A high-order <span class="hlt">Lagrangian</span>-decoupling method is presented for the unsteady convection-diffusion and incompressible Navier-Stokes equations. The method is based upon: (1) <span class="hlt">Lagrangian</span> variational forms that reduce the convection-diffusion equation to a symmetric initial value problem; (2) implicit high-order backward-differentiation <span class="hlt">finite</span>-difference schemes for integration along characteristics; (3) <span class="hlt">finite</span> <span class="hlt">element</span> or spectral <span class="hlt">element</span> spatial discretizations; and (4) mesh-invariance procedures and high-order explicit time-stepping schemes for deducing function values at convected space-time points. The method improves upon previous <span class="hlt">finite</span> <span class="hlt">element</span> characteristic methods through the systematic and efficient extension to high order accuracy, and the introduction of a simple structure-preserving characteristic-foot calculation procedure which is readily implemented on modern architectures. The new method is significantly more efficient than explicit-convection schemes for the Navier-Stokes equations due to the decoupling of the convection and Stokes operators and the attendant increase in temporal stability. Numerous numerical examples are given for the convection-diffusion and Navier-Stokes equations for the particular case of a spectral <span class="hlt">element</span> spatial discretization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24235888','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24235888"><span>Incomplete augmented <span class="hlt">Lagrangian</span> preconditioner for steady incompressible Navier-Stokes equations.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun</p> <p>2013-01-01</p> <p>An incomplete augmented <span class="hlt">Lagrangian</span> preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable <span class="hlt">finite</span> <span class="hlt">elements</span>, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented <span class="hlt">Lagrangian</span>-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_7");'>7</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li class="active"><span>9</span></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_9 --> <div id="page_10" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="181"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3819930','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3819930"><span>Incomplete Augmented <span class="hlt">Lagrangian</span> Preconditioner for Steady Incompressible Navier-Stokes Equations</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Tan, Ning-Bo; Huang, Ting-Zhu; Hu, Ze-Jun</p> <p>2013-01-01</p> <p>An incomplete augmented <span class="hlt">Lagrangian</span> preconditioner, for the steady incompressible Navier-Stokes equations discretized by stable <span class="hlt">finite</span> <span class="hlt">elements</span>, is proposed. The eigenvalues of the preconditioned matrix are analyzed. Numerical experiments show that the incomplete augmented <span class="hlt">Lagrangian</span>-based preconditioner proposed is very robust and performs quite well by the Picard linearization or the Newton linearization over a wide range of values of the viscosity on both uniform and stretched grids. PMID:24235888</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008AGUFM.V41C2097D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008AGUFM.V41C2097D"><span>Numerical Simulation of Two-Fluid Mingling Using the Particle <span class="hlt">Finite</span> <span class="hlt">Element</span> Method with Applications to Magmatic and Volcanic Processes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>de Mier, M.; Costa, F.; Idelsohn, S.</p> <p>2008-12-01</p> <p>Many magmatic and volcanic processes (e.g., magma differentiation, mingling, transport in the volcanic conduit) are controlled by the physical properties and flow styles of high-temperature silicate melts. Such processes can be experimentally investigated using analog systems and scaling methods, but it is difficult to find the suitable material and it is generally not possible to quantitatively extrapolate the results to the natural system. An alternative means of studying fluid dynamics in volcanic systems is with numerical models. We have chosen the Particle <span class="hlt">Finite</span> <span class="hlt">Element</span> Method (PFEM), which is based on a Delaunay mesh that moves with the fluid velocity, the Navier-Stokes equations in <span class="hlt">Lagrangian</span> formulation, and linear <span class="hlt">elements</span> for velocity, pressure, and temperature. Remeshing is performed when the grid becomes too distorted [E. Oñate et al., 2004. The Particle <span class="hlt">Finite</span> <span class="hlt">Element</span> Method: An Overview. Int. J. Comput. Meth. 1, 267-307]. The method is ideal for tracking material interfaces between different fluids or media. Methods based on <span class="hlt">Eulerian</span> reference frames need special techniques, such as level-set or volume-of-fluid, to capture the interface position, and these techniques add a significant numerical diffusion at the interface. We have performed a series of two-dimensional simulations of a classical problem of fluid dynamics in magmatic and volcanic systems: intrusion of a basaltic melt in a silica-rich magma reservoir. We have used realistic physical properties and equations of state for the silicate melts (e.g., temperature, viscosity, and density) and tracked the changes in the system for geologically relevant time scales (up to 100 years). The problem is modeled by the low-Mach-number equations derived from an asymptotic analysis of the compressible Navier-Stokes equations that removes shock waves from the flow but allows however large variations of density due to temperature variations. Non-constant viscosity and volume changes are taken into account</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/21279359','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/21279359"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> formulation.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Chen, Zhan; Baker, Nathan A; Wei, G W</p> <p>2011-12-01</p> <p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> formulation of our differential geometry based solvation models. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The optimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and PB equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for the purpose of</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3113640"><span>Differential geometry based solvation model II: <span class="hlt">Lagrangian</span> formulation</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Chen, Zhan; Baker, Nathan A.; Wei, G. W.</p> <p>2010-01-01</p> <p>Solvation is an elementary process in nature and is of paramount importance to more sophisticated chemical, biological and biomolecular processes. The understanding of solvation is an essential prerequisite for the quantitative description and analysis of biomolecular systems. This work presents a <span class="hlt">Lagrangian</span> formulation of our differential geometry based solvation model. The <span class="hlt">Lagrangian</span> representation of biomolecular surfaces has a few utilities/advantages. First, it provides an essential basis for biomolecular visualization, surface electrostatic potential map and visual perception of biomolecules. Additionally, it is consistent with the conventional setting of implicit solvent theories and thus, many existing theoretical algorithms and computational software packages can be directly employed. Finally, the <span class="hlt">Lagrangian</span> representation does not need to resort to artificially enlarged van der Waals radii as often required by the <span class="hlt">Eulerian</span> representation in solvation analysis. The main goal of the present work is to analyze the connection, similarity and difference between the <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> formalisms of the solvation model. Such analysis is important to the understanding of the differential geometry based solvation model. The present model extends the scaled particle theory (SPT) of nonpolar solvation model with a solvent-solute interaction potential. The nonpolar solvation model is completed with a Poisson-Boltzmann (PB) theory based polar solvation model. The differential geometry theory of surfaces is employed to provide a natural description of solvent-solute interfaces. The minimization of the total free energy functional, which encompasses the polar and nonpolar contributions, leads to coupled potential driven geometric flow and Poisson-Boltzmann equations. Due to the development of singularities and nonsmooth manifolds in the <span class="hlt">Lagrangian</span> representation, the resulting potential-driven geometric flow equation is embedded into the <span class="hlt">Eulerian</span> representation for</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/17152055','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/17152055"><span>Cine phase contrast MRI to measure continuum <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> strain fields in contracting skeletal muscle.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhou, Hehe; Novotny, John E</p> <p>2007-01-01</p> <p>To measure the complex mechanics and <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> strain of contracting human skeletal muscle in vivo with cine phase contrast MRI (CPC-MRI) applied to the human supraspinatus muscle of the shoulder. Processing techniques are applied to transform velocities from CPC-MRI images to displacements and planar <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> strain. An interpolation method describing the continuity of the velocity field and forward-backward and Fourier transform methods were used to track the displacement of regions of interest during a cyclic abduction motion of a subject's arm. The components of the <span class="hlt">Lagrangian</span> strain tensor were derived during the motion and principal and maximum in-plane shear strain fields calculated. Derived displacement and strain fields are shown that describe the contraction mechanics of the supraspinatus. Strains vary over time during the cyclic motion and are highly nonuniform throughout the muscle. This method presented overcomes the physical resolution of the MRI scanner, which is crucial for the detection of detailed information within muscles, such as the changes that might occur with partial tears of the supraspinatus. These can then be used as input or validation data for modeling human skeletal muscle.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5643019"><span>Acoustic streaming: an arbitrary Lagrangian–<span class="hlt">Eulerian</span> perspective</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Nama, Nitesh; Huang, Tony Jun; Costanzo, Francesco</p> <p>2017-01-01</p> <p>We analyse acoustic streaming flows using an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) perspective. The formulation stems from an explicit separation of time scales resulting in two subproblems: a first-order problem, formulated in terms of the fluid displacement at the fast scale, and a second-order problem, formulated in terms of the <span class="hlt">Lagrangian</span> flow velocity at the slow time scale. Following a rigorous time-averaging procedure, the second-order problem is shown to be intrinsically steady, and with exact boundary conditions at the oscillating walls. Also, as the second-order problem is solved directly for the <span class="hlt">Lagrangian</span> velocity, the formulation does not need to employ the notion of Stokes drift, or any associated post-processing, thus facilitating a direct comparison with experiments. Because the first-order problem is formulated in terms of the displacement field, our formulation is directly applicable to more complex fluid–structure interaction problems in microacoustofluidic devices. After the formulation’s exposition, we present numerical results that illustrate the advantages of the formulation with respect to current approaches. PMID:29051631</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018IJMPC..2950038G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018IJMPC..2950038G"><span>Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-<span class="hlt">Finite</span> <span class="hlt">Element</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gong, Chun-Lin; Fang, Zhe; Chen, Gang</p> <p></p> <p>A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on <span class="hlt">Eulerian</span> grid, the behaviors of flexible objects are calculated through nonlinear dynamic <span class="hlt">finite</span> <span class="hlt">element</span> method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-<span class="hlt">Finite</span> <span class="hlt">Element</span> method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JPhA...49g5501W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JPhA...49g5501W"><span>Vorticity and symplecticity in multi-symplectic, <span class="hlt">Lagrangian</span> gas dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Webb, G. M.; Anco, S. C.</p> <p>2016-02-01</p> <p>The <span class="hlt">Lagrangian</span>, multi-dimensional, ideal, compressible gas dynamic equations are written in a multi-symplectic form, in which the <span class="hlt">Lagrangian</span> fluid labels, m i (the <span class="hlt">Lagrangian</span> mass coordinates) and time t are the independent variables, and in which the <span class="hlt">Eulerian</span> position of the fluid <span class="hlt">element</span> {x}={x}({m},t) and the entropy S=S({m},t) are the dependent variables. Constraints in the variational principle are incorporated by means of Lagrange multipliers. The constraints are: the entropy advection equation S t = 0, the <span class="hlt">Lagrangian</span> map equation {{x}}t={u} where {u} is the fluid velocity, and the mass continuity equation which has the form J=τ where J={det}({x}{ij}) is the Jacobian of the <span class="hlt">Lagrangian</span> map in which {x}{ij}=\\partial {x}i/\\partial {m}j and τ =1/ρ is the specific volume of the gas. The internal energy per unit volume of the gas \\varepsilon =\\varepsilon (ρ ,S) corresponds to a non-barotropic gas. The <span class="hlt">Lagrangian</span> is used to define multi-momenta, and to develop de Donder-Weyl Hamiltonian equations. The de Donder-Weyl equations are cast in a multi-symplectic form. The pullback conservation laws and the symplecticity conservation laws are obtained. One class of symplecticity conservation laws give rise to vorticity and potential vorticity type conservation laws, and another class of symplecticity laws are related to derivatives of the <span class="hlt">Lagrangian</span> energy conservation law with respect to the <span class="hlt">Lagrangian</span> mass coordinates m i . We show that the vorticity-symplecticity laws can be derived by a Lie dragging method, and also by using Noether’s second theorem and a fluid relabelling symmetry which is a divergence symmetry of the action. We obtain the Cartan-Poincaré form describing the equations and we discuss a set of differential forms representing the equation system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23944559','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23944559"><span><span class="hlt">Lagrangian</span> coherent structures separate dynamically distinct regions in fluid flows.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Kelley, Douglas H; Allshouse, Michael R; Ouellette, Nicholas T</p> <p>2013-07-01</p> <p>Using filter-space techniques, we study the scale-to-scale transport of energy in a quasi-two-dimensional, weakly turbulent fluid flow averaged along the trajectories of fluid <span class="hlt">elements</span>. We find that although the spatial mean of this <span class="hlt">Lagrangian</span>-averaged flux is nearly unchanged from its <span class="hlt">Eulerian</span> counterpart, the spatial structure of the scale-to-scale energy flux changes significantly. In particular, its features appear to correlate with the positions of <span class="hlt">Lagrangian</span> coherent structures (LCS's). We show that the LCS's tend to lie at zeros of the scale-to-scale flux, and therefore that the LCS's separate regions that have qualitatively different dynamics. Since LCS's are also known to be impenetrable barriers to advection and mixing, we therefore find that the fluid on either side of an LCS is both kinematically and dynamically distinct. Our results extend the utility of LCS's by making clear the role they play in the flow dynamics in addition to the kinematics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/20868706','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/20868706"><span>Patient-specific non-linear <span class="hlt">finite</span> <span class="hlt">element</span> modelling for predicting soft organ deformation in real-time: application to non-rigid neuroimage registration.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Wittek, Adam; Joldes, Grand; Couton, Mathieu; Warfield, Simon K; Miller, Karol</p> <p>2010-12-01</p> <p>Long computation times of non-linear (i.e. accounting for geometric and material non-linearity) biomechanical models have been regarded as one of the key factors preventing application of such models in predicting organ deformation for image-guided surgery. This contribution presents real-time patient-specific computation of the deformation field within the brain for six cases of brain shift induced by craniotomy (i.e. surgical opening of the skull) using specialised non-linear <span class="hlt">finite</span> <span class="hlt">element</span> procedures implemented on a graphics processing unit (GPU). In contrast to commercial <span class="hlt">finite</span> <span class="hlt">element</span> codes that rely on an updated <span class="hlt">Lagrangian</span> formulation and implicit integration in time domain for steady state solutions, our procedures utilise the total <span class="hlt">Lagrangian</span> formulation with explicit time stepping and dynamic relaxation. We used patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> meshes consisting of hexahedral and non-locking tetrahedral <span class="hlt">elements</span>, together with realistic material properties for the brain tissue and appropriate contact conditions at the boundaries. The loading was defined by prescribing deformations on the brain surface under the craniotomy. Application of the computed deformation fields to register (i.e. align) the preoperative and intraoperative images indicated that the models very accurately predict the intraoperative deformations within the brain. For each case, computing the brain deformation field took less than 4 s using an NVIDIA Tesla C870 GPU, which is two orders of magnitude reduction in computation time in comparison to our previous study in which the brain deformation was predicted using a commercial <span class="hlt">finite</span> <span class="hlt">element</span> solver executed on a personal computer. Copyright © 2010 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26753780','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26753780"><span>Geometric effects in microfluidics on heterogeneous cell stress using an <span class="hlt">Eulerian-Lagrangian</span> approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Warren, K M; Mpagazehe, J N; LeDuc, P R; Higgs, C F</p> <p>2016-02-07</p> <p>The response of individual cells at the micro-scale in cell mechanics is important in understanding how they are affected by changing environments. To control cell stresses, microfluidics can be implemented since there is tremendous control over the geometry of the devices. Designing microfluidic devices to induce and manipulate stress levels on biological cells can be aided by computational modeling approaches. Such approaches serve as an efficient precursor to fabricating various microfluidic geometries that induce predictable levels of stress on biological cells, based on their mechanical properties. Here, a three-dimensional, multiphase computational fluid dynamics (CFD) modeling approach was implemented for soft biological materials. The computational model incorporates the physics of the particle dynamics, fluid dynamics and solid mechanics, which allows us to study how stresses affect the cells. By using an <span class="hlt">Eulerian-Lagrangian</span> approach to treat the fluid domain as a continuum in the microfluidics, we are conducting studies of the cells' movement and the stresses applied to the cell. As a result of our studies, we were able to determine that a channel with periodically alternating columns of obstacles was capable of stressing cells at the highest rate, and that microfluidic systems can be engineered to impose heterogenous cell stresses through geometric configuring. We found that when using controlled geometries of the microfluidics channels with staggered obstructions, we could increase the maximum cell stress by nearly 200 times over cells flowing through microfluidic channels with no obstructions. Incorporating computational modeling in the design of microfluidic configurations for controllable cell stressing could help in the design of microfludic devices for stressing cells such as cell homogenizers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950023403','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950023403"><span>ANSYS duplicate <span class="hlt">finite-element</span> checker routine</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ortega, R.</p> <p>1995-01-01</p> <p>An ANSYS <span class="hlt">finite-element</span> code routine to check for duplicated <span class="hlt">elements</span> within the volume of a three-dimensional (3D) <span class="hlt">finite-element</span> mesh was developed. The routine developed is used for checking floating <span class="hlt">elements</span> within a mesh, identically duplicated <span class="hlt">elements</span>, and intersecting <span class="hlt">elements</span> with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump <span class="hlt">finite-element</span> model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate <span class="hlt">element</span> checking of 3D <span class="hlt">finite-element</span> models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015AGUFM.H21A1348C"><span>A new approach to enforce <span class="hlt">element</span>-wise mass/species balance using the augmented <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chang, J.; Nakshatrala, K.</p> <p>2015-12-01</p> <p>The least-squares <span class="hlt">finite</span> <span class="hlt">element</span> method (LSFEM) is one of many ways in which one can discretize and express a set of first ordered partial differential equations as a mixed formulation. However, the standard LSFEM is not locally conservative by design. The absence of this physical property can have serious implications in the numerical simulation of subsurface flow and transport. Two commonly employed ways to circumvent this issue is through the Lagrange multiplier method, which explicitly satisfies the <span class="hlt">element</span>-wise divergence by introducing new unknowns, or through appending a penalty factor to the continuity constraint, which reduces the violation in the mass balance. However, these methodologies have some well-known drawbacks. Herein, we propose a new approach to improve the local balance of species/mass balance. The approach augments constraints to a least-square function by a novel mathematical construction of the local species/mass balance, which is different from the conventional ways. The resulting constrained optimization problem is solved using the augmented <span class="hlt">Lagrangian</span>, which corrects the balance errors in an iterative fashion. The advantages of this methodology are that the problem size is not increased (thus preserving the symmetry and positive definite-ness) and that one need not provide an accurate guess for the initial penalty to reach a prescribed mass balance tolerance. We derive the least-squares weighting needed to ensure accurate solutions. We also demonstrate the robustness of the weighted LSFEM coupled with the augmented <span class="hlt">Lagrangian</span> by solving large-scale heterogenous and variably saturated flow through porous media problems. The performance of the iterative solvers with respect to various user-defined augmented <span class="hlt">Lagrangian</span> parameters will be documented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20010078964&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20010078964&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3DLagrangian"><span>A <span class="hlt">Finite</span>-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the <span class="hlt">Finite</span>-Volume GCM with a <span class="hlt">Lagrangian</span> Control-Volume Vertical Coordinate</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)</p> <p>2001-01-01</p> <p>Toward the development of a <span class="hlt">finite</span>-volume Data Assimilation System (fvDAS), a consistent <span class="hlt">finite</span>-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR <span class="hlt">finite</span> volume CCM3 (fvCCM3). To take advantage of the <span class="hlt">Lagrangian</span> control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the <span class="hlt">Lagrangian</span> layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940011492','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940011492"><span>Clouding tracing: Visualization of the mixing of fluid <span class="hlt">elements</span> in convection-diffusion systems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ma, Kwan-Liu; Smith, Philip J.</p> <p>1993-01-01</p> <p>This paper describes a highly interactive method for computer visualization of the basic physical process of dispersion and mixing of fluid <span class="hlt">elements</span> in convection-diffusion systems. It is based on transforming the vector field from a traditionally <span class="hlt">Eulerian</span> reference frame into a <span class="hlt">Lagrangian</span> reference frame. Fluid <span class="hlt">elements</span> are traced through the vector field for the mean path as well as the statistical dispersion of the fluid <span class="hlt">elements</span> about the mean position by using added scalar information about the root mean square value of the vector field and its <span class="hlt">Lagrangian</span> time scale. In this way, clouds of fluid <span class="hlt">elements</span> are traced and are not just mean paths. We have used this method to visualize the simulation of an industrial incinerator to help identify mechanisms for poor mixing.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3065030','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=3065030"><span>A Spectral <span class="hlt">Finite</span> <span class="hlt">Element</span> Approach to Modeling Soft Solids Excited with High-Frequency Harmonic Loads</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Brigham, John C.; Aquino, Wilkins; Aguilo, Miguel A.; Diamessis, Peter J.</p> <p>2010-01-01</p> <p>An approach for efficient and accurate <span class="hlt">finite</span> <span class="hlt">element</span> analysis of harmonically excited soft solids using high-order spectral <span class="hlt">finite</span> <span class="hlt">elements</span> is presented and evaluated. The Helmholtz-type equations used to model such systems suffer from additional numerical error known as pollution when excitation frequency becomes high relative to stiffness (i.e. high wave number), which is the case, for example, for soft tissues subject to ultrasound excitations. The use of high-order polynomial <span class="hlt">elements</span> allows for a reduction in this pollution error, but requires additional consideration to counteract Runge's phenomenon and/or poor linear system conditioning, which has led to the use of spectral <span class="hlt">element</span> approaches. This work examines in detail the computational benefits and practical applicability of high-order spectral <span class="hlt">elements</span> for such problems. The spectral <span class="hlt">elements</span> examined are tensor product <span class="hlt">elements</span> (i.e. quad or brick <span class="hlt">elements</span>) of high-order <span class="hlt">Lagrangian</span> polynomials with non-uniformly distributed Gauss-Lobatto-Legendre nodal points. A shear plane wave example is presented to show the dependence of the accuracy and computational expense of high-order <span class="hlt">elements</span> on wave number. Then, a convergence study for a viscoelastic acoustic-structure interaction <span class="hlt">finite</span> <span class="hlt">element</span> model of an actual ultrasound driven vibroacoustic experiment is shown. The number of degrees of freedom required for a given accuracy level was found to consistently decrease with increasing <span class="hlt">element</span> order. However, the computationally optimal <span class="hlt">element</span> order was found to strongly depend on the wave number. PMID:21461402</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19950063861&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method for subsonic flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing; Loh, Ching Y.</p> <p>1992-01-01</p> <p>It is well known that fluid motion can be specified by either the <span class="hlt">Eulerian</span> of <span class="hlt">Lagrangian</span> description. Most of Computational Fluid Dynamics (CFD) developments over the last three decades have been based on the <span class="hlt">Eulerian</span> description and considerable progress has been made. In particular, the upwind methods, inspired and guided by the work of Gudonov, have met with many successes in dealing with complex flows, especially where discontinuities exist. However, this shock capturing property has proven to be accurate only when the discontinuity is aligned with one of the grid lines since most upwind methods are strictly formulated in 1-D framework and only formally extended to multi-dimensions. Consequently, the attractive property of crisp resolution of these discontinuities is lost and research on genuine multi-dimensional approach has just been undertaken by several leading researchers. Nevertheless they are still based on the <span class="hlt">Eulerian</span> description.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1414156-lagrangian-discontinuous-galerkin-hydrodynamic-method','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1414156-lagrangian-discontinuous-galerkin-hydrodynamic-method"><span>A <span class="hlt">Lagrangian</span> discontinuous Galerkin hydrodynamic method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.</p> <p></p> <p>Here, we present a new <span class="hlt">Lagrangian</span> discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the <span class="hlt">element</span>. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain <span class="hlt">finite</span> <span class="hlt">element</span> methods and uses the strong mass conservation to calculate the density field at a location inside the <span class="hlt">element</span> or on the <span class="hlt">element</span> surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new <span class="hlt">Lagrangian</span> DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1414156-lagrangian-discontinuous-galerkin-hydrodynamic-method','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1414156-lagrangian-discontinuous-galerkin-hydrodynamic-method"><span>A <span class="hlt">Lagrangian</span> discontinuous Galerkin hydrodynamic method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Liu, Xiaodong; Morgan, Nathaniel Ray; Burton, Donald E.</p> <p>2017-12-11</p> <p>Here, we present a new <span class="hlt">Lagrangian</span> discontinuous Galerkin (DG) hydrodynamic method for solving the two-dimensional gas dynamic equations on unstructured hybrid meshes. The physical conservation laws for the momentum and total energy are discretized using a DG method based on linear Taylor expansions. Three different approaches are investigated for calculating the density variation over the <span class="hlt">element</span>. The first approach evolves a Taylor expansion of the specific volume field. The second approach follows certain <span class="hlt">finite</span> <span class="hlt">element</span> methods and uses the strong mass conservation to calculate the density field at a location inside the <span class="hlt">element</span> or on the <span class="hlt">element</span> surface. The thirdmore » approach evolves a Taylor expansion of the density field. The nodal velocity, and the corresponding forces, are explicitly calculated by solving a multidirectional approximate Riemann problem. An effective limiting strategy is presented that ensures monotonicity of the primitive variables. This new <span class="hlt">Lagrangian</span> DG hydrodynamic method conserves mass, momentum, and total energy. Results from a suite of test problems are presented to demonstrate the robustness and expected second-order accuracy of this new method.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1011313','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1011313"><span>Sensitivity of Particle Size in Discrete <span class="hlt">Element</span> Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2016-06-12</p> <p>Particle Size in Discrete <span class="hlt">Element</span> Method to Particle Gas Method (DEM_PGM) Coupling in Underbody Blast Simulations Venkatesh Babu, Kumar Kulkarni, Sanjay...buried in soil viz., (1) coupled discrete <span class="hlt">element</span> & particle gas methods (DEM-PGM) and (2) Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE), are investigated. The...DEM_PGM and identify the limitations/strengths compared to the ALE method. Discrete <span class="hlt">Element</span> Method (DEM) can model individual particle directly, and</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_8");'>8</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li class="active"><span>10</span></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_10 --> <div id="page_11" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="201"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDD17004A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDD17004A"><span>Getting Things Sorted With <span class="hlt">Lagrangian</span> Coherent Structures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Atis, Severine; Peacock, Thomas; Environmental Dynamics Laboratory Team</p> <p>2014-11-01</p> <p>The dispersion of a tracer in a fluid flow is influenced by the <span class="hlt">Lagrangian</span> motion of fluid <span class="hlt">elements</span>. Even in laminar regimes, the irregular chaotic behavior of a fluid flow can lead to effective stirring that rapidly redistributes a tracer throughout the domain. For flows with arbitrary time-dependence, the modern approach of <span class="hlt">Lagrangian</span> Coherent Structures (LCSs) provide a method for identifying the key material lines that organize flow transport. When the advected tracer particles possess a <span class="hlt">finite</span> size and nontrivial shape, however, their dynamics can differ markedly from passive tracers, thus affecting the dispersion phenomena. We present details of numerical simulations and laboratory experiments that investigate the behavior of <span class="hlt">finite</span> size particles in 2-dimensional chaotic flows. We show that the shape and the size of the particles alter the underlying LCSs, facilitating segregation between tracers of different shape in the same flow field.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012SPIE.8316E..0HL','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012SPIE.8316E..0HL"><span>Neurosurgery simulation using non-linear <span class="hlt">finite</span> <span class="hlt">element</span> modeling and haptic interaction</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet</p> <p>2012-02-01</p> <p>Real-time surgical simulation is becoming an important component of surgical training. To meet the realtime requirement, however, the accuracy of the biomechancial modeling of soft tissue is often compromised due to computing resource constraints. Furthermore, haptic integration presents an additional challenge with its requirement for a high update rate. As a result, most real-time surgical simulation systems employ a linear elasticity model, simplified numerical methods such as the boundary <span class="hlt">element</span> method or spring-particle systems, and coarse volumetric meshes. However, these systems are not clinically realistic. We present here an ongoing work aimed at developing an efficient and physically realistic neurosurgery simulator using a non-linear <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) with haptic interaction. Real-time <span class="hlt">finite</span> <span class="hlt">element</span> analysis is achieved by utilizing the total <span class="hlt">Lagrangian</span> explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-<span class="hlt">element</span> operations. We employ a virtual coupling method for separating deformable body simulation and collision detection from haptic rendering, which needs to be updated at a much higher rate than the visual simulation. The system provides accurate biomechancial modeling of soft tissue while retaining a real-time performance with haptic interaction. However, our experiments showed that the stability of the simulator depends heavily on the material property of the tissue and the speed of colliding objects. Hence, additional efforts including dynamic relaxation are required to improve the stability of the system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19790032202&hterms=difference+principle&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Ddifference%2Bprinciple','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19790032202&hterms=difference+principle&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Ddifference%2Bprinciple"><span><span class="hlt">Finite</span> <span class="hlt">elements</span> and <span class="hlt">finite</span> differences for transonic flow calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hafez, M. M.; Murman, E. M.; Wellford, L. C.</p> <p>1978-01-01</p> <p>The paper reviews the chief <span class="hlt">finite</span> difference and <span class="hlt">finite</span> <span class="hlt">element</span> techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. <span class="hlt">Finite</span> difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. <span class="hlt">Finite</span> <span class="hlt">element</span> methods include <span class="hlt">finite</span> <span class="hlt">element</span> Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930061006&hterms=sing&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dsing"><span>An extended <span class="hlt">Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liou, Meng-Sing</p> <p>1993-01-01</p> <p>A unique formulation of describing fluid motion is presented. The method, referred to as 'extended <span class="hlt">Lagrangian</span> method', is interesting from both theoretical and numerical points of view. The formulation offers accuracy in numerical solution by avoiding numerical diffusion resulting from mixing of fluxes in the <span class="hlt">Eulerian</span> description. Meanwhile, it also avoids the inaccuracy incurred due to geometry and variable interpolations used by the previous <span class="hlt">Lagrangian</span> methods. The present method is general and capable of treating subsonic flows as well as supersonic flows. The method proposed in this paper is robust and stable. It automatically adapts to flow features without resorting to clustering, thereby maintaining rather uniform grid spacing throughout and large time step. Moreover, the method is shown to resolve multidimensional discontinuities with a high level of accuracy, similar to that found in 1D problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22572306-numerical-methods-weakly-compressible-generalized-langevin-model-eulerian-reference-frame"><span>Numerical methods for the weakly compressible Generalized Langevin Model in <span class="hlt">Eulerian</span> reference frame</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Azarnykh, Dmitrii, E-mail: d.azarnykh@tum.de; Litvinov, Sergey; Adams, Nikolaus A.</p> <p>2016-06-01</p> <p>A well established approach for the computation of turbulent flow without resolving all turbulent flow scales is to solve a filtered or averaged set of equations, and to model non-resolved scales by closures derived from transported probability density functions (PDF) for velocity fluctuations. Effective numerical methods for PDF transport employ the equivalence between the Fokker–Planck equation for the PDF and a Generalized Langevin Model (GLM), and compute the PDF by transporting a set of sampling particles by GLM (Pope (1985) [1]). The natural representation of GLM is a system of stochastic differential equations in a <span class="hlt">Lagrangian</span> reference frame, typically solvedmore » by particle methods. A representation in a <span class="hlt">Eulerian</span> reference frame, however, has the potential to significantly reduce computational effort and to allow for the seamless integration into a <span class="hlt">Eulerian</span>-frame numerical flow solver. GLM in a <span class="hlt">Eulerian</span> frame (GLMEF) formally corresponds to the nonlinear fluctuating hydrodynamic equations derived by Nakamura and Yoshimori (2009) [12]. Unlike the more common Landau–Lifshitz Navier–Stokes (LLNS) equations these equations are derived from the underdamped Langevin equation and are not based on a local equilibrium assumption. Similarly to LLNS equations the numerical solution of GLMEF requires special considerations. In this paper we investigate different numerical approaches to solving GLMEF with respect to the correct representation of stochastic properties of the solution. We find that a discretely conservative staggered <span class="hlt">finite</span>-difference scheme, adapted from a scheme originally proposed for turbulent incompressible flow, in conjunction with a strongly stable (for non-stochastic PDE) Runge–Kutta method performs better for GLMEF than schemes adopted from those proposed previously for the LLNS. We show that equilibrium stochastic fluctuations are correctly reproduced.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20180002538','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20180002538"><span>Acoustic Radiation Pressure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Cantrell, John H.</p> <p>2018-01-01</p> <p>The theoretical foundation of acoustic radiation pressure in plane wave beams is reexamined. It is shown from <span class="hlt">finite</span> deformation theory and the Boltzmann-Ehrenfest Adiabatic Principle that the Brillouin stress tensor (BST) is the radiation stress in <span class="hlt">Lagrangian</span> coordinates (not <span class="hlt">Eulerian</span> coordinates) and that the terms in the BST are not the momentum flux density and mean excess <span class="hlt">Eulerian</span> stress but are simply contributions to the variation in the wave oscillation period resulting from changes in path length and true wave velocity, respectively, from virtual variations in the strain. It is shown that the radiation stress in <span class="hlt">Eulerian</span> coordinates is the mean Cauchy stress (not the momentum flux density, as commonly assumed) and that Langevin's second relation does not yield an assessment of the mean <span class="hlt">Eulerian</span> pressure, since the enthalpy used in the traditional derivations is a function of the thermodynamic tensions - not the <span class="hlt">Eulerian</span> pressure. It is shown that the transformation between <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> quantities cannot be obtained from the commonly-used expansion of one of the quantities in terms of the particle displacement, since the expansion provides only the difference between the value of the quantity at two different points in Cartesian space separated by the displacement. The proper transformation is obtained only by employing the transformation coefficients of <span class="hlt">finite</span> deformation theory, which are defined in terms of the displacement gradients. <span class="hlt">Finite</span> deformation theory leads to the result that for laterally unconfined, plane waves the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> radiation pressures are equal with the value (1/4)(2K) along the direction of wave propagation, where (K) is the mean kinetic energy density, and zero in directions normal to the propagation direction. This is contrary to the Langevin result that the <span class="hlt">Lagrangian</span> radiation pressure in the propagation direction is equal to (2K) and the BST result that the <span class="hlt">Eulerian</span> radiation pressure in that direction</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23637222','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23637222"><span>Patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling of bones.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A</p> <p>2013-04-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in <span class="hlt">finite</span> <span class="hlt">element</span> model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of <span class="hlt">finite</span> <span class="hlt">element</span> modeling has increased vastly and <span class="hlt">finite</span> <span class="hlt">element</span> models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> method, and judgment is passed on the feasibility of application of patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling are needed before <span class="hlt">finite</span> <span class="hlt">element</span> modeling can be used as a routine clinical tool.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992JCoPh.100..143B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992JCoPh.100..143B"><span>Momentum Advection on a Staggered Mesh</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Benson, David J.</p> <p>1992-05-01</p> <p><span class="hlt">Eulerian</span> and ALE (arbitrary <span class="hlt">Lagrangian-Eulerian</span>) hydrodynamics programs usually split a timestep into two parts. The first part is a <span class="hlt">Lagrangian</span> step, which calculates the incremental motion of the material. The second part is referred to as the <span class="hlt">Eulerian</span> step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most <span class="hlt">finite</span> difference and <span class="hlt">finite</span> <span class="hlt">element</span> formulations, all the solution variables except the velocities are cell-centered while the velocities are edge- or vertex-centered. As a result, the advection algorithm for the momentum is, by necessity, different than the algorithm used for the other variables. This paper reviews three momentum advection methods and proposes a new one. One method, pioneered in YAQUI, creates a new staggered mesh, while the other two, used in SALE and SHALE, are cell-centered. The new method is cell-centered and its relationship to the other methods is discussed. Both pure advection and strong shock calculations are presented to substantiate the mathematical analysis. From the standpoint of numerical accuracy, both the staggered mesh and the cell-centered algorithms can give good results, while the computational costs are highly dependent on the overall architecture of a code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950025782','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950025782"><span>A survey of the core-congruential formulation for geometrically nonlinear TL <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Felippa, Carlos A.; Crivelli, Luis A.; Haugen, Bjorn</p> <p>1994-01-01</p> <p>This article presents a survey of the core-congruential formulation (CCF) for geometrically nonlinear mechanical <span class="hlt">finite</span> <span class="hlt">elements</span> based on the total <span class="hlt">Lagrangian</span> (TL) kinematic description. Although the key ideas behind the CCF can be traced back to Rajasekaran and Murray in 1973, it has not subsequently received serious attention. The CCF is distinguished by a two-phase development of the <span class="hlt">finite</span> <span class="hlt">element</span> stiffness equations. The initial phase developed equations for individual particles. These equations are expressed in terms of displacement gradients as degrees of freedom. The second phase involves congruential-type transformations that eventually binds the <span class="hlt">element</span> particles of an individual <span class="hlt">element</span> in terms of its node-displacement degrees of freedom. Two versions of the CCF, labeled direct and generalized, are distinguished. The direct CCF (DCCF) is first described in general form and then applied to the derivation of geometrically nonlinear bar, and plane stress <span class="hlt">elements</span> using the Green-Lagrange strain measure. The more complex generalized CCF (GCCF) is described and applied to the derivation of 2D and 3D Timoshenko beam <span class="hlt">elements</span>. Several advantages of the CCF, notably the physically clean separation of material and geometric stiffnesses, and its independence with respect to the ultimate choice of shape functions and <span class="hlt">element</span> degrees of freedom, are noted. Application examples involving very large motions solved with the 3D beam <span class="hlt">element</span> display the range of applicability of this formulation, which transcends the kinematic limitations commonly attributed to the TL description.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014APS..DFDH23005V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014APS..DFDH23005V"><span>Estimates of <span class="hlt">Lagrangian</span> particle transport by wave groups: forward transport by Stokes drift and backward transport by the return flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>van den Bremer, Ton S.; Taylor, Paul H.</p> <p>2014-11-01</p> <p>Although the literature has examined Stokes drift, the net <span class="hlt">Lagrangian</span> transport by particles due to of surface gravity waves, in great detail, the motion of fluid particles transported by surface gravity wave groups has received considerably less attention. In practice nevertheless, the wave field on the open sea often has a group-like structure. The motion of particles is different, as particles at sufficient depth are transported backwards by the <span class="hlt">Eulerian</span> return current that was first described by Longuet-Higgins & Stewart (1962) and forms an inseparable counterpart of Stokes drift for wave groups ensuring the (irrotational) mass balance holds. We use WKB theory to study the variation of the <span class="hlt">Lagrangian</span> transport by the return current with depth distinguishing two-dimensional seas, three-dimensional seas, infinite depth and <span class="hlt">finite</span> depth. We then provide dimensional estimates of the net horizontal <span class="hlt">Lagrangian</span> transport by the Stokes drift on the one hand and the return flow on the other hand for realistic sea states in all four cases. Finally we propose a simple scaling relationship for the transition depth: the depth above which <span class="hlt">Lagrangian</span> particles are transported forwards by the Stokes drift and below which such particles are transported backwards by the return current.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790005846','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790005846"><span>Numerical computation of transonic flows by <span class="hlt">finite-element</span> and <span class="hlt">finite</span>-difference methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.</p> <p>1978-01-01</p> <p>Studies on applications of the <span class="hlt">finite</span> <span class="hlt">element</span> approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. <span class="hlt">Finite</span> <span class="hlt">element</span> analogs of Murman's mixed type <span class="hlt">finite</span> difference operators for small disturbance formulations were constructed and the time dependent approach (using <span class="hlt">finite</span> differences in time and <span class="hlt">finite</span> <span class="hlt">elements</span> in space) was examined.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1364765','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1364765"><span>Drekar v.2.0</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Seefeldt, Ben; Sondak, David; Hensinger, David M.</p> <p></p> <p>Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous <span class="hlt">finite</span> <span class="hlt">element</span> formulations, stabilized <span class="hlt">finite</span> <span class="hlt">element</span> formulations, mixed integration <span class="hlt">finite</span> <span class="hlt">element</span> bases (nodal, edge, face, volume) and an initial arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general <span class="hlt">finite</span> <span class="hlt">element</span> discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19720043659&hterms=Continuum+theory&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DContinuum%2Btheory','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19720043659&hterms=Continuum+theory&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DContinuum%2Btheory"><span><span class="hlt">Finite</span> <span class="hlt">elements</span> of nonlinear continua.</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oden, J. T.</p> <p>1972-01-01</p> <p>The <span class="hlt">finite</span> <span class="hlt">element</span> method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the <span class="hlt">finite</span> <span class="hlt">element</span> method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in <span class="hlt">finite</span> elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of <span class="hlt">finite</span> <span class="hlt">element</span> models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, <span class="hlt">finite</span> elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011APS..DFD.G6009Y"><span><span class="hlt">Lagrangian</span> statistics in compressible isotropic homogeneous turbulence</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yang, Yantao; Wang, Jianchun; Shi, Yipeng; Chen, Shiyi</p> <p>2011-11-01</p> <p>In this work we conducted the Direct Numerical Simulation (DNS) of a forced compressible isotropic homogeneous turbulence and investigated the flow statistics from the <span class="hlt">Lagrangian</span> point of view, namely the statistics is computed following the passive tracers trajectories. The numerical method combined the <span class="hlt">Eulerian</span> field solver which was developed by Wang et al. (2010, J. Comp. Phys., 229, 5257-5279), and a <span class="hlt">Lagrangian</span> module for tracking the tracers and recording the data. The <span class="hlt">Lagrangian</span> probability density functions (p.d.f.'s) have then been calculated for both kinetic and thermodynamic quantities. In order to isolate the shearing part from the compressing part of the flow, we employed the Helmholtz decomposition to decompose the flow field (mainly the velocity field) into the solenoidal and compressive parts. The solenoidal part was compared with the incompressible case, while the compressibility effect showed up in the compressive part. The <span class="hlt">Lagrangian</span> structure functions and cross-correlation between various quantities will also be discussed. This work was supported in part by the China's Turbulence Program under Grant No.2009CB724101.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018GMD....11..103G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018GMD....11..103G"><span><span class="hlt">Lagrangian</span> condensation microphysics with Twomey CCN activation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Grabowski, Wojciech W.; Dziekan, Piotr; Pawlowska, Hanna</p> <p>2018-01-01</p> <p>We report the development of a novel <span class="hlt">Lagrangian</span> microphysics methodology for simulations of warm ice-free clouds. The approach applies the traditional <span class="hlt">Eulerian</span> method for the momentum and continuous thermodynamic fields such as the temperature and water vapor mixing ratio, and uses <span class="hlt">Lagrangian</span> <q>super-droplets</q> to represent condensed phase such as cloud droplets and drizzle or rain drops. In other applications of the <span class="hlt">Lagrangian</span> warm-rain microphysics, the super-droplets outside clouds represent unactivated cloud condensation nuclei (CCN) that become activated upon entering a cloud and can further grow through diffusional and collisional processes. The original methodology allows for the detailed study of not only effects of CCN on cloud microphysics and dynamics, but also CCN processing by a cloud. However, when cloud processing is not of interest, a simpler and computationally more efficient approach can be used with super-droplets forming only when CCN is activated and no super-droplet existing outside a cloud. This is possible by applying the Twomey activation scheme where the local supersaturation dictates the concentration of cloud droplets that need to be present inside a cloudy volume, as typically used in <span class="hlt">Eulerian</span> bin microphysics schemes. Since a cloud volume is a small fraction of the computational domain volume, the Twomey super-droplets provide significant computational advantage when compared to the original super-droplet methodology. Additional advantage comes from significantly longer time steps that can be used when modeling of CCN deliquescence is avoided. Moreover, other formulation of the droplet activation can be applied in case of low vertical resolution of the host model, for instance, linking the concentration of activated cloud droplets to the local updraft speed. This paper discusses the development and testing of the Twomey super-droplet methodology, focusing on the activation and diffusional growth. Details of the activation</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1998PhDT.......312B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1998PhDT.......312B"><span>Nonlinear thermo-mechanical analysis of stiffened composite laminates by a new <span class="hlt">finite</span> <span class="hlt">element</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Barut, Atila</p> <p></p> <p>A new stiffened shell <span class="hlt">element</span> combining shallow beam and shallow shell <span class="hlt">elements</span> is developed for geometrically nonlinear analysis of stiffened composite laminates under thermal and/or mechanical loading. The formulation of this <span class="hlt">element</span> is based on the principal of virtual displacements in conjunction with the co-rotational form of the total <span class="hlt">Lagrangian</span> description of motion. In the <span class="hlt">finite</span> <span class="hlt">element</span> formulation, both the shell and the beam (stiffener) <span class="hlt">elements</span> account for transverse shear deformations and material anisotropy. The cross-section of the stiffener (beam) can be arbitrary in geometry and lamination. In order to combine the stiffener with the shell <span class="hlt">element</span>, constraint conditions are applied to the displacement and rotation fields of the stiffener. These constraint conditions ensure that the cross-section of the stiffener remains co-planar with the shell section after deformation. The resulting expressions for the displacement and rotation fields of the stiffener involve only the nodal unknowns of the shell <span class="hlt">element</span>, thus reducing the total number of degrees of freedom. Also, the discretization of the entire stiffened shell structure becomes more flexible.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980219348','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980219348"><span>A Posteriori Bounds for Linear-Functional Outputs of Crouzeix-Raviart <span class="hlt">Finite</span> <span class="hlt">Element</span> Discretizations of the Incompressible Stokes Problem</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Patera, Anthony T.; Paraschivoiu, Marius</p> <p>1998-01-01</p> <p>We present a <span class="hlt">finite</span> <span class="hlt">element</span> technique for the efficient generation of lower and upper bounds to outputs which are linear functionals of the solutions to the incompressible Stokes equations in two space dimensions; the <span class="hlt">finite</span> <span class="hlt">element</span> discretization is effected by Crouzeix-Raviart <span class="hlt">elements</span>, the discontinuous pressure approximation of which is central to our approach. The bounds are based upon the construction of an augmented <span class="hlt">Lagrangian</span>: the objective is a quadratic "energy" reformulation of the desired output; the constraints are the <span class="hlt">finite</span> <span class="hlt">element</span> equilibrium equations (including the incompressibility constraint), and the intersubdomain continuity conditions on velocity. Appeal to the dual max-min problem for appropriately chosen candidate Lagrange multipliers then yields inexpensive bounds for the output associated with a fine-mesh discretization; the Lagrange multipliers are generated by exploiting an associated coarse-mesh approximation. In addition to the requisite coarse-mesh calculations, the bound technique requires solution only of local subdomain Stokes problems on the fine-mesh. The method is illustrated for the Stokes equations, in which the outputs of interest are the flowrate past, and the lift force on, a body immersed in a channel.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA588350','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA588350"><span>Nonlinear <span class="hlt">Eulerian</span> Thermoelasticity for Anisotropic Crystals</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2013-08-01</p> <p>the applied pressure. However, some crystalline materials such as ceramics and hard minerals may retain significant shear strength at <span class="hlt">finite</span> strain...which elastic properties have been measured. Benefits of using <span class="hlt">Eulerian</span> strain measures for nonlinear elasticity of isotropic materials were extolled by...highly symmetric anharmonic properties . Deviations may be expected for highly anisotropic materials , as shown in Section 4. This work is focused</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA062335','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA062335"><span>Incorporation of the NAG-FRAG Model for Ductile and Brittle Fracture into Help, a 2D Multimaterial <span class="hlt">Eulerian</span> Program</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1978-09-01</p> <p>Models HELP Ductile Material HEMP Brittle Material PUFF Iron Aluminum <span class="hlt">Eulerian</span> Codea Tap«.r«»H Flyor Pl^«-» rmp«^» tO. ABITRACT (Conllmjm M r«v... HEMP ) code with those obtained by the <span class="hlt">Eulerian</span> (HELP) code 5.3 Relative void volume of damage regions at three times after impact in the 1145...plate calculation 5.5 Relative void volume of material in the 1145 aluminum target at 1.46 us after impact as computed by the <span class="hlt">Lagrangian</span> ( HEMP</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CNSNS..20..516I','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CNSNS..20..516I"><span>Transport induced by mean-eddy interaction: I. Theory, and relation to <span class="hlt">Lagrangian</span> lobe dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ide, Kayo; Wiggins, Stephen</p> <p>2015-02-01</p> <p>In this paper we develop a method for the estimation of Transport Induced by the Mean-Eddy interaction (TIME) in two-dimensional unsteady flows. The method is based on the dynamical systems approach to fluid transport and can be viewed as a hybrid combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods. The (<span class="hlt">Eulerian</span>) boundaries across which we consider (<span class="hlt">Lagrangian</span>) transport are kinematically defined by appropriately chosen streamlines of the mean flow. By evaluating the impact of the mean-eddy interaction on transport, the TIME method can be used as a diagnostic tool for transport processes that occur during a specified time interval along a specified boundary segment. We introduce two types of TIME functions: one that quantifies the accumulation of flow properties and another that measures the displacement of the transport geometry. The spatial geometry of transport is described by the so-called pseudo-lobes, and temporal evolution of transport by their dynamics. In the case where the TIME functions are evaluated along a separatrix, the pseudo-lobes have a relationship to the lobes of <span class="hlt">Lagrangian</span> transport theory. In fact, one of the TIME functions is identical to the Melnikov function that is used to measure the distance, at leading order in a small parameter, between the two invariant manifolds that define the <span class="hlt">Lagrangian</span> lobes. We contrast the similarities and differences between the TIME and <span class="hlt">Lagrangian</span> lobe dynamics in detail. An application of the TIME method is carried out for inter-gyre transport in the wind-driven oceanic circulation model and a comparison with the <span class="hlt">Lagrangian</span> transport theory is made.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_9");'>9</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li class="active"><span>11</span></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_11 --> <div id="page_12" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="221"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900019806','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900019806"><span>Second order tensor <span class="hlt">finite</span> <span class="hlt">element</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.</p> <p>1990-01-01</p> <p>The results of a research and software development effort are presented for the <span class="hlt">finite</span> <span class="hlt">element</span> modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid <span class="hlt">finite</span> <span class="hlt">elements</span> were implemented and compared with displacement-based <span class="hlt">elements</span>. Both static and dynamic cases are considered. The hybrid <span class="hlt">elements</span> developed in the project were incorporated into the SPAR <span class="hlt">finite</span> <span class="hlt">element</span> code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19840035292&hterms=stremel&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dstremel','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19840035292&hterms=stremel&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dstremel"><span>A method for modeling <span class="hlt">finite</span>-core vortices in wake-flow calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Stremel, P. M.</p> <p>1984-01-01</p> <p>A numerical method for computing nonplanar vortex wakes represented by <span class="hlt">finite</span>-core vortices is presented. The approach solves for the velocity on an <span class="hlt">Eulerian</span> grid, using standard <span class="hlt">finite</span>-difference techniques; the vortex wake is tracked by <span class="hlt">Lagrangian</span> methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the <span class="hlt">finite</span>-core model. Two distributions of vorticity, or core models, are investigated: a <span class="hlt">finite</span> distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920051740&hterms=topology&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dtopology','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920051740&hterms=topology&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Dtopology"><span><span class="hlt">Element</span>-topology-independent preconditioners for parallel <span class="hlt">finite</span> <span class="hlt">element</span> computations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Park, K. C.; Alexander, Scott</p> <p>1992-01-01</p> <p>A family of preconditioners for the solution of <span class="hlt">finite</span> <span class="hlt">element</span> equations are presented, which are <span class="hlt">element</span>-topology independent and thus can be applicable to <span class="hlt">element</span> order-free parallel computations. A key feature of the present preconditioners is the repeated use of <span class="hlt">element</span> connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> matrices for implicit time integration computations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016TCry...10.1513R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016TCry...10.1513R"><span>Arctic sea-ice diffusion from observed and simulated <span class="hlt">Lagrangian</span> trajectories</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Rampal, Pierre; Bouillon, Sylvain; Bergh, Jon; Ólason, Einar</p> <p>2016-07-01</p> <p>We characterize sea-ice drift by applying a <span class="hlt">Lagrangian</span> diffusion analysis to buoy trajectories from the International Arctic Buoy Programme (IABP) dataset and from two different models: the standalone <span class="hlt">Lagrangian</span> sea-ice model neXtSIM and the <span class="hlt">Eulerian</span> coupled ice-ocean model used for the TOPAZ reanalysis. By applying the diffusion analysis to the IABP buoy trajectories over the period 1979-2011, we confirm that sea-ice diffusion follows two distinct regimes (ballistic and Brownian) and we provide accurate values for the diffusivity and integral timescale that could be used in <span class="hlt">Eulerian</span> or <span class="hlt">Lagrangian</span> passive tracers models to simulate the transport and diffusion of particles moving with the ice. We discuss how these values are linked to the evolution of the fluctuating displacements variance and how this information could be used to define the size of the search area around the position predicted by the mean drift. By comparing observed and simulated sea-ice trajectories for three consecutive winter seasons (2007-2011), we show how the characteristics of the simulated motion may differ from or agree well with observations. This comparison illustrates the usefulness of first applying a diffusion analysis to evaluate the output of modeling systems that include a sea-ice model before using these in, e.g., oil spill trajectory models or, more generally, to simulate the transport of passive tracers in sea ice.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960049629','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960049629"><span>Atomization simulations using an <span class="hlt">Eulerian-VOF-Lagrangian</span> method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chen, Yen-Sen; Shang, Huan-Min; Liaw, Paul; Chen, C. P.</p> <p>1994-01-01</p> <p>This paper summarizes the technical development and validation of a multiphase computational fluid dynamics (CFD) numerical method using the volume-of-fluid (VOF) model and a <span class="hlt">Lagrangian</span> tracking model which can be employed to analyze general multiphase flow problems with free surface mechanism. The gas-liquid interface mass, momentum and energy conservations are modeled by continuum surface mechanisms. A new solution method is developed such that the present VOF model can be applied for all-speed flow regimes. The objectives of the present study are to develop and verify the fractional volume-of-fluid cell partitioning approach into a predictor-corrector algorithm and to demonstrate the effectiveness of the present innovative approach by simulating benchmark problems including the coaxial jet atomization.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011icov.conf..765K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011icov.conf..765K"><span>Numerical Simulation of Interaction of Human Vocal Folds and Fluid Flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Kosík, A.; Feistauer, M.; Horáček, J.; Sváček, P.</p> <p></p> <p>Our goal is to simulate airflow in human vocal folds and their flow-induced vibrations. We consider two-dimensional viscous incompressible flow in a time-dependent domain. The fluid flow is described by the Navier-Stokes equations in the arbitrary <span class="hlt">Lagrangian-Eulerian</span> formulation. The flow problem is coupled with the elastic behaviour of the solid bodies. The developed solution of the coupled problem based on the <span class="hlt">finite</span> <span class="hlt">element</span> method is demonstrated by numerical experiments.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvD..96l3538A"><span><span class="hlt">Lagrangian</span> theory of structure formation in relativistic cosmology. IV. <span class="hlt">Lagrangian</span> approach to gravitational waves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Al Roumi, Fosca; Buchert, Thomas; Wiegand, Alexander</p> <p>2017-12-01</p> <p>The relativistic generalization of the Newtonian <span class="hlt">Lagrangian</span> perturbation theory is investigated. In previous works, the perturbation and solution schemes that are generated by the spatially projected gravitoelectric part of the Weyl tensor were given to any order of the perturbations, together with extensions and applications for accessing the nonperturbative regime. We here discuss more in detail the general first-order scheme within the Cartan formalism including and concentrating on the gravitational wave propagation in matter. We provide master equations for all parts of <span class="hlt">Lagrangian</span>-linearized perturbations propagating in the perturbed spacetime, and we outline the solution procedure that allows one to find general solutions. Particular emphasis is given to global properties of the <span class="hlt">Lagrangian</span> perturbation fields by employing results of Hodge-de Rham theory. We here discuss how the Hodge decomposition relates to the standard scalar-vector-tensor decomposition. Finally, we demonstrate that we obtain the known linear perturbation solutions of the standard relativistic perturbation scheme by performing two steps: first, by restricting our solutions to perturbations that propagate on a flat unperturbed background spacetime and, second, by transforming to <span class="hlt">Eulerian</span> background coordinates with truncation of nonlinear terms.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870013357','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870013357"><span>Probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Belytschko, Ted; Wing, Kam Liu</p> <p>1987-01-01</p> <p>In the Probabilistic <span class="hlt">Finite</span> <span class="hlt">Element</span> Method (PFEM), <span class="hlt">finite</span> <span class="hlt">element</span> methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170001234','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170001234"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Simulation of Three Full-Scale Crash Tests for Cessna 172 Aircraft</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mason, Brian H.; Warren, Jerry E., Jr.</p> <p>2017-01-01</p> <p>The NASA Emergency Locator Transmitter Survivability and Reliability (ELT-SAR) project was initiated in 2013 to assess the crash performance standards for the next generation of emergency locator transmitter (ELT) systems. Three Cessna 172 aircraft were acquired to perform crash testing at NASA Langley Research Center's Landing and Impact Research Facility. Full-scale crash tests were conducted in the summer of 2015 and each test article was subjected to severe, but survivable, impact conditions including a flare-to-stall during emergency landing, and two controlled-flight-into-terrain scenarios. Full-scale <span class="hlt">finite</span> <span class="hlt">element</span> analyses were performed using a commercial explicit solver, ABAQUS. The first test simulated impacting a concrete surface represented analytically by a rigid plane. Tests 2 and 3 simulated impacting a dirt surface represented analytically by an <span class="hlt">Eulerian</span> grid of brick <span class="hlt">elements</span> using a Mohr-Coulomb material model. The objective of this paper is to summarize the test and analysis results for the three full-scale crash tests. Simulation models of the airframe which correlate well with the tests are needed for future studies of alternate ELT mounting configurations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19810016800','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19810016800"><span>Integrated transient thermal-structural <span class="hlt">finite</span> <span class="hlt">element</span> analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, E. A.; Dechaumphai, P.; Wieting, A. R.; Tamma, K. K.</p> <p>1981-01-01</p> <p>An integrated thermal structural <span class="hlt">finite</span> <span class="hlt">element</span> approach for efficient coupling of transient thermal and structural analysis is presented. Integrated thermal structural rod and one dimensional axisymmetric <span class="hlt">elements</span> considering conduction and convection are developed and used in transient thermal structural applications. The improved accuracy of the integrated approach is illustrated by comparisons with exact transient heat conduction elasticity solutions and conventional <span class="hlt">finite</span> <span class="hlt">element</span> thermal <span class="hlt">finite</span> <span class="hlt">element</span> structural analyses.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24277435','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24277435"><span>Source apportion of atmospheric particulate matter: a joint <span class="hlt">Eulerian/Lagrangian</span> approach.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Riccio, A; Chianese, E; Agrillo, G; Esposito, C; Ferrara, L; Tirimberio, G</p> <p>2014-12-01</p> <p>PM2.5 samples were collected during an annual monitoring campaign (January 2012-January 2013) in the urban area of Naples, one of the major cities in Southern Italy. Samples were collected by means of a standard gravimetric sampler (Tecora Echo model) and characterized from a chemical point of view by ion chromatography. As a result, 143 samples together with their ionic composition have been collected. We extend traditional source apportionment techniques, usually based on multivariate factor analysis, interpreting the chemical analysis results within a <span class="hlt">Lagrangian</span> framework. The Hybrid Single-Particle <span class="hlt">Lagrangian</span> Integrated Trajectory Model (HYSPLIT) model was used, providing linkages to the source regions in the upwind areas. Results were analyzed in order to quantify the relative weight of different source types/areas. Model results suggested that PM concentrations are strongly affected not only by local emissions but also by transboundary emissions, especially from the Eastern and Northern European countries and African Saharan dust episodes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19890027801&hterms=differential+equations+application&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Ddifferential%2Bequations%2Bapplication','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19890027801&hterms=differential+equations+application&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Ddifferential%2Bequations%2Bapplication"><span><span class="hlt">Finite</span> <span class="hlt">elements</span>: Theory and application</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)</p> <p>1988-01-01</p> <p>Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic <span class="hlt">finite-element</span> equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving <span class="hlt">finite</span> <span class="hlt">elements</span> in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular <span class="hlt">finite</span> <span class="hlt">elements</span> and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035182&hterms=difference+engine&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Ddifference%2Bengine"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.; Willis, E. A.</p> <p>1990-01-01</p> <p>A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit <span class="hlt">finite</span> volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the <span class="hlt">finite</span> difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900004433','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900004433"><span>Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Raju, M. S.; Willis, E. A.</p> <p>1989-01-01</p> <p>A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an <span class="hlt">Eulerian</span> <span class="hlt">Lagrangian</span> approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, <span class="hlt">Eulerian</span> coordinates on a moving grid by making use of an implicit <span class="hlt">finite</span> volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in <span class="hlt">Lagrangian</span> coordinates. Both the details of the numerical algorithm and the <span class="hlt">finite</span> difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CompM..51..129Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CompM..51..129Z"><span>A three dimensional immersed smoothed <span class="hlt">finite</span> <span class="hlt">element</span> method (3D IS-FEM) for fluid-structure interaction problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong</p> <p>2013-02-01</p> <p>A three-dimensional immersed smoothed <span class="hlt">finite</span> <span class="hlt">element</span> method (3D IS-FEM) using four-node tetrahedral <span class="hlt">element</span> is proposed to solve 3D fluid-structure interaction (FSI) problems. The 3D IS-FEM is able to determine accurately the physical deformation of the nonlinear solids placed within the incompressible viscous fluid governed by Navier-Stokes equations. The method employs the semi-implicit characteristic-based split scheme to solve the fluid flows and smoothed <span class="hlt">finite</span> <span class="hlt">element</span> methods to calculate the transient dynamics responses of the nonlinear solids based on explicit time integration. To impose the FSI conditions, a novel, effective and sufficiently general technique via simple linear interpolation is presented based on <span class="hlt">Lagrangian</span> fictitious fluid meshes coinciding with the moving and deforming solid meshes. In the comparisons to the referenced works including experiments, it is clear that the proposed 3D IS-FEM ensures stability of the scheme with the second order spatial convergence property; and the IS-FEM is fairly independent of a wide range of mesh size ratio.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=finite+AND+element&pg=2&id=EJ241217','ERIC'); return false;" href="https://eric.ed.gov/?q=finite+AND+element&pg=2&id=EJ241217"><span>Infinite Possibilities for the <span class="hlt">Finite</span> <span class="hlt">Element</span>.</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Finlayson, Bruce A.</p> <p>1981-01-01</p> <p>Describes the uses of <span class="hlt">finite</span> <span class="hlt">element</span> methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of <span class="hlt">finite</span> <span class="hlt">element</span> methods. (Author/WB)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170001235','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170001235"><span>Stabilized <span class="hlt">Finite</span> <span class="hlt">Elements</span> in FUN3D</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Anderson, W. Kyle; Newman, James C.; Karman, Steve L.</p> <p>2017-01-01</p> <p>A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized <span class="hlt">finite-element</span> discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic <span class="hlt">elements</span> by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the <span class="hlt">finite</span>-volume formulation that is currently the primary method employed for routine engineering applications. The <span class="hlt">finite-element</span> methodology is demonstrated to be more accurate than the <span class="hlt">finite</span>-volume technology, particularly on tetrahedral meshes where the solutions obtained using the <span class="hlt">finite</span>-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the <span class="hlt">finite-element</span> scheme is competitive with the <span class="hlt">finite</span>-volume scheme in terms of computer time to reach convergence.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019171','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019171"><span>Solution of mixed convection heat transfer from isothermal in-line fins</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Khalilollahi, Amir</p> <p>1993-01-01</p> <p>Transient and steady state combined natural and forced convective flows over two in-line <span class="hlt">finite</span> thickness fins (louvers) in a vertical channel are numerically solved using two methods. The first method of solution is based on the 'Simple Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span>' (SALE) technique which incorporates mainly two computational phases: (1) a <span class="hlt">Lagrangian</span> phase in which the velocity field is updated by the effects of all forces, and (2) an <span class="hlt">Eulerian</span> phase that executes all advective fluxes of mass, momentum and energy. The second method of solution uses the <span class="hlt">finite</span> <span class="hlt">element</span> code entitled FIDAP. In the first part, comparison of the results by FIDAP, SALE, and available experimental work were done and discussed for steady state forced convection over louvered fins. Good agreements were deduced between the three sets of results especially for the flow over a single fin. In the second part and in the absence of experimental literature, the numerical predictions were extended to the transient transports and to the opposing flow where pressure drop is reversed. Results are presented and discussed for heat transfer and pressure drop in assisting and opposing mixed convection flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2006JPhy4.133..587K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2006JPhy4.133..587K"><span>Modeling NIF experimental designs with adaptive mesh refinement and <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Koniges, A. E.; Anderson, R. W.; Wang, P.; Gunney, B. T. N.; Becker, R.; Eder, D. C.; MacGowan, B. J.; Schneider, M. B.</p> <p>2006-06-01</p> <p>Incorporation of adaptive mesh refinement (AMR) into <span class="hlt">Lagrangian</span> hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target <span class="hlt">elements</span>. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/wri/1986/4145/report.pdf','USGSPUBS'); return false;" href="https://pubs.usgs.gov/wri/1986/4145/report.pdf"><span>Users manual for a one-dimensional <span class="hlt">Lagrangian</span> transport model</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Schoellhamer, D.H.; Jobson, H.E.</p> <p>1986-01-01</p> <p>A Users Manual for the <span class="hlt">Lagrangian</span> Transport Model (LTM) is presented. The LTM uses <span class="hlt">Lagrangian</span> calculations that are based on a reference frame moving with the river flow. The <span class="hlt">Lagrangian</span> reference frame eliminates the need to numerically solve the convective term of the convection-diffusion equation and provides significant numerical advantages over the more commonly used <span class="hlt">Eulerian</span> reference frame. When properly applied, the LTM can simulate riverine transport and decay processes within the accuracy required by most water quality studies. The LTM is applicable to steady or unsteady one-dimensional unidirectional flows in fixed channels with tributary and lateral inflows. Application of the LTM is relatively simple and optional capabilities improve the model 's convenience. Appendices give file formats and three example LTM applications that include the incorporation of the QUAL II water quality model 's reaction kinetics into the LTM. (Author 's abstract)</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_10");'>10</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li class="active"><span>12</span></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_12 --> <div id="page_13" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="241"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880009736','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880009736"><span>Toward automatic <span class="hlt">finite</span> <span class="hlt">element</span> analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kela, Ajay; Perucchio, Renato; Voelcker, Herbert</p> <p>1987-01-01</p> <p>Two problems must be solved if the <span class="hlt">finite</span> <span class="hlt">element</span> method is to become a reliable and affordable blackbox engineering tool. <span class="hlt">Finite</span> <span class="hlt">element</span> meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870007120','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870007120"><span>DYCAST: A <span class="hlt">finite</span> <span class="hlt">element</span> program for the crash analysis of structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pifko, A. B.; Winter, R.; Ogilvie, P.</p> <p>1987-01-01</p> <p>DYCAST is a nonlinear structural dynamic <span class="hlt">finite</span> <span class="hlt">element</span> computer code developed for crash simulation. The <span class="hlt">element</span> library contains stringers, beams, membrane skin triangles, plate bending triangles and spring <span class="hlt">elements</span>. Changing stiffnesses in the structure are accounted for by plasticity and very large deflections. Material nonlinearities are accommodated by one of three options: elastic-perfectly plastic, elastic-linear hardening plastic, or elastic-nonlinear hardening plastic of the Ramberg-Osgood type. Geometric nonlinearities are handled in an updated <span class="hlt">Lagrangian</span> formulation by reforming the structure into its deformed shape after small time increments while accumulating deformations, strains, and forces. The nonlinearities due to combined loadings are maintained, and stiffness variation due to structural failures are computed. Numerical time integrators available are fixed-step central difference, modified Adams, Newmark-beta, and Wilson-theta. The last three have a variable time step capability, which is controlled internally by a solution convergence error measure. Other features include: multiple time-load history tables to subject the structure to time dependent loading; gravity loading; initial pitch, roll, yaw, and translation of the structural model with respect to the global system; a bandwidth optimizer as a pre-processor; and deformed plots and graphics as post-processors.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/332751','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/332751"><span>ALEGRA -- A massively parallel h-adaptive code for solid dynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Summers, R.M.; Wong, M.K.; Boucheron, E.A.</p> <p>1997-12-31</p> <p>ALEGRA is a multi-material, arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) code for solid dynamics designed to run on massively parallel (MP) computers. It combines the features of modern <span class="hlt">Eulerian</span> shock codes, such as CTH, with modern <span class="hlt">Lagrangian</span> structural analysis codes using an unstructured grid. ALEGRA is being developed for use on the teraflop supercomputers to conduct advanced three-dimensional (3D) simulations of shock phenomena important to a variety of systems. ALEGRA was designed with the Single Program Multiple Data (SPMD) paradigm, in which the mesh is decomposed into sub-meshes so that each processor gets a single sub-mesh with approximately the same number of <span class="hlt">elements</span>. Usingmore » this approach the authors have been able to produce a single code that can scale from one processor to thousands of processors. A current major effort is to develop efficient, high precision simulation capabilities for ALEGRA, without the computational cost of using a global highly resolved mesh, through flexible, robust h-adaptivity of <span class="hlt">finite</span> <span class="hlt">elements</span>. H-adaptivity is the dynamic refinement of the mesh by subdividing <span class="hlt">elements</span>, thus changing the characteristic <span class="hlt">element</span> size and reducing numerical error. The authors are working on several major technical challenges that must be met to make effective use of HAMMER on MP computers.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910022373','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910022373"><span>Improved <span class="hlt">finite-element</span> methods for rotorcraft structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hinnant, Howard E.</p> <p>1991-01-01</p> <p>An overview of the research directed at improving <span class="hlt">finite-element</span> methods for rotorcraft airframes is presented. The development of a modification to the <span class="hlt">finite</span> <span class="hlt">element</span> method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick <span class="hlt">finite</span> <span class="hlt">element</span> program.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70025921','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70025921"><span>A <span class="hlt">finite</span>-volume ELLAM for three-dimensional solute-transport modeling</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.</p> <p>2003-01-01</p> <p>A three-dimensional <span class="hlt">finite</span>-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time <span class="hlt">finite</span> volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of <span class="hlt">Eulerian-Lagrangian</span> characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a <span class="hlt">Lagrangian</span> treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19750024435','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19750024435"><span>Studies of <span class="hlt">finite</span> <span class="hlt">element</span> analysis of composite material structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.</p> <p>1975-01-01</p> <p>Research in the area of <span class="hlt">finite</span> <span class="hlt">element</span> analysis is summarized. Topics discussed include <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a <span class="hlt">finite</span> <span class="hlt">element</span> mesh generation program based on isoparametric zones), and <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a composite bolted joint specimens.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19860037878&hterms=divided+attention&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Ddivided%2Battention','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19860037878&hterms=divided+attention&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Ddivided%2Battention"><span>Books and monographs on <span class="hlt">finite</span> <span class="hlt">element</span> technology</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, A. K.</p> <p>1985-01-01</p> <p>The present paper proviees a listing of all of the English books and some of the foreign books on <span class="hlt">finite</span> <span class="hlt">element</span> technology, taking into account also a list of the conference proceedings devoted solely to <span class="hlt">finite</span> <span class="hlt">elements</span>. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary <span class="hlt">element</span> methods, proceedings of symmposia and conferences on <span class="hlt">finite</span> <span class="hlt">element</span> technology, bibliographies, handbooks, and historical accounts.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880045120&hterms=PFEM&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DPFEM','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880045120&hterms=PFEM&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DPFEM"><span>Probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span> for fracture mechanics</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Besterfield, Glen</p> <p>1988-01-01</p> <p>The probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM) is developed for probabilistic fracture mechanics (PFM). A <span class="hlt">finite</span> <span class="hlt">element</span> which has the near crack-tip singular strain embedded in the <span class="hlt">element</span> is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20070011612','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20070011612"><span>SUPG <span class="hlt">Finite</span> <span class="hlt">Element</span> Simulations of Compressible Flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kirk, Brnjamin, S.</p> <p>2006-01-01</p> <p>The Streamline-Upwind Petrov-Galerkin (SUPG) <span class="hlt">finite</span> <span class="hlt">element</span> simulations of compressible flows is presented. The topics include: 1) Introduction; 2) SUPG Galerkin <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods; 3) Applications; and 4) Bibliography.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930058875&hterms=stiffness+direct+method&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dstiffness%2Bdirect%2Bmethod','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930058875&hterms=stiffness+direct+method&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dstiffness%2Bdirect%2Bmethod"><span>Solution of free-boundary problems using <span class="hlt">finite-element</span>/Newton methods and locally refined grids - Application to analysis of solidification microstructure</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Tsiveriotis, K.; Brown, R. A.</p> <p>1993-01-01</p> <p>A new method is presented for the solution of free-boundary problems using <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of <span class="hlt">elemental</span> stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of <span class="hlt">elemental</span> data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19820020790','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19820020790"><span>Improved <span class="hlt">finite</span> <span class="hlt">element</span> methodology for integrated thermal structural analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dechaumphai, P.; Thornton, E. A.</p> <p>1982-01-01</p> <p>An integrated thermal-structural <span class="hlt">finite</span> <span class="hlt">element</span> approach for efficient coupling of thermal and structural analysis is presented. New thermal <span class="hlt">finite</span> <span class="hlt">elements</span> which yield exact nodal and <span class="hlt">element</span> temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal <span class="hlt">finite</span> <span class="hlt">elements</span> for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal <span class="hlt">finite</span> <span class="hlt">elements</span> provide detailed temperature distributions without using additional <span class="hlt">element</span> nodes and permit a common discretization with lower order congruent structural <span class="hlt">finite</span> <span class="hlt">elements</span>. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional <span class="hlt">finite</span> <span class="hlt">element</span> thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFM.C32B..06D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFM.C32B..06D"><span>Discrete-<span class="hlt">element</span> simulation of sea-ice mechanics: Contact mechanics and granular jamming</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Damsgaard, A.; Adcroft, A.; Sergienko, O. V.; Stern, A. A.</p> <p>2017-12-01</p> <p><span class="hlt">Lagrangian</span> models of sea-ice dynamics offer several advantages to <span class="hlt">Eulerian</span> continuum methods. Spatial discretization on the ice-floe scale is natural for <span class="hlt">Lagrangian</span> models, which additionally offer the convenience of being able to handle arbitrary sea-ice concentrations. This is likely to improve model performance in ice-marginal zones with strong advection. Furthermore, phase transitions in granular rheology around the jamming limit, such as observed when sea ice moves through geometric confinements, includes sharp thresholds in effective viscosity which are typically ignored in <span class="hlt">Eulerian</span> models. Granular jamming is a stochastic process dependent on having the right grains in the right place at the right time, and the jamming likelihood over time can be described by a probabilistic model. Difficult to parameterize in continuum formulations, jamming occurs naturally in dense granular systems simulated in a <span class="hlt">Lagrangian</span> framework, and is a very relevant process controlling sea-ice transport through narrow straits. We construct a flexible discrete-<span class="hlt">element</span> framework for simulating <span class="hlt">Lagrangian</span> sea-ice dynamics at the ice-floe scale, forced by ocean and atmosphere velocity fields. Using this framework, we demonstrate that frictionless contact models based on compressive stiffness alone are unlikely to jam, and describe two different approaches based on friction and tensile strength which both result in increased bulk shear strength of the granular assemblage. The frictionless but cohesive contact model, with certain tensile strength values, can display jamming behavior which on the large scale is very similar to a more complex and realistic model with contact friction and ice-floe rotation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017OcDyn..67.1567C"><span>Laboratory experiment on the 3D tide-induced <span class="hlt">Lagrangian</span> residual current using the PIV technique</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chen, Yang; Jiang, Wensheng; Chen, Xu; Wang, Tao; Bian, Changwei</p> <p>2017-12-01</p> <p>The 3D structure of the tide-induced <span class="hlt">Lagrangian</span> residual current was studied using the particle image velocimetry (PIV) technique in a long shallow narrow tank in the laboratory. At the mouth of the tank, a wave generator was used to make periodic wave which represents the tide movement, and at the head of the tank, a laterally sloping topography with the length of one fifth of the water tank was installed, above which the tide-induced <span class="hlt">Lagrangian</span> residual current was studied. Under the weakly nonlinear condition in the present experiment setup, the results show that the <span class="hlt">Lagrangian</span> residual velocity (LRV) field has a three-layer structure. The residual current flows inwards (towards the head) in the bottom layer and flows outwards in the middle layer, while in the surface layer, it flows inwards along the shallow side of the sloping topography and outwards along the deep side. The depth-averaged and breadth-averaged LRV are also analyzed based on the 3D LRV observations. Our results are in good agreement with the previous experiment studies, the analytical solutions with similar conditions and the observational results in real bays. Moreover, the volume flux comparison between the <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> residual currents shows that the <span class="hlt">Eulerian</span> residual velocity violates the mass conservation law while the LRV truly represents the inter-tidal water transport. This work enriches the laboratory studies of the LRV and offers valuable references for the LRV studies in real bays.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26613354','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26613354"><span>Dredging for dilution: A simulation based case study in a Tidal River.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Bilgili, Ata; Proehl, Jeffrey A; Swift, M Robinson</p> <p>2016-02-01</p> <p>A 2-D hydrodynamic <span class="hlt">finite</span> <span class="hlt">element</span> model with a <span class="hlt">Lagrangian</span> particle module is used to investigate the effects of dredging on the hydrodynamics and the horizontal dilution of pollutant particles originating from a wastewater treatment facility (WWTF) in tidal Oyster River in New Hampshire, USA. The model is driven by the semi-diurnal (M2) tidal component and includes the effect of flooding and drying of riverine mud flats. The particle tracking method consists of tidal advection plus a horizontal random walk model of sub-grid scale turbulent processes. Our approach is to perform continuous pollutant particle releases from the outfall, simulating three different scenarios: a base-case representing the present conditions and two different dredged channel/outfall location configurations. Hydrodynamics are investigated in an <span class="hlt">Eulerian</span> framework and <span class="hlt">Lagrangian</span> particle dilution improvement ratios are calculated for all cases. Results show that the simulated hydrodynamics are consistent with observed conditions. <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> residuals predict an outward path suggesting flushing of pollutants on longer (>M2) time scales. Simulated dilution maps show that, in addition to dredging, the relocation of the WWTF outfall into the dredged main channel is required for increased dilution performance. The methodology presented here can be applied to similar managerial problems in all similar systems worldwide with relatively little effort, with the combination of <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> methods working together towards a better solution. The statistical significance brought into methodology, by using a large number of particles (16000 in this case), is to be emphasized, especially with the growing number of networked parallel computer clusters worldwide. This paper improves on the study presented in Bilgili et al., 2006b, by adding an <span class="hlt">Eulerian</span> analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011CompM..48..307O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011CompM..48..307O"><span>Possibilities of the particle <span class="hlt">finite</span> <span class="hlt">element</span> method for fluid-soil-structure interaction problems</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Oñate, Eugenio; Celigueta, Miguel Angel; Idelsohn, Sergio R.; Salazar, Fernando; Suárez, Benjamín</p> <p>2011-09-01</p> <p>We present some developments in the particle <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM) for analysis of complex coupled problems in mechanics involving fluid-soil-structure interaction (FSSI). The PFEM uses an updated <span class="hlt">Lagrangian</span> description to model the motion of nodes (particles) in both the fluid and the solid domains (the later including soil/rock and structures). A mesh connects the particles (nodes) defining the discretized domain where the governing equations for each of the constituent materials are solved as in the standard FEM. The stabilization for dealing with an incompressibility continuum is introduced via the <span class="hlt">finite</span> calculus method. An incremental iterative scheme for the solution of the non linear transient coupled FSSI problem is described. The procedure to model frictional contact conditions and material erosion at fluid-solid and solid-solid interfaces is described. We present several examples of application of the PFEM to solve FSSI problems such as the motion of rocks by water streams, the erosion of a river bed adjacent to a bridge foundation, the stability of breakwaters and constructions sea waves and the study of landslides.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004PhR...392..279S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004PhR...392..279S"><span><span class="hlt">Lagrangian</span> fluid description with simple applications in compressible plasma and gas dynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schamel, Hans</p> <p>2004-03-01</p> <p>The <span class="hlt">Lagrangian</span> fluid description, in which the dynamics of fluids is formulated in terms of trajectories of fluid <span class="hlt">elements</span>, not only presents an alternative to the more common <span class="hlt">Eulerian</span> description but has its own merits and advantages. This aspect, which seems to be not fully explored yet, is getting increasing attention in fluid dynamics and related areas as <span class="hlt">Lagrangian</span> codes and experimental techniques are developed utilizing the <span class="hlt">Lagrangian</span> point of view with the ultimate goal of a deeper understanding of flow dynamics. In this tutorial review we report on recent progress made in the analysis of compressible, more or less perfect flows such as plasmas and dilute gases. The equations of motion are exploited to get further insight into the formation and evolution of coherent structures, which often exhibit a singular or collapse type behavior occurring in <span class="hlt">finite</span> time. It is argued that this technique of solution has a broad applicability due to the simplicity and generality of equations used. The focus is on four different topics, the physics of which being governed by simple fluid equations subject to initial and/or boundary conditions. Whenever possible also experimental results are mentioned. In the expansion of a semi-infinite plasma into a vacuum the energetic ion peak propagating supersonically towards the vacuum-as seen in laboratory experiments-is interpreted by means of the <span class="hlt">Lagrangian</span> fluid description as a relic of a wave breaking scenario of the corresponding inviscid ion dynamics. The inclusion of viscosity is shown numerically to stabilize the associated density collapse giving rise to a well defined fast ion peak reminiscent of adhesive matter. In purely convection driven flows the <span class="hlt">Lagrangian</span> flow velocity is given by its initial value and hence the <span class="hlt">Lagrangian</span> velocity gradient tensor can be evaluated accurately to find out the appearance of singularities in density and vorticity and the emergence of new structures such as wavelets in one-dimension (1D</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013AIPC.1558...18D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013AIPC.1558...18D"><span>Recent advances in high-order WENO <span class="hlt">finite</span> volume methods for compressible multiphase flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Dumbser, Michael</p> <p>2013-10-01</p> <p>We present two new families of better than second order accurate Godunov-type <span class="hlt">finite</span> volume methods for the solution of nonlinear hyperbolic partial differential equations with nonconservative products. One family is based on a high order Arbitrary-<span class="hlt">Lagrangian-Eulerian</span> (ALE) formulation on moving meshes, which allows to resolve the material contact wave in a very sharp way when the mesh is moved at the speed of the material interface. The other family of methods is based on a high order Adaptive Mesh Refinement (AMR) strategy, where the mesh can be strongly refined in the vicinity of the material interface. Both classes of schemes have several building blocks in common, in particular: a high order WENO reconstruction operator to obtain high order of accuracy in space; the use of an <span class="hlt">element</span>-local space-time Galerkin predictor step which evolves the reconstruction polynomials in time and that allows to reach high order of accuracy in time in one single step; the use of a path-conservative approach to treat the nonconservative terms of the PDE. We show applications of both methods to the Baer-Nunziato model for compressible multiphase flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016IzMat..80.1257T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016IzMat..80.1257T"><span>Special Bohr-Sommerfeld <span class="hlt">Lagrangian</span> submanifolds</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tyurin, N. A.</p> <p>2016-12-01</p> <p>We introduce a new notion in symplectic geometry, that of speciality for <span class="hlt">Lagrangian</span> submanifolds satisfying the Bohr- Sommerfeld condition. We show that it enables one to construct <span class="hlt">finite</span>-dimensional moduli spaces of special Bohr- Sommerfeld <span class="hlt">Lagrangian</span> submanifolds with respect to any ample line bundle on an algebraic variety with a Hodge metric regarded as the symplectic form. This construction can be used to study mirror symmetry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012EGUGA..1412096D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012EGUGA..1412096D"><span>Mean <span class="hlt">Lagrangian</span> drift in continental shelf waves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Drivdal, M.; Weber, J. E. H.</p> <p>2012-04-01</p> <p>The time- and depth-averaged mean drift induced by barotropic continental shelf waves (CSW's) is studied theoretically for idealized shelf topography by calculating the mean volume fluxes to second order in wave amplitude. The waves suffer weak spatial damping due to bottom friction, which leads to radiation stress forcing of the mean fluxes. In terms of the total wave energy density E¯ over the shelf region, the radiation stress tensor component S¯11 for CSW's is found to be different from that of shallow water surface waves in a non-rotating ocean. For CSW's, the ratio ¯S11/¯E depends strongly on the wave number. The mean <span class="hlt">Lagrangian</span> flow forced by the radiation stress can be subdivided into a Stokes drift and a mean <span class="hlt">Eulerian</span> drift current. The magnitude of the latter depends on the ratio between the radiation stress and the bottom stress acting on the mean flow. When the effect of bottom friction acts equally strong on the waves and the mean current, calculations for short CSW's show that the Stokes drift and the friction-dependent wave-induced mean <span class="hlt">Eulerian</span> current varies approximately in anti-phase over the shelf, and that the latter is numerically the largest. For long CSW's they are approximately in phase. In both cases the mean <span class="hlt">Lagrangian</span> current, which is responsible for the net particle drift, has its largest numerical value at the coast on the shallow part of the shelf. Enhancing the effect of bottom friction on the <span class="hlt">Eulerian</span> mean flow, results in a general current speed reduction, as well as a change in spatial structure for long waves. Applying realistic physical parameters for the continental shelf west of Norway, calculations yield along-shelf mean drift velocities for short CSW's that may be important for the transport of biological material, neutral tracers, and underwater plumes of dissolved oil from deep water drilling accidents.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19790002282','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19790002282"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of helicopter structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Rich, M. J.</p> <p>1978-01-01</p> <p>Application of the <span class="hlt">finite</span> <span class="hlt">element</span> analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of <span class="hlt">finite</span> <span class="hlt">element</span> analysis for helicopter structures are projected.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_11");'>11</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li class="active"><span>13</span></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_13 --> <div id="page_14" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="261"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740020296','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740020296"><span>On numerically accurate <span class="hlt">finite</span> <span class="hlt">element</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Nagtegaal, J. C.; Parks, D. M.; Rice, J. R.</p> <p>1974-01-01</p> <p>A general criterion for testing a mesh with topologically similar repeat units is given, and the analysis shows that only a few conventional <span class="hlt">element</span> types and arrangements are, or can be made suitable for computations in the fully plastic range. Further, a new variational principle, which can easily and simply be incorporated into an existing <span class="hlt">finite</span> <span class="hlt">element</span> program, is presented. This allows accurate computations to be made even for <span class="hlt">element</span> designs that would not normally be suitable. Numerical results are given for three plane strain problems, namely pure bending of a beam, a thick-walled tube under pressure, and a deep double edge cracked tensile specimen. The effects of various <span class="hlt">element</span> designs and of the new variational procedure are illustrated. Elastic-plastic computation at <span class="hlt">finite</span> strain are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA079305','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA079305"><span>Recent Developments in Computational Techniques for Applied Hydrodynamics.</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1979-12-07</p> <p>by block number) Numerical Method Fluids Incompressible Flow <span class="hlt">Finite</span> Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. <span class="hlt">Finite</span> - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> - difference techniques suffer, discussed in</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018PhyA..506..350S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018PhyA..506..350S"><span>A new <span class="hlt">Eulerian</span> model for viscous and heat conducting compressible flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Svärd, Magnus</p> <p>2018-09-01</p> <p>In this article, a suite of physically inconsistent properties of the Navier-Stokes equations, associated with the lack of mass diffusion and the definition of velocity, is presented. We show that these inconsistencies are consequences of the <span class="hlt">Lagrangian</span> derivation that models viscous stresses rather than diffusion. A new model for compressible and diffusive (viscous and heat conducting) flows of an ideal gas, is derived in a purely <span class="hlt">Eulerian</span> framework. We propose that these equations supersede the Navier-Stokes equations. A few numerical experiments demonstrate some differences and similarities between the new system and the Navier-Stokes equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017EGUGA..19.1333D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017EGUGA..19.1333D"><span>Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D <span class="hlt">finite-element</span> model with a vertically adaptive mesh</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric</p> <p>2017-04-01</p> <p>Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For <span class="hlt">finite</span> <span class="hlt">element</span> methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary <span class="hlt">Lagrangian-Eulerian</span> (ALE) formulation, the mesh can be adapted to increase the resolution in regions with strong shear or stratification. In such an application, consistency and conservativity must be strictly enforced. SLIM 3D, a discontinuous-Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> model for shallow-water flows (www.climate.be/slim, e.g. Kärnä et al., 2013, Delandmeter et al., 2015), was designed to be strictly consistent and conservative in its discrete formulation. In this context, special care must be paid to the coupling of the external and internal modes of the model and the moving mesh algorithm. In this framework, the mesh can be adapted arbitrarily in the vertical direction. Two moving mesh algorithms were implemented: the first one computes an a-priori optimal mesh; the second one diffuses vertically the mesh (Burchard et al., 2004, Hofmeister et al., 2010). The criteria used to define the optimal mesh and the diffusion function are related to a suitable measure of shear and stratification. We will present in detail the design of the model and how the consistency and conservativity is obtained. Then we will apply it to both idealised benchmarks and the wind-forced thermocline oscillations in Lake Tanganyika (Naithani et al. 2002). References Tuomas Kärnä, Vincent Legat and Eric Deleersnijder. A baroclinic discontinuous Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> model for coastal flows, Ocean Modelling, 61:1-20, 2013. Philippe Delandmeter, Stephen E Lewis, Jonathan Lambrechts, Eric Deleersnijder, Vincent Legat and Eric Wolanski. The transport and fate of riverine fine sediment exported to a semi-open system. Estuarine, Coastal and Shelf Science, 167:336-346, 2015. Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids in</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007SPIE.6707E..0WJ','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007SPIE.6707E..0WJ"><span><span class="hlt">Finite</span> <span class="hlt">element</span> Compton tomography</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jannson, Tomasz; Amouzou, Pauline; Menon, Naresh; Gertsenshteyn, Michael</p> <p>2007-09-01</p> <p>In this paper a new approach to 3D Compton imaging is presented, based on a kind of <span class="hlt">finite</span> <span class="hlt">element</span> (FE) analysis. A window for X-ray incoherent scattering (or Compton scattering) attenuation coefficients is identified for breast cancer diagnosis, for hard X-ray photon energy of 100-300 keV. The point-by-point power/energy budget is computed, based on a 2D array of X-ray pencil beams, scanned vertically. The acceptable medical doses are also computed. The proposed <span class="hlt">finite</span> <span class="hlt">element</span> tomography (FET) can be an alternative to X-ray mammography, tomography, and tomosynthesis. In experiments, 100 keV (on average) X-ray photons are applied, and a new type of pencil beam collimation, based on a Lobster-Eye Lens (LEL), is proposed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29772869','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29772869"><span>[Progression on <span class="hlt">finite</span> <span class="hlt">element</span> modeling method in scoliosis].</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Fan, Ning; Zang, Lei; Hai, Yong; Du, Peng; Yuan, Shuo</p> <p>2018-04-25</p> <p>Scoliosis is a complex spinal three-dimensional malformation with complicated pathogenesis, often associated with complications as thoracic deformity and shoulder imbalance. Because the acquisition of specimen or animal models are difficult, the biomechanical study of scoliosis is limited. In recent years, along with the development of the computer technology, software and image, the technology of establishing a <span class="hlt">finite</span> <span class="hlt">element</span> model of human spine is maturing and it has been providing strong support for the research of pathogenesis of scoliosis, the design and application of brace, and the selection of surgical methods. The <span class="hlt">finite</span> <span class="hlt">element</span> model method is gradually becoming an important tool in the biomechanical study of scoliosis. Establishing a high quality <span class="hlt">finite</span> <span class="hlt">element</span> model is the basis of analysis and future study. However, the <span class="hlt">finite</span> <span class="hlt">element</span> modeling process can be complex and modeling methods are greatly varied. Choosing the appropriate modeling method according to research objectives has become researchers' primary task. In this paper, the author reviews the national and international literature in recent years and concludes the <span class="hlt">finite</span> <span class="hlt">element</span> modeling methods in scoliosis, including data acquisition, establishment of the geometric model, the material properties, parameters setting, the validity of the <span class="hlt">finite</span> <span class="hlt">element</span> model validation and so on. Copyright© 2018 by the China Journal of Orthopaedics and Traumatology Press.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26328583','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26328583"><span>Dissipative inertial transport patterns near coherent <span class="hlt">Lagrangian</span> eddies in the ocean.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Beron-Vera, Francisco J; Olascoaga, María J; Haller, George; Farazmand, Mohammad; Triñanes, Joaquín; Wang, Yan</p> <p>2015-08-01</p> <p>Recent developments in dynamical systems theory have revealed long-lived and coherent <span class="hlt">Lagrangian</span> (i.e., material) eddies in incompressible, satellite-derived surface ocean velocity fields. Paradoxically, observed drifting buoys and floating matter tend to create dissipative-looking patterns near oceanic eddies, which appear to be inconsistent with the conservative fluid particle patterns created by coherent <span class="hlt">Lagrangian</span> eddies. Here, we show that inclusion of inertial effects (i.e., those produced by the buoyancy and size <span class="hlt">finiteness</span> of an object) in a rotating two-dimensional incompressible flow context resolves this paradox. Specifically, we obtain that anticyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) negatively (positively) buoyant <span class="hlt">finite</span>-size particles, while cyclonic coherent <span class="hlt">Lagrangian</span> eddies attract (repel) positively (negatively) buoyant <span class="hlt">finite</span>-size particles. We show how these results explain dissipative-looking satellite-tracked surface drifter and subsurface float trajectories, as well as satellite-derived Sargassum distributions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19840023625&hterms=Anal&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DAnal','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19840023625&hterms=Anal&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3DAnal"><span>Automatic <span class="hlt">finite</span> <span class="hlt">element</span> generators</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wang, P. S.</p> <p>1984-01-01</p> <p>The design and implementation of a software system for generating <span class="hlt">finite</span> <span class="hlt">elements</span> and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and <span class="hlt">element</span> stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/24077258','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/24077258"><span>Dental application of novel <span class="hlt">finite</span> <span class="hlt">element</span> analysis software for three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> modeling of a dentulous mandible from its computed tomography images.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich</p> <p>2013-12-01</p> <p>This study focused on the application of novel <span class="hlt">finite-element</span> analysis software for constructing a <span class="hlt">finite-element</span> model from the computed tomography data of a human dentulous mandible. The <span class="hlt">finite-element</span> model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based <span class="hlt">finite-element</span> analysis software was solely applied to the <span class="hlt">finite-element</span> analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed <span class="hlt">finite-element</span> model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell <span class="hlt">elements</span>. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional <span class="hlt">finite-element</span> model of a dentulous mandible from the computed tomography data without the need for any other software.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29879869','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29879869"><span>Improving <span class="hlt">finite</span> <span class="hlt">element</span> results in modeling heart valve mechanics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Earl, Emily; Mohammadi, Hadi</p> <p>2018-06-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> analysis is a well-established computational tool which can be used for the analysis of soft tissue mechanics. Due to the structural complexity of the leaflet tissue of the heart valve, the currently available <span class="hlt">finite</span> <span class="hlt">element</span> models do not adequately represent the leaflet tissue. A method of addressing this issue is to implement computationally expensive <span class="hlt">finite</span> <span class="hlt">element</span> models, characterized by precise constitutive models including high-order and high-density mesh techniques. In this study, we introduce a novel numerical technique that enhances the results obtained from coarse mesh <span class="hlt">finite</span> <span class="hlt">element</span> models to provide accuracy comparable to that of fine mesh <span class="hlt">finite</span> <span class="hlt">element</span> models while maintaining a relatively low computational cost. Introduced in this study is a method by which the computational expense required to solve linear and nonlinear constitutive models, commonly used in heart valve mechanics simulations, is reduced while continuing to account for large and infinitesimal deformations. This continuum model is developed based on the least square algorithm procedure coupled with the <span class="hlt">finite</span> difference method adhering to the assumption that the components of the strain tensor are available at all nodes of the <span class="hlt">finite</span> <span class="hlt">element</span> mesh model. The suggested numerical technique is easy to implement, practically efficient, and requires less computational time compared to currently available commercial <span class="hlt">finite</span> <span class="hlt">element</span> packages such as ANSYS and/or ABAQUS.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018AIPC.1960g0012E','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018AIPC.1960g0012E"><span>Estimation of the influence of tool wear on force signals: A <span class="hlt">finite</span> <span class="hlt">element</span> approach in AISI 1045 orthogonal cutting</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Equeter, Lucas; Ducobu, François; Rivière-Lorphèvre, Edouard; Abouridouane, Mustapha; Klocke, Fritz; Dehombreux, Pierre</p> <p>2018-05-01</p> <p>Industrial concerns arise regarding the significant cost of cutting tools in machining process. In particular, their improper replacement policy can lead either to scraps, or to early tool replacements, which would waste fine tools. ISO 3685 provides the flank wear end-of-life criterion. Flank wear is also the nominal type of wear for longest tool lifetimes in optimal cutting conditions. Its consequences include bad surface roughness and dimensional discrepancies. In order to aid the replacement decision process, several tool condition monitoring techniques are suggested. Force signals were shown in the literature to be strongly linked with tools flank wear. It can therefore be assumed that force signals are highly relevant for monitoring the condition of cutting tools and providing decision-aid information in the framework of their maintenance and replacement. The objective of this work is to correlate tools flank wear with numerically computed force signals. The present work uses a <span class="hlt">Finite</span> <span class="hlt">Element</span> Model with a Coupled <span class="hlt">Eulerian-Lagrangian</span> approach. The geometry of the tool is changed for different runs of the model, in order to obtain results that are specific to a certain level of wear. The model is assessed by comparison with experimental data gathered earlier on fresh tools. Using the model at constant cutting parameters, force signals under different tool wear states are computed and provide force signals for each studied tool geometry. These signals are qualitatively compared with relevant data from the literature. At this point, no quantitative comparison could be performed on worn tools because the reviewed literature failed to provide similar studies in this material, either numerical or experimental. Therefore, further development of this work should include experimental campaigns aiming at collecting cutting forces signals and assessing the numerical results that were achieved through this work.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20140002508','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20140002508"><span>Very Large Eddy Simulations of a Jet-A Spray Reacting Flow in a Single <span class="hlt">Element</span> LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar DWFDF Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shih, Tsan-Hsing; Liu, Nan-Suey</p> <p>2013-01-01</p> <p>This paper presents the very large eddy simulations (VLES) of a Jet-A spray reacting flow in a single <span class="hlt">element</span> lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the <span class="hlt">Eulerian</span> scalar DWFDF method, in which DWFDF is defined as the density weighted time filtered fine grained probability density function. The flow field is calculated by using the time filtered compressible Navier-Stokes equations (TFNS) with nonlinear subscale turbulence models, and when the <span class="hlt">Eulerian</span> scalar DWFDF method is invoked, the energy and species mass fractions are calculated by solving the equation of DWFDF. A nonlinear subscale model for closing the convection term of the <span class="hlt">Eulerian</span> scalar DWFDF equation is used and will be briefly described in this paper. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar DWFDF method in both improving the simulation quality and maintaining economic computing cost are observed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22809180','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22809180"><span><span class="hlt">Lagrangian</span> motion, coherent structures, and lines of persistent material strain.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Samelson, R M</p> <p>2013-01-01</p> <p><span class="hlt">Lagrangian</span> motion in geophysical fluids may be strongly influenced by coherent structures that support distinct regimes in a given flow. The problems of identifying and demarcating <span class="hlt">Lagrangian</span> regime boundaries associated with dynamical coherent structures in a given velocity field can be studied using approaches originally developed in the context of the abstract geometric theory of ordinary differential equations. An essential insight is that when coherent structures exist in a flow, <span class="hlt">Lagrangian</span> regime boundaries may often be indicated as material curves on which the <span class="hlt">Lagrangian</span>-mean principal-axis strain is large. This insight is the foundation of many numerical techniques for identifying such features in complex observed or numerically simulated ocean flows. The basic theoretical ideas are illustrated with a simple, kinematic traveling-wave model. The corresponding numerical algorithms for identifying candidate <span class="hlt">Lagrangian</span> regime boundaries and lines of principal <span class="hlt">Lagrangian</span> strain (also called <span class="hlt">Lagrangian</span> coherent structures) are divided into parcel and bundle schemes; the latter include the <span class="hlt">finite</span>-time and <span class="hlt">finite</span>-size Lyapunov exponent/<span class="hlt">Lagrangian</span> strain (FTLE/FTLS and FSLE/FSLS) metrics. Some aspects and results of oceanographic studies based on these approaches are reviewed, and the results are discussed in the context of oceanographic observations of dynamical coherent structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.fs.usda.gov/treesearch/pubs/5741','TREESEARCH'); return false;" href="https://www.fs.usda.gov/treesearch/pubs/5741"><span>Nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> modeling of corrugated board</span></a></p> <p><a target="_blank" href="http://www.fs.usda.gov/treesearch/">Treesearch</a></p> <p>A. C. Gilchrist; J. C. Suhling; T. J. Urbanik</p> <p>1999-01-01</p> <p>In this research, an investigation on the mechanical behavior of corrugated board has been performed using <span class="hlt">finite</span> <span class="hlt">element</span> analysis. Numerical <span class="hlt">finite</span> <span class="hlt">element</span> models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1227915','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1227915"><span>Peridynamic Multiscale <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Costa, Timothy; Bond, Stephen D.; Littlewood, David John</p> <p></p> <p>The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic andmore » local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale <span class="hlt">finite</span> <span class="hlt">element</span> methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale <span class="hlt">Finite</span> <span class="hlt">Element</span> Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build <span class="hlt">element</span>-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale <span class="hlt">Finite</span> <span class="hlt">Element</span> Method. Given decades of research and development into <span class="hlt">finite</span> <span class="hlt">element</span> codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/22393117','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/22393117"><span><span class="hlt">Eulerian-Lagrangian</span> analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Umeyama, Motohiko</p> <p>2012-04-13</p> <p>This paper investigates the velocity and the trajectory of water particles under surface waves, which propagate at a constant water depth, using particle image velocimetry (PIV). The vector fields and vertical distributions of velocities are presented at several phases in one wave cycle. The third-order Stokes wave theory was employed to express the physical quantities. The PIV technique's ability to measure both temporal and spatial variations of the velocity was proved after a series of attempts. This technique was applied to the prediction of particle trajectory in an <span class="hlt">Eulerian</span> scheme. Furthermore, the measured particle path was compared with the positions found theoretically by integrating the <span class="hlt">Eulerian</span> velocity to the higher order of a Taylor series expansion. The profile of average travelling distance is also presented with a solution of zero net mass flux in a closed wave flume.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010062151','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010062151"><span>Impact Cratering Calculations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ahrens, Thomas J.</p> <p>2001-01-01</p> <p>This research is computational /theoretical and complements the Caltech experimental program. We have developed an understanding of the basic physical processes and produced computational models and implemented these into <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> codes. The key issues we have addressed include the conditions required for: faulting (strain localization), elastic moduli weakening, dynamic weakening (layering elastic instabilities and fluidization), bulking (creation of porosity at zero pressure) and compaction of pores, frictional melting (creation of pseudotachylytes), partial and selective devolatilization of materials (e.g. CaCO3, water/ice mixtures), and debris flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1014426','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1014426"><span>The Blended <span class="hlt">Finite</span> <span class="hlt">Element</span> Method for Multi-fluid Plasma Modeling</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2016-07-01</p> <p>Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended <span class="hlt">Finite</span> <span class="hlt">Element</span> Method for Multi-fluid Plasma...BLENDED <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> METHOD Blended <span class="hlt">Finite</span> <span class="hlt">Element</span> Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JQSRT.212...59B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JQSRT.212...59B"><span>Vectorial <span class="hlt">finite</span> <span class="hlt">elements</span> for solving the radiative transfer equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.</p> <p>2018-06-01</p> <p>The discrete ordinate method coupled with the <span class="hlt">finite</span> <span class="hlt">element</span> method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard <span class="hlt">finite</span> <span class="hlt">elements</span>, we reformulate the radiative transfer equation using vectorial <span class="hlt">finite</span> <span class="hlt">elements</span>. In comparison to standard <span class="hlt">finite</span> <span class="hlt">elements</span>, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial <span class="hlt">finite</span> <span class="hlt">element</span> discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial <span class="hlt">finite</span> <span class="hlt">element</span> method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19770003308&hterms=inertia+cracked&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dinertia%2Bcracked','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19770003308&hterms=inertia+cracked&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dinertia%2Bcracked"><span><span class="hlt">Finite-element</span> analysis of dynamic fracture</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Aberson, J. A.; Anderson, J. M.; King, W. W.</p> <p>1976-01-01</p> <p>Applications of the <span class="hlt">finite</span> <span class="hlt">element</span> method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a <span class="hlt">finite</span> <span class="hlt">element</span> simulation of rapid crack propagation in an infinite body are discussed.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_12");'>12</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li class="active"><span>14</span></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_14 --> <div id="page_15" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="281"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19870059100&hterms=quality+control&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dquality%2Bcontrol','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19870059100&hterms=quality+control&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dquality%2Bcontrol"><span>Quality assessment and control of <span class="hlt">finite</span> <span class="hlt">element</span> solutions</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, Ahmed K.; Babuska, Ivo</p> <p>1987-01-01</p> <p>Status and some recent developments in the techniques for assessing the reliability of <span class="hlt">finite</span> <span class="hlt">element</span> solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the <span class="hlt">finite</span> <span class="hlt">element</span> solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the <span class="hlt">finite</span> <span class="hlt">element</span> solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20090007598','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20090007598"><span>Ablative Thermal Response Analysis Using the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Dec John A.; Braun, Robert D.</p> <p>2009-01-01</p> <p>A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the <span class="hlt">finite</span> <span class="hlt">element</span> and <span class="hlt">finite</span> difference methods are described. As a first step in developing a three dimensional <span class="hlt">finite</span> <span class="hlt">element</span> based ablative thermal response capability, a one dimensional computer tool has been developed. The <span class="hlt">finite</span> <span class="hlt">element</span> method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the <span class="hlt">element</span> equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016icaa.book..681G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016icaa.book..681G"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Peen Forming Simulation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gariépy, Alexandre; Larose, Simon; Perron, Claude; Bocher, Philippe; Lévesque, Martin</p> <p></p> <p>Shot peening consists of projecting multiple small particles onto a ductile part in order to induce compressive residual stresses near the surface. Peen forming, a derivative of shot peening, is a process that creates an unbalanced stress state which in turn leads to a deformation to shape thin parts. This versatile and cost-effective process is commonly used to manufacture aluminum wing skins and rocket panels. This paper presents the <span class="hlt">finite</span> <span class="hlt">element</span> modelling approach that was developed by the authors to simulate the process. The method relies on shell <span class="hlt">elements</span> and calculated stress profiles and uses an approximation equation to take into account the incremental nature of the process. <span class="hlt">Finite</span> <span class="hlt">element</span> predictions were in good agreement with experimental results for small-scale tests. The method was extended to a hypothetical wing skin model to show its potential applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28989316','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28989316"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cotter, C J; Gottwald, G A; Holm, D D</p> <p>2017-09-01</p> <p>In Holm (Holm 2015 Proc. R. Soc. A 471 , 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880057664&hterms=multitasking&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dmultitasking','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880057664&hterms=multitasking&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dmultitasking"><span>Parallel processing in <span class="hlt">finite</span> <span class="hlt">element</span> structural analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, Ahmed K.</p> <p>1987-01-01</p> <p>A brief review is made of the fundamental concepts and basic issues of parallel processing. Discussion focuses on parallel numerical algorithms, performance evaluation of machines and algorithms, and parallelism in <span class="hlt">finite</span> <span class="hlt">element</span> computations. A computational strategy is proposed for maximizing the degree of parallelism at different levels of the <span class="hlt">finite</span> <span class="hlt">element</span> analysis process including: 1) formulation level (through the use of mixed <span class="hlt">finite</span> <span class="hlt">element</span> models); 2) analysis level (through additive decomposition of the different arrays in the governing equations into the contributions to a symmetrized response plus correction terms); 3) numerical algorithm level (through the use of operator splitting techniques and application of iterative processes); and 4) implementation level (through the effective combination of vectorization, multitasking and microtasking, whenever available).</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840007526','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840007526"><span>The GPRIME approach to <span class="hlt">finite</span> <span class="hlt">element</span> modeling</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Wallace, D. R.; Mckee, J. H.; Hurwitz, M. M.</p> <p>1983-01-01</p> <p>GPRIME, an interactive modeling system, runs on the CDC 6000 computers and the DEC VAX 11/780 minicomputer. This system includes three components: (1) GPRIME, a user friendly geometric language and a processor to translate that language into geometric entities, (2) GGEN, an interactive data generator for 2-D models; and (3) SOLIDGEN, a 3-D solid modeling program. Each component has a computer user interface of an extensive command set. All of these programs make use of a comprehensive B-spline mathematics subroutine library, which can be used for a wide variety of interpolation problems and other geometric calculations. Many other user aids, such as automatic saving of the geometric and <span class="hlt">finite</span> <span class="hlt">element</span> data bases and hidden line removal, are available. This interactive <span class="hlt">finite</span> <span class="hlt">element</span> modeling capability can produce a complete <span class="hlt">finite</span> <span class="hlt">element</span> model, producing an output file of grid and <span class="hlt">element</span> data.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740006509','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740006509"><span>An interactive graphics system to facilitate <span class="hlt">finite</span> <span class="hlt">element</span> structural analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Burk, R. C.; Held, F. H.</p> <p>1973-01-01</p> <p>The characteristics of an interactive graphics systems to facilitate the <span class="hlt">finite</span> <span class="hlt">element</span> method of structural analysis are described. The <span class="hlt">finite</span> <span class="hlt">element</span> model analysis consists of three phases: (1) preprocessing (model generation), (2) problem solution, and (3) postprocessing (interpretation of results). The advantages of interactive graphics to <span class="hlt">finite</span> <span class="hlt">element</span> structural analysis are defined.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012CompM..50..789Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012CompM..50..789Y"><span>Immersed smoothed <span class="hlt">finite</span> <span class="hlt">element</span> method for fluid-structure interaction simulation of aortic valves</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yao, Jianyao; Liu, G. R.; Narmoneva, Daria A.; Hinton, Robert B.; Zhang, Zhi-Qian</p> <p>2012-12-01</p> <p>This paper presents a novel numerical method for simulating the fluid-structure interaction (FSI) problems when blood flows over aortic valves. The method uses the immersed boundary/<span class="hlt">element</span> method and the smoothed <span class="hlt">finite</span> <span class="hlt">element</span> method and hence it is termed as IS-FEM. The IS-FEM is a partitioned approach and does not need a body-fitted mesh for FSI simulations. It consists of three main modules: the fluid solver, the solid solver and the FSI force solver. In this work, the blood is modeled as incompressible viscous flow and solved using the characteristic-based-split scheme with FEM for spacial discretization. The leaflets of the aortic valve are modeled as Mooney-Rivlin hyperelastic materials and solved using smoothed <span class="hlt">finite</span> <span class="hlt">element</span> method (or S-FEM). The FSI force is calculated on the <span class="hlt">Lagrangian</span> fictitious fluid mesh that is identical to the moving solid mesh. The octree search and neighbor-to-neighbor schemes are used to detect efficiently the FSI pairs of fluid and solid cells. As an example, a 3D idealized model of aortic valve is modeled, and the opening process of the valve is simulated using the proposed IS-FEM. Numerical results indicate that the IS-FEM can serve as an efficient tool in the study of aortic valve dynamics to reveal the details of stresses in the aortic valves, the flow velocities in the blood, and the shear forces on the interfaces. This tool can also be applied to animal models studying disease processes and may ultimately translate to a new adaptive methods working with magnetic resonance images, leading to improvements on diagnostic and prognostic paradigms, as well as surgical planning, in the care of patients.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930065024&hterms=fashion+models&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfashion%2Bmodels','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930065024&hterms=fashion+models&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfashion%2Bmodels"><span>Updating <span class="hlt">finite</span> <span class="hlt">element</span> dynamic models using an <span class="hlt">element-by-element</span> sensitivity methodology</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Farhat, Charbel; Hemez, Francois M.</p> <p>1993-01-01</p> <p>A sensitivity-based methodology for improving the <span class="hlt">finite</span> <span class="hlt">element</span> model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the <span class="hlt">finite</span> <span class="hlt">element</span> model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an <span class="hlt">element-by-element</span> fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920006444','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920006444"><span>Optimal least-squares <span class="hlt">finite</span> <span class="hlt">element</span> method for elliptic problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jiang, Bo-Nan; Povinelli, Louis A.</p> <p>1991-01-01</p> <p>An optimal least squares <span class="hlt">finite</span> <span class="hlt">element</span> method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares <span class="hlt">finite</span> <span class="hlt">element</span> method. In the usual least squares <span class="hlt">finite</span> <span class="hlt">element</span> method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares <span class="hlt">finite</span> <span class="hlt">element</span> method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880009731','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880009731"><span><span class="hlt">Finite</span> <span class="hlt">element</span> meshing of ANSYS (trademark) solid models</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kelley, F. S.</p> <p>1987-01-01</p> <p>A large scale, general purpose <span class="hlt">finite</span> <span class="hlt">element</span> computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive <span class="hlt">finite</span> <span class="hlt">element</span> model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/332738','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/332738"><span>An 8-node tetrahedral <span class="hlt">finite</span> <span class="hlt">element</span> suitable for explicit transient dynamic simulations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Key, S.W.; Heinstein, M.W.; Stone, C.M.</p> <p>1997-12-31</p> <p>Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral <span class="hlt">finite</span> <span class="hlt">elements</span>. Today the <span class="hlt">element</span> is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral <span class="hlt">finite</span> <span class="hlt">element</span> is a notoriously poor performer, and the 10-node quadratic tetrahedral <span class="hlt">finite</span> <span class="hlt">element</span> while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral <span class="hlt">finite</span> <span class="hlt">element</span> (a four-node tetrahedral <span class="hlt">finite</span> elementmore » enriched with four midface nodal points). The derivation of the <span class="hlt">element`s</span> gradient operator, studies in obtaining a suitable mass lumping and the <span class="hlt">element`s</span> performance in applications are presented. In particular, they examine the 80node tetrahedral <span class="hlt">finite</span> <span class="hlt">element`s</span> behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The <span class="hlt">element</span> only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral <span class="hlt">finite</span> <span class="hlt">element</span>. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral <span class="hlt">finite</span> <span class="hlt">element</span> is a suitable replacement for the 8-node hexahedral <span class="hlt">finite</span> <span class="hlt">element</span> and handbuilt meshes.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940009400','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940009400"><span>Variational approach to probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.</p> <p>1991-01-01</p> <p>Probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> methods (PFEM), synthesizing the power of <span class="hlt">finite</span> <span class="hlt">element</span> methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in <span class="hlt">finite</span> <span class="hlt">element</span> methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1991nwu..rept.....B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1991nwu..rept.....B"><span>Variational approach to probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.</p> <p>1991-08-01</p> <p>Probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> methods (PFEM), synthesizing the power of <span class="hlt">finite</span> <span class="hlt">element</span> methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in <span class="hlt">finite</span> <span class="hlt">element</span> methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870019779','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870019779"><span>Variational approach to probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.</p> <p>1987-01-01</p> <p>Probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM), synthesizing the power of <span class="hlt">finite</span> <span class="hlt">element</span> methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in <span class="hlt">finite</span> <span class="hlt">element</span> methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970001271','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970001271"><span>Verification of Orthogrid <span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling Techniques</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Steeve, B. E.</p> <p>1996-01-01</p> <p>The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using <span class="hlt">finite</span> <span class="hlt">elements</span>. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The <span class="hlt">finite</span> <span class="hlt">element</span> models include a beam, shell, and mixed beam and shell <span class="hlt">element</span> model. Results show that the shell <span class="hlt">element</span> model performs the best, but that the simpler beam and beam and shell <span class="hlt">element</span> models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19860027687&hterms=divided+attention&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Ddivided%2Battention','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19860027687&hterms=divided+attention&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Ddivided%2Battention"><span><span class="hlt">Finite</span> <span class="hlt">element</span> methods on supercomputers - The scatter-problem</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Loehner, R.; Morgan, K.</p> <p>1985-01-01</p> <p>Certain problems arise in connection with the use of supercomputers for the implementation of <span class="hlt">finite-element</span> methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the <span class="hlt">finite-element</span> method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of <span class="hlt">finite-element</span> programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=5627383"><span>Stochastic partial differential fluid equations as a diffusive limit of deterministic <span class="hlt">Lagrangian</span> multi-time dynamics</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Cotter, C. J.</p> <p>2017-01-01</p> <p>In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic <span class="hlt">Lagrangian</span> particle dynamics. Here we show that the same stochastic <span class="hlt">Lagrangian</span> dynamics naturally arises in a multi-scale decomposition of the deterministic <span class="hlt">Lagrangian</span> flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the <span class="hlt">Eulerian</span> formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow. PMID:28989316</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1429643-nonlocal-mixed-locality-multiscale-finite-element-methods','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1429643-nonlocal-mixed-locality-multiscale-finite-element-methods"><span>Nonlocal and Mixed-Locality Multiscale <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Costa, Timothy B.; Bond, Stephen D.; Littlewood, David J.</p> <p>2018-03-27</p> <p>In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, inmore » this study, we present the first work toward application of the multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale <span class="hlt">finite</span> <span class="hlt">element</span> methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1429643-nonlocal-mixed-locality-multiscale-finite-element-methods','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1429643-nonlocal-mixed-locality-multiscale-finite-element-methods"><span>Nonlocal and Mixed-Locality Multiscale <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Costa, Timothy B.; Bond, Stephen D.; Littlewood, David J.</p> <p></p> <p>In many applications the resolution of small-scale heterogeneities remains a significant hurdle to robust and reliable predictive simulations. In particular, while material variability at the mesoscale plays a fundamental role in processes such as material failure, the resolution required to capture mechanisms at this scale is often computationally intractable. Multiscale methods aim to overcome this difficulty through judicious choice of a subscale problem and a robust manner of passing information between scales. One promising approach is the multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method, which increases the fidelity of macroscale simulations by solving lower-scale problems that produce enriched multiscale basis functions. Here, inmore » this study, we present the first work toward application of the multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method to the nonlocal peridynamic theory of solid mechanics. This is achieved within the context of a discontinuous Galerkin framework that facilitates the description of material discontinuities and does not assume the existence of spatial derivatives. Analysis of the resulting nonlocal multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method is achieved using the ambulant Galerkin method, developed here with sufficient generality to allow for application to multiscale <span class="hlt">finite</span> <span class="hlt">element</span> methods for both local and nonlocal models that satisfy minimal assumptions. Finally, we conclude with preliminary results on a mixed-locality multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method in which a nonlocal model is applied at the fine scale and a local model at the coarse scale.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_13");'>13</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li class="active"><span>15</span></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_15 --> <div id="page_16" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="301"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000085863','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000085863"><span>Validation of High Displacement Piezoelectric Actuator <span class="hlt">Finite</span> <span class="hlt">Element</span> Models</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Taleghani, B. K.</p> <p>2000-01-01</p> <p>The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) <span class="hlt">finite</span> <span class="hlt">element</span> codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, <span class="hlt">finite</span> <span class="hlt">element</span> models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric <span class="hlt">finite</span> <span class="hlt">elements</span>. The results of <span class="hlt">finite</span> <span class="hlt">element</span> models were validated by using the experimental results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016RMRE...49.4441T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016RMRE...49.4441T"><span>Dynamic Analysis of Tunnel in Weathered Rock Subjected to Internal Blast Loading</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tiwari, Rohit; Chakraborty, Tanusree; Matsagar, Vasant</p> <p>2016-11-01</p> <p>The present study deals with three-dimensional nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> (FE) analyses of a tunnel in rock with reinforced concrete (RC) lining subjected to internal blast loading. The analyses have been performed using the coupled <span class="hlt">Eulerian-Lagrangian</span> analysis tool available in FE software Abaqus/Explicit. Rock and RC lining are modeled using three-dimensional <span class="hlt">Lagrangian</span> <span class="hlt">elements</span>. Beam <span class="hlt">elements</span> have been used to model reinforcement in RC lining. Three different rock types with different weathering conditions have been used to understand the response of rock when subjected to blast load. The trinitrotoluene (TNT) explosive and surrounding air have been modeled using the <span class="hlt">Eulerian</span> <span class="hlt">elements</span>. The Drucker-Prager plasticity model with strain rate-dependent material properties has been used to simulate the stress-strain response of rock. The concrete damaged plasticity model and Johnson-Cook plasticity model have been used for the simulation of stress-strain response of concrete and steel, respectively. The explosive (TNT) has been modeled using Jones-Wilkins-Lee (JWL) equation of state. The analysis results have been studied for stresses, deformation and damage of RC lining and the surrounding rock. It is observed that damage in RC lining results in higher stress in rock. Rocks with low modulus and high weathering conditions show higher attenuation of shock wave. Higher amount of ground shock wave propagation is observed in case of less weathered rock. Ground heave is observed under blast loading for tunnel close to ground surface.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900035993&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DLagrangian"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary-layer separation. I - General theory</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Van Dommelen, Leon L.; Cowley, Stephen J.</p> <p>1990-01-01</p> <p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid <span class="hlt">element</span> inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2014CompM..54..123S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2014CompM..54..123S"><span>A particle <span class="hlt">finite</span> <span class="hlt">element</span> method for machining simulations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sabel, Matthias; Sator, Christian; Müller, Ralf</p> <p>2014-07-01</p> <p>The particle <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable <span class="hlt">finite</span> <span class="hlt">element</span> formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard <span class="hlt">finite</span> <span class="hlt">element</span> method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine <span class="hlt">finite</span> <span class="hlt">element</span> discretisation) leads to converged results of process parameters, such as the cutting force.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20120013786','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20120013786"><span>Simulations of Spray Reacting Flows in a Single <span class="hlt">Element</span> LDI Injector With and Without Invoking an <span class="hlt">Eulerian</span> Scalar PDF Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shih, Tsan-Hsing; Liu, Nan-Suey</p> <p>2012-01-01</p> <p>This paper presents the numerical simulations of the Jet-A spray reacting flow in a single <span class="hlt">element</span> lean direct injection (LDI) injector by using the National Combustion Code (NCC) with and without invoking the <span class="hlt">Eulerian</span> scalar probability density function (PDF) method. The flow field is calculated by using the Reynolds averaged Navier-Stokes equations (RANS and URANS) with nonlinear turbulence models, and when the scalar PDF method is invoked, the energy and compositions or species mass fractions are calculated by solving the equation of an ensemble averaged density-weighted fine-grained probability density function that is referred to here as the averaged probability density function (APDF). A nonlinear model for closing the convection term of the scalar APDF equation is used in the presented simulations and will be briefly described. Detailed comparisons between the results and available experimental data are carried out. Some positive findings of invoking the <span class="hlt">Eulerian</span> scalar PDF method in both improving the simulation quality and reducing the computing cost are observed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015CompM..55.1091B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015CompM..55.1091B"><span>A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the Particle <span class="hlt">Finite</span> <span class="hlt">Element</span> Method with fixed mesh</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Becker, P.; Idelsohn, S. R.; Oñate, E.</p> <p>2015-06-01</p> <p>This paper describes a strategy to solve multi-fluid and fluid-structure interaction (FSI) problems using <span class="hlt">Lagrangian</span> particles combined with a fixed <span class="hlt">finite</span> <span class="hlt">element</span> (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2-2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1022784','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1022784"><span>Wave Scattering in Heterogeneous Media using the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2016-10-21</p> <p>AFRL-AFOSR-JP-TR-2016-0086 Wave Scattering in Heterogeneous Media using the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method Chiruvai Vendhan INDIAN INSTITUTE OF TECHNOLOGY...Scattering in Heterogeneous Media using the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method 5a.  CONTRACT NUMBER 5b.  GRANT NUMBER FA2386-12-1-4026 5c.  PROGRAM <span class="hlt">ELEMENT</span> NUMBER 61102F 6...14.  ABSTRACT The primary aim of this study is to develop a <span class="hlt">finite</span> <span class="hlt">element</span> model for elastic scattering by axisymmetric bodies submerged in a</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19770003411','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19770003411"><span>Application of <span class="hlt">finite</span> <span class="hlt">element</span> approach to transonic flow problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hafez, M. M.; Murman, E. M.; Wellford, L. C., Jr.</p> <p>1976-01-01</p> <p>A variational <span class="hlt">finite</span> <span class="hlt">element</span> model for transonic small disturbance calculations is described. Different strategy is adopted in subsonic and supersonic regions, and blending <span class="hlt">elements</span> are introduced between different regions. In the supersonic region, no upstream effect is allowed. If rectangular <span class="hlt">elements</span> with linear shape functions are used, the model is similar to Murman's <span class="hlt">finite</span> difference operators. Higher order shape functions, nonrectangular <span class="hlt">elements</span>, and discontinuous approximation of shock waves are also discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29350015','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29350015"><span>[Application of <span class="hlt">finite</span> <span class="hlt">element</span> method in spinal biomechanics].</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei</p> <p>2017-02-25</p> <p>The <span class="hlt">finite</span> <span class="hlt">element</span> model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the <span class="hlt">finite</span> <span class="hlt">element</span> is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. <span class="hlt">Finite</span> <span class="hlt">element</span> method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's <span class="hlt">finite</span> <span class="hlt">element</span>.Although <span class="hlt">finite</span> <span class="hlt">element</span> method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900007758','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900007758"><span>Optimum <span class="hlt">element</span> density studies for <span class="hlt">finite-element</span> thermal analysis of hypersonic aircraft structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ko, William L.; Olona, Timothy; Muramoto, Kyle M.</p> <p>1990-01-01</p> <p>Different <span class="hlt">finite</span> <span class="hlt">element</span> models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. <span class="hlt">Element</span> density criteria are established for the <span class="hlt">finite</span> <span class="hlt">element</span> thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different <span class="hlt">finite</span> <span class="hlt">element</span> models having different <span class="hlt">element</span> densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established <span class="hlt">element</span> density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density <span class="hlt">elements</span> for transient thermal analysis is possible if a CPU optimization technique was used.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=48361&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50','EPA-EIMS'); return false;" href="https://cfpub.epa.gov/si/si_public_record_report.cfm?dirEntryId=48361&Lab=ORD&keyword=finite+AND+element&actType=&TIMSType=+&TIMSSubTypeID=&DEID=&epaNumber=&ntisID=&archiveStatus=Both&ombCat=Any&dateBeginCreated=&dateEndCreated=&dateBeginPublishedPresented=&dateEndPublishedPresented=&dateBeginUpdated=&dateEndUpdated=&dateBeginCompleted=&dateEndCompleted=&personID=&role=Any&journalID=&publisherID=&sortBy=revisionDate&count=50"><span><span class="hlt">FINITE-ELEMENT</span> ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS</span></a></p> <p><a target="_blank" href="http://oaspub.epa.gov/eims/query.page">EPA Science Inventory</a></p> <p></p> <p></p> <p>A <span class="hlt">finite-element</span> model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the <span class="hlt">finite-element</span> formulation corresponding to the coupled differential equation...</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......215H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......215H"><span><span class="hlt">Eulerian</span> Formulation of Spatially Constrained Elastic Rods</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Huynen, Alexandre</p> <p></p> <p>Slender elastic rods are ubiquitous in nature and technology. For a vast majority of applications, the rod deflection is restricted by an external constraint and a significant part of the elastic body is in contact with a stiff constraining surface. The research work presented in this doctoral dissertation formulates a computational model for the solution of elastic rods constrained inside or around frictionless tube-like surfaces. The segmentation strategy adopted to cope with this complex class of problems consists in sequencing the global problem into, comparatively simpler, elementary problems either in continuous contact with the constraint or contact-free between their extremities. Within the conventional <span class="hlt">Lagrangian</span> formulation of elastic rods, this approach is however associated with two major drawbacks. First, the boundary conditions specifying the locations of the rod centerline at both extremities of each elementary problem lead to the establishment of isoperimetric constraints, i.e., integral constraints on the unknown length of the rod. Second, the assessment of the unilateral contact condition requires, in principle, the comparison of two curves parametrized by distinct curvilinear coordinates, viz. the rod centerline and the constraint axis. Both conspire to burden the computations associated with the method. To streamline the solution along the elementary problems and rationalize the assessment of the unilateral contact condition, the rod governing equations are reformulated within the <span class="hlt">Eulerian</span> framework of the constraint. The methodical exploration of both types of elementary problems leads to specific formulations of the rod governing equations that stress the profound connection between the mechanics of the rod and the geometry of the constraint surface. The proposed <span class="hlt">Eulerian</span> reformulation, which restates the rod local equilibrium in terms of the curvilinear coordinate associated with the constraint axis, describes the rod deformed configuration</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017CompM..60..181L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017CompM..60..181L"><span>An enriched <span class="hlt">finite</span> <span class="hlt">element</span> method to fractional advection-diffusion equation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam</p> <p>2017-08-01</p> <p>In this paper, an enriched <span class="hlt">finite</span> <span class="hlt">element</span> method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional <span class="hlt">element</span> Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched <span class="hlt">finite</span> <span class="hlt">element</span> method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040070719','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040070719"><span>Global-Local <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis of Bonded Single-Lap Joints</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.</p> <p>2004-01-01</p> <p>Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the <span class="hlt">finite</span> <span class="hlt">element</span> method is well suited to model the bonded lap joints, traditional <span class="hlt">finite</span> <span class="hlt">elements</span> are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a <span class="hlt">finite</span> <span class="hlt">element</span> technique utilizing a global (special) <span class="hlt">element</span> coupled with traditional <span class="hlt">elements</span>. The global <span class="hlt">element</span> includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA093401','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA093401"><span>The Constraint Method for Solid <span class="hlt">Finite</span> <span class="hlt">Elements</span>.</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1980-09-30</p> <p>9. ’Hierarchical Approximation in <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis", by I. Norman Katz, International Symposium on Innovative Numerical Analysis In Applied ... Engineering Science, Versailles, France, May 23-27, 1977. 10. "Efficient Generation of Hierarchal <span class="hlt">Finite</span> Elamnts Through the Use of Precomputed Arrays</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29892139','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29892139"><span>Functional Data Approximation on Bounded Domains using Polygonal <span class="hlt">Finite</span> <span class="hlt">Elements</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit</p> <p>2018-07-01</p> <p>We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric <span class="hlt">finite</span> <span class="hlt">elements</span>, and particularly quadratic serendipity <span class="hlt">elements</span> for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity <span class="hlt">finite</span> <span class="hlt">elements</span> through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity <span class="hlt">elements</span> have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity <span class="hlt">finite</span> <span class="hlt">elements</span> on polygonal domains versus traditional <span class="hlt">finite</span> <span class="hlt">elements</span> over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity <span class="hlt">finite</span> <span class="hlt">elements</span> obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960001867','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960001867"><span>Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.</p> <p>1995-01-01</p> <p>A thin film draining on an inclined plate has been studied numerically using <span class="hlt">finite</span> <span class="hlt">element</span> method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19820012687','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19820012687"><span>Application of the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method to Rotary Wing Aeroelasticity</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Straub, F. K.; Friedmann, P. P.</p> <p>1982-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the <span class="hlt">finite</span> <span class="hlt">element</span> equations is based on weighted Galerkin residuals. This Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method are studied numerically by refining the discretization process. Results indicate that four or five <span class="hlt">elements</span> suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20160006300','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20160006300"><span>Scalable Implementation of <span class="hlt">Finite</span> <span class="hlt">Elements</span> by NASA _ Implicit (ScIFEi)</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.</p> <p>2016-01-01</p> <p>Scalable Implementation of <span class="hlt">Finite</span> <span class="hlt">Elements</span> by NASA (ScIFEN) is a parallel <span class="hlt">finite</span> <span class="hlt">element</span> analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of <span class="hlt">finite</span> <span class="hlt">element</span> types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to <span class="hlt">finite</span> <span class="hlt">element</span> analysis using a commercial code.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AIPC.1890d0118W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AIPC.1890d0118W"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis (FEA) analysis of the preflex beam</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wan, Lijuan; Gao, Qilang</p> <p>2017-10-01</p> <p>The development of <span class="hlt">finite</span> <span class="hlt">element</span> analysis (FEA) has been relatively mature, and is one of the important means of structural analysis. This method changes the problem that the research of complex structure in the past needs to be done by a large number of experiments. Through the <span class="hlt">finite</span> <span class="hlt">element</span> method, the numerical simulation of the structure can be used to achieve a variety of static and dynamic simulation analysis of the mechanical problems, it is also convenient to study the parameters of the structural parameters. Combined with a certain number of experiments to verify the simulation model can be completed in the past all the needs of experimental research. The nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> method is used to simulate the flexural behavior of the prestressed composite beams with corrugated steel webs. The <span class="hlt">finite</span> <span class="hlt">element</span> analysis is used to understand the mechanical properties of the structure under the action of bending load.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_14");'>14</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li class="active"><span>16</span></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_16 --> <div id="page_17" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="321"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70012388','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70012388"><span>Littoral transport in the surf zone elucidated by an <span class="hlt">Eulerian</span> sediment tracer.</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Duane, D.B.; James, W.R.</p> <p>1980-01-01</p> <p>An <span class="hlt">Eulerian</span>, or time integration, sand tracer experiment was designed and carried out in the surf zone near Pt. Mugu, California on April 19, 1972. Data indicate that conditions of stationarity and <span class="hlt">finite</span> boundaries required for proper application of <span class="hlt">Eulerian</span> tracer theory exist for short time periods in the surf zone. Grain counts suggest time required for tracer sand to attain equilibrium concentration is on the order of 30-60 minutes. Grain counts also indicate transport (discharge) was strongly dependent upon grain size, with the maximum rate occurring in the size 2.5-2.75 phi, decreasing to both finer and coarser sizes. The measured instantaneous transport was at the annual rate of 2.4 x 106 m3/yr.- Authors</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28376059','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28376059"><span>Skeletal assessment with <span class="hlt">finite</span> <span class="hlt">element</span> analysis: relevance, pitfalls and interpretation.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Campbell, Graeme Michael; Glüer, Claus-C</p> <p>2017-07-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> models simulate the mechanical response of bone under load, enabling noninvasive assessment of strength. Models generated from quantitative computed tomography (QCT) incorporate the geometry and spatial distribution of bone mineral density (BMD) to simulate physiological and traumatic loads as well as orthopaedic implant behaviour. The present review discusses the current strengths and weakness of <span class="hlt">finite</span> <span class="hlt">element</span> models for application to skeletal biomechanics. In cadaver studies, <span class="hlt">finite</span> <span class="hlt">element</span> models provide better estimations of strength compared to BMD. Data from clinical studies are encouraging; however, the superiority of <span class="hlt">finite</span> <span class="hlt">element</span> models over BMD measures for fracture prediction has not been shown conclusively, and may be sex and site dependent. Therapeutic effects on bone strength are larger than for BMD; however, model validation has only been performed on untreated bone. High-resolution modalities and novel image processing methods may enhance the structural representation and predictive ability. Despite extensive use of <span class="hlt">finite</span> <span class="hlt">element</span> models to study orthopaedic implant stability, accurate simulation of the bone-implant interface and fracture progression remains a significant challenge. Skeletal <span class="hlt">finite</span> <span class="hlt">element</span> models provide noninvasive assessments of strength and implant stability. Improved structural representation and implant surface interaction may enable more accurate models of fragility in the future.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017AGUFMOS41B..06L"><span>A Skill Score of Trajectory Model Evaluation Using Reinitialized Series of Normalized Cumulative <span class="hlt">Lagrangian</span> Separation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Y.; Weisberg, R. H.</p> <p>2017-12-01</p> <p>The <span class="hlt">Lagrangian</span> separation distance between the endpoints of simulated and observed drifter trajectories is often used to assess the performance of numerical particle trajectory models. However, the separation distance fails to indicate relative model performance in weak and strong current regions, such as a continental shelf and its adjacent deep ocean. A skill score is proposed based on the cumulative <span class="hlt">Lagrangian</span> separation distances normalized by the associated cumulative trajectory lengths. The new metrics correctly indicates the relative performance of the Global HYCOM in simulating the strong currents of the Gulf of Mexico Loop Current and the weaker currents of the West Florida Shelf in the eastern Gulf of Mexico. In contrast, the <span class="hlt">Lagrangian</span> separation distance alone gives a misleading result. Also, the observed drifter position series can be used to reinitialize the trajectory model and evaluate its performance along the observed trajectory, not just at the drifter end position. The proposed dimensionless skill score is particularly useful when the number of drifter trajectories is limited and neither a conventional <span class="hlt">Eulerian</span>-based velocity nor a <span class="hlt">Lagrangian</span>-based probability density function may be estimated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19990046090','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19990046090"><span>Non-Linear <span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling of THUNDER Piezoelectric Actuators</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Taleghani, Barmac K.; Campbell, Joel F.</p> <p>1999-01-01</p> <p>A NASTRAN non-linear <span class="hlt">finite</span> <span class="hlt">element</span> model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the <span class="hlt">finite</span> <span class="hlt">element</span> model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN <span class="hlt">finite</span> <span class="hlt">element</span> model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890014450','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890014450"><span>On the <span class="hlt">Lagrangian</span> description of unsteady boundary layer separation. Part 1: General theory</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Vandommelen, Leon L.; Cowley, Stephen J.</p> <p>1989-01-01</p> <p>Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of <span class="hlt">Eulerian</span> coordinates, a <span class="hlt">Lagrangian</span> approach may have significant analytical and computational advantages. In <span class="hlt">Lagrangian</span> coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid <span class="hlt">element</span> inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19840023619&hterms=slaves&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dslaves','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19840023619&hterms=slaves&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Dslaves"><span>Slave <span class="hlt">finite</span> <span class="hlt">elements</span>: The temporal <span class="hlt">element</span> approach to nonlinear analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gellin, S.</p> <p>1984-01-01</p> <p>A formulation method for <span class="hlt">finite</span> <span class="hlt">elements</span> in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the <span class="hlt">element</span> domain, and only explicit integration over space and time. While applications are general, the plate and shell <span class="hlt">elements</span> that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20010032392','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20010032392"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis of Reverberation Chambers</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bunting, Charles F.; Nguyen, Duc T.</p> <p>2000-01-01</p> <p>The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of <span class="hlt">finite</span> <span class="hlt">element</span> analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of <span class="hlt">finite</span> <span class="hlt">element</span> techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing <span class="hlt">finite</span> <span class="hlt">element</span> techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the <span class="hlt">finite</span> <span class="hlt">element</span> analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19820015607','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19820015607"><span>Evaluation of an improved <span class="hlt">finite-element</span> thermal stress calculation technique</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Camarda, C. J.</p> <p>1982-01-01</p> <p>A procedure for generating accurate thermal stresses with coarse <span class="hlt">finite</span> <span class="hlt">element</span> grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the <span class="hlt">finite</span> <span class="hlt">element</span> and the second due to the local variation of the temperature in the <span class="hlt">element</span>. The first contribution can be accurately predicted with a coarse <span class="hlt">finite-element</span> mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse <span class="hlt">finite</span> <span class="hlt">element</span> structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR <span class="hlt">finite</span> <span class="hlt">element</span> program. Results are obtained for rods, membranes, a box beam and a stiffened panel.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics"><span>A multi-scale residual-based anti-hourglass control for compatible staggered <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich</p> <p></p> <p>Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of <span class="hlt">Lagrangian</span> methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible <span class="hlt">Lagrangian</span> methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the <span class="hlt">finite</span> <span class="hlt">element</span> approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1408834-multi-scale-residual-based-anti-hourglass-control-compatible-staggered-lagrangian-hydrodynamics"><span>A multi-scale residual-based anti-hourglass control for compatible staggered <span class="hlt">Lagrangian</span> hydrodynamics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Kucharik, M.; Scovazzi, Guglielmo; Shashkov, Mikhail Jurievich; ...</p> <p>2017-10-28</p> <p>Hourglassing is a well-known pathological numerical artifact affecting the robustness and accuracy of <span class="hlt">Lagrangian</span> methods. There exist a large number of hourglass control/suppression strategies. In the community of the staggered compatible <span class="hlt">Lagrangian</span> methods, the approach of sub-zonal pressure forces is among the most widely used. However, this approach is known to add numerical strength to the solution, which can cause potential problems in certain types of simulations, for instance in simulations of various instabilities. To avoid this complication, we have adapted the multi-scale residual-based stabilization typically used in the <span class="hlt">finite</span> <span class="hlt">element</span> approach for staggered compatible framework. In this study, wemore » describe two discretizations of the new approach and demonstrate their properties and compare with the method of sub-zonal pressure forces on selected numerical problems.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19730045391&hterms=armen&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Darmen','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19730045391&hterms=armen&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D30%26Ntt%3Darmen"><span>Plasticity - Theory and <span class="hlt">finite</span> <span class="hlt">element</span> applications.</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Armen, H., Jr.; Levine, H. S.</p> <p>1972-01-01</p> <p>A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the <span class="hlt">finite-element</span> method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The <span class="hlt">finite-element</span> analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19780011858&hterms=concept+accounting&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dconcept%2Baccounting','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19780011858&hterms=concept+accounting&qs=N%3D0%26Ntk%3DAll%26Ntx%3Dmode%2Bmatchall%26Ntt%3Dconcept%2Baccounting"><span><span class="hlt">Finite</span> <span class="hlt">element</span> concepts in computational aerodynamics</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Baker, A. J.</p> <p>1978-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the <span class="hlt">finite</span> <span class="hlt">element</span> concept for computational aerodynamics is made.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018EPJWC.17303010G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018EPJWC.17303010G"><span>High-Accuracy <span class="hlt">Finite</span> <span class="hlt">Element</span> Method: Benchmark Calculations</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel</p> <p>2018-02-01</p> <p>We describe a new high-accuracy <span class="hlt">finite</span> <span class="hlt">element</span> scheme with simplex <span class="hlt">elements</span> for solving the elliptic boundary-value problems and show its efficiency on benchmark solutions of the Helmholtz equation for the triangle membrane and hypercube.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017MS%26E..274a2096D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017MS%26E..274a2096D"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of thrust angle contact ball slewing bearing</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin</p> <p>2017-12-01</p> <p>In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity <span class="hlt">finite</span> <span class="hlt">element</span> model of thrust angular contact ball bearing was established by using <span class="hlt">finite</span> <span class="hlt">element</span> analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of <span class="hlt">finite</span> <span class="hlt">element</span> method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the <span class="hlt">finite</span> <span class="hlt">element</span> method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the <span class="hlt">finite</span> <span class="hlt">element</span> method are more in line with the actual situation of the slewing bearing in the engineering.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19840007528','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19840007528"><span>Generalizing the TRAPRG and TRAPAX <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hurwitz, M. M.</p> <p>1983-01-01</p> <p>The NASTRAN TRAPRG and TRAPAX <span class="hlt">finite</span> <span class="hlt">elements</span> are very restrictive as to shape and grid point numbering. The <span class="hlt">elements</span> must be trapezoidal with two sides parallel to the radial axis. In addition, the ordering of the grid points on the <span class="hlt">element</span> connection card must follow strict rules. The paper describes the generalization of these <span class="hlt">elements</span> so that these restrictions no longer apply.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910009993','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910009993"><span>A <span class="hlt">finite</span> <span class="hlt">element</span> conjugate gradient FFT method for scattering</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.</p> <p>1991-01-01</p> <p>Validated results are presented for the new 3D body of revolution <span class="hlt">finite</span> <span class="hlt">element</span> boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the <span class="hlt">finite</span> <span class="hlt">element</span> mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the <span class="hlt">finite</span> <span class="hlt">element</span> boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000028370','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000028370"><span>Wavelet and Multiresolution Analysis for <span class="hlt">Finite</span> <span class="hlt">Element</span> Networking Paradigms</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kurdila, Andrew J.; Sharpley, Robert C.</p> <p>1999-01-01</p> <p>This paper presents a final report on Wavelet and Multiresolution Analysis for <span class="hlt">Finite</span> <span class="hlt">Element</span> Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional <span class="hlt">finite</span> <span class="hlt">element</span> geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale <span class="hlt">finite</span> <span class="hlt">element</span> simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20110000526','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20110000526"><span>Modeling Progressive Failure of Bonded Joints Using a Single Joint <span class="hlt">Finite</span> <span class="hlt">Element</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.</p> <p>2010-01-01</p> <p>Enhanced <span class="hlt">finite</span> <span class="hlt">elements</span> are <span class="hlt">elements</span> with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent <span class="hlt">finite</span> <span class="hlt">element</span> analysis. In the present study, an enhanced <span class="hlt">finite</span> <span class="hlt">element</span> is applied to generate a general framework capable of modeling an array of joint types. The joint field equations are derived using the principle of minimum potential energy, and the resulting solutions for the displacement fields are used to generate shape functions and a stiffness matrix for a single joint <span class="hlt">finite</span> <span class="hlt">element</span>. This single <span class="hlt">finite</span> <span class="hlt">element</span> thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural <span class="hlt">finite</span> <span class="hlt">element</span> model. The costs associated with a fine mesh of the joint can thus be avoided while still obtaining a detailed solution for the joint. Additionally, the capability to model non-linear adhesive constitutive behavior has been included within the method, and progressive failure of the adhesive can be modeled by using a strain-based failure criteria and re-sizing the joint as the adhesive fails. Results of the model compare favorably with experimental and <span class="hlt">finite</span> <span class="hlt">element</span> results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910004136','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910004136"><span>Periodic trim solutions with hp-version <span class="hlt">finite</span> <span class="hlt">elements</span> in time</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Peters, David A.; Hou, Lin-Jun</p> <p>1990-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">elements</span> in time as an alternative strategy for rotorcraft trim problems are studied. The research treats linear flap and linearized flap-lag response both for quasi-trim and trim cases. The connection between Fourier series analysis and hp-<span class="hlt">finite</span> <span class="hlt">elements</span> for periodic a problem is also examined. It is proved that Fourier series is a special case of space-time <span class="hlt">finite</span> <span class="hlt">elements</span> in which one <span class="hlt">element</span> is used with a strong displacement formulation. Comparisons are made with respect to accuracy among Fourier analysis, displacement methods, and mixed methods over a variety parameters. The hp trade-off is studied for the periodic trim problem to provide an optimum step size and order of polynomial for a given error criteria. It is found that <span class="hlt">finite</span> <span class="hlt">elements</span> in time can outperform Fourier analysis for periodic problems, and for some given error criteria. The mixed method provides better results than does the displacement method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018EPJWC.17303009G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018EPJWC.17303009G"><span>Interpolation Hermite Polynomials For <span class="hlt">Finite</span> <span class="hlt">Element</span> Method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Gusev, Alexander; Vinitsky, Sergue; Chuluunbaatar, Ochbadrakh; Chuluunbaatar, Galmandakh; Gerdt, Vladimir; Derbov, Vladimir; Góźdź, Andrzej; Krassovitskiy, Pavel</p> <p>2018-02-01</p> <p>We describe a new algorithm for analytic calculation of high-order Hermite interpolation polynomials of the simplex and give their classification. A typical example of triangle <span class="hlt">element</span>, to be built in high accuracy <span class="hlt">finite</span> <span class="hlt">element</span> schemes, is given.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_15");'>15</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li class="active"><span>17</span></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_17 --> <div id="page_18" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="341"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20150008760&hterms=finite+element&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dfinite%2Belement','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20150008760&hterms=finite+element&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D50%26Ntt%3Dfinite%2Belement"><span>Determining Wheel-Soil Interaction Loads Using a Meshfree <span class="hlt">Finite</span> <span class="hlt">Element</span> Approach Assisting Future Missions with Rover Wheel Design</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Contreras, Michael T.; Peng, Chia-Yen; Wang, Dongdong; Chen, Jiun-Shyan</p> <p>2012-01-01</p> <p>A wheel experiencing sinkage and slippage events poses a high risk to rover missions as evidenced by recent mobility challenges on the Mars Exploration Rover (MER) project. Because several factors contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc., there are significant benefits to modeling these events to a sufficient degree of complexity. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree <span class="hlt">finite</span> <span class="hlt">element</span> approaches enable simulations that capture sufficient detail of wheel-soil interaction while remaining computationally feasible. This study demonstrates some of the large deformation modeling capability of meshfree methods and the realistic solutions obtained by accounting for the soil material properties. A benchmark wheel-soil interaction problem is developed and analyzed using a specific class of meshfree methods called Reproducing Kernel Particle Method (RKPM). The benchmark problem is also analyzed using a commercially available <span class="hlt">finite</span> <span class="hlt">element</span> approach with <span class="hlt">Lagrangian</span> meshing for comparison. RKPM results are comparable to classical pressure-sinkage terramechanics relationships proposed by Bekker-Wong. Pending experimental calibration by future work, the meshfree modeling technique will be a viable simulation tool for trade studies assisting rover wheel design.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19910056098&hterms=Lagrangian&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3DLagrangian"><span>A new <span class="hlt">Lagrangian</span> random choice method for steady two-dimensional supersonic/hypersonic flow</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Loh, C. Y.; Hui, W. H.</p> <p>1991-01-01</p> <p>Glimm's (1965) random choice method has been successfully applied to compute steady two-dimensional supersonic/hypersonic flow using a new <span class="hlt">Lagrangian</span> formulation. The method is easy to program, fast to execute, yet it is very accurate and robust. It requires no grid generation, resolves slipline and shock discontinuities crisply, can handle boundary conditions most easily, and is applicable to hypersonic as well as supersonic flow. It represents an accurate and fast alternative to the existing <span class="hlt">Eulerian</span> methods. Many computed examples are given.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhPl...24d2702V','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhPl...24d2702V"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR code</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; Molvig, K.; Simakov, A. N.; Haines, B. M.</p> <p>2017-04-01</p> <p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions to flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JNS...tmp..835K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JNS...tmp..835K"><span>From Large Deviations to Semidistances of Transport and Mixing: Coherence Analysis for <span class="hlt">Finite</span> <span class="hlt">Lagrangian</span> Data</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Koltai, Péter; Renger, D. R. Michiel</p> <p>2018-06-01</p> <p>One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, <span class="hlt">finite</span> time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given <span class="hlt">finite</span> <span class="hlt">Lagrangian</span> trajectory data we derive a discrete-time-and-space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, and hence they occur as extremal regions on a spanning structure of the state space under this semidistance—in fact, under any distance measure arising from the physical notion of transport. Based on this notion, we develop a tool to analyze the state space (or the <span class="hlt">finite</span> trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900031178&hterms=mathematics+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmathematics%2Bmethods','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900031178&hterms=mathematics+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dmathematics%2Bmethods"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis in fluids; Proceedings of the Seventh International Conference on <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chung, T. J. (Editor); Karr, Gerald R. (Editor)</p> <p>1989-01-01</p> <p>Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on <span class="hlt">finite-element</span> methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume <span class="hlt">finite</span> <span class="hlt">elements</span>, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of <span class="hlt">finite</span> <span class="hlt">elements</span>, and mesh generation. Also discussed are mixed <span class="hlt">finite</span> <span class="hlt">elements</span>, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19830056839&hterms=mixed+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dmixed%2Bmethods','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19830056839&hterms=mixed+methods&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D40%26Ntt%3Dmixed%2Bmethods"><span>On conforming mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods for incompressible viscous flow problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.</p> <p>1982-01-01</p> <p>The application of conforming mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various <span class="hlt">finite</span> <span class="hlt">element</span> approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the <span class="hlt">finite</span> <span class="hlt">element</span> space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by <span class="hlt">finite</span> <span class="hlt">element</span> discretizations of linear partial differential equations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19890014547','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19890014547"><span><span class="hlt">Finite</span> <span class="hlt">element</span> modeling of frictionally restrained composite interfaces</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ballarini, Roberto; Ahmed, Shamim</p> <p>1989-01-01</p> <p>The use of special interface <span class="hlt">finite</span> <span class="hlt">elements</span> to model frictional restraint in composite interfaces is described. These <span class="hlt">elements</span> simulate Coulomb friction at the interface, and are incorporated into a standard <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these <span class="hlt">elements</span> in micromechanical modeling of fiber-reinforced composite materials is highlighted.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1045822','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1045822"><span>Artificial Boundary Conditions for <span class="hlt">Finite</span> <span class="hlt">Element</span> Model Update and Damage Detection</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2017-03-01</p> <p>BOUNDARY CONDITIONS FOR <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> MODEL UPDATE AND DAMAGE DETECTION by Emmanouil Damanakis March 2017 Thesis Advisor: Joshua H. Gordis...REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE ARTIFICIAL BOUNDARY CONDITIONS FOR <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> MODEL UPDATE AND DAMAGE DETECTION...release. Distribution is unlimited. 12b. DISTRIBUTION CODE 13. ABSTRACT (maximum 200 words) In structural engineering, a <span class="hlt">finite</span> <span class="hlt">element</span> model is often</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19780024520','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19780024520"><span>A computer graphics program for general <span class="hlt">finite</span> <span class="hlt">element</span> analyses</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, E. A.; Sawyer, L. M.</p> <p>1978-01-01</p> <p>Documentation for a computer graphics program for displays from general <span class="hlt">finite</span> <span class="hlt">element</span> analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid <span class="hlt">finite</span> <span class="hlt">element</span> analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26679833','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26679833"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices--How numerical implementation affects the results.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Marom, Gil; Bluestein, Danny</p> <p>2016-01-01</p> <p>This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4932905"><span><span class="hlt">Lagrangian</span> methods for blood damage estimation in cardiovascular devices - How numerical implementation affects the results</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Marom, Gil; Bluestein, Danny</p> <p>2016-01-01</p> <p>Summary This paper evaluated the influence of various numerical implementation assumptions on predicting blood damage in cardiovascular devices using <span class="hlt">Lagrangian</span> methods with <span class="hlt">Eulerian</span> computational fluid dynamics. The implementation assumptions that were tested included various seeding patterns, stochastic walk model, and simplified trajectory calculations with pathlines. Post processing implementation options that were evaluated included single passage and repeated passages stress accumulation and time averaging. This study demonstrated that the implementation assumptions can significantly affect the resulting stress accumulation, i.e., the blood damage model predictions. Careful considerations should be taken in the use of <span class="hlt">Lagrangian</span> models. Ultimately, the appropriate assumptions should be considered based the physics of the specific case and sensitivity analysis, similar to the ones presented here, should be employed. PMID:26679833</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/4711','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/4711"><span>SEACAS Theory Manuals: Part III. <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis in Nonlinear Solid Mechanics</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.</p> <p>1999-03-01</p> <p>This report outlines the application of <span class="hlt">finite</span> <span class="hlt">element</span> methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective <span class="hlt">finite</span> <span class="hlt">element</span> formulations must address. The presentation is organized into three major portions: first, a discussion of <span class="hlt">finite</span> <span class="hlt">element</span> discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of <span class="hlt">finite</span> <span class="hlt">element</span> technology, emphasizing the important theoretical and practical features associated with an individual <span class="hlt">finite</span> <span class="hlt">element</span>; and third, detailed description of specific <span class="hlt">elements</span> that enjoy widespread use, providing some examples ofmore » the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992nwu..rept.....B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992nwu..rept.....B"><span>Probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span> for fatigue and fracture analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Belytschko, Ted; Liu, Wing Kam</p> <p></p> <p>Attenuation is focused on the development of Probabilistic <span class="hlt">Finite</span> <span class="hlt">Element</span> Method (PFEM), which combines the <span class="hlt">finite</span> <span class="hlt">element</span> method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary <span class="hlt">Element</span> Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040086465','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040086465"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Model Development For Aircraft Fuselage Structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.</p> <p>2000-01-01</p> <p>The ability to extend the valid frequency range for <span class="hlt">finite</span> <span class="hlt">element</span> based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid <span class="hlt">element</span> models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The <span class="hlt">finite</span> <span class="hlt">element</span> models are validated using experimental modal analysis results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930003841','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930003841"><span>Probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span> for fatigue and fracture analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Belytschko, Ted; Liu, Wing Kam</p> <p>1992-01-01</p> <p>Attenuation is focused on the development of Probabilistic <span class="hlt">Finite</span> <span class="hlt">Element</span> Method (PFEM), which combines the <span class="hlt">finite</span> <span class="hlt">element</span> method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary <span class="hlt">Element</span> Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25138612','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25138612"><span>Biomechanical investigation of naso-orbitoethmoid trauma by <span class="hlt">finite</span> <span class="hlt">element</span> analysis.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Huempfner-Hierl, Heike; Schaller, Andreas; Hemprich, Alexander; Hierl, Thomas</p> <p>2014-11-01</p> <p>Naso-orbitoethmoid fractures account for 5% of all facial fractures. We used data derived from a white 34-year-old man to make a transient dynamic <span class="hlt">finite</span> <span class="hlt">element</span> model, which consisted of about 740 000 <span class="hlt">elements</span>, to simulate fist-like impacts to this anatomically complex area. <span class="hlt">Finite</span> <span class="hlt">element</span> analysis showed a pattern of von Mises stresses beyond the yield criterion of bone that corresponded with fractures commonly seen clinically. <span class="hlt">Finite</span> <span class="hlt">element</span> models can be used to simulate injuries to the human skull, and provide information about the pathogenesis of different types of fracture. Copyright © 2014 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000076807','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000076807"><span>Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order <span class="hlt">Finite</span> <span class="hlt">Elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gould, Dana C.</p> <p>2000-01-01</p> <p>This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version <span class="hlt">finite</span> <span class="hlt">elements</span>. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the <span class="hlt">finite</span> <span class="hlt">element</span> mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version <span class="hlt">finite</span> <span class="hlt">elements</span>. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version <span class="hlt">finite</span> <span class="hlt">elements</span>. In the first method, higher-order <span class="hlt">elements</span> are divided into a number of sub-<span class="hlt">elements</span>. Traditional methods are used to determine radiation heat flux along each sub-<span class="hlt">element</span> and then mapped back to the parent <span class="hlt">element</span>. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order <span class="hlt">element</span>. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-<span class="hlt">element</span> method. Comparison to results from traditional <span class="hlt">finite</span> <span class="hlt">elements</span> shows that significant reduction in the number of <span class="hlt">elements</span> in the mesh is possible using higher-order (p-version) <span class="hlt">finite</span> <span class="hlt">elements</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29081829','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29081829"><span>The Applications of <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis in Proximal Humeral Fractures.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Ye, Yongyu; You, Wei; Zhu, Weimin; Cui, Jiaming; Chen, Kang; Wang, Daping</p> <p>2017-01-01</p> <p>Proximal humeral fractures are common and most challenging, due to the complexity of the glenohumeral joint, especially in the geriatric population with impacted fractures, that the development of implants continues because currently the problems with their fixation are not solved. Pre-, intra-, and postoperative assessments are crucial in management of those patients. <span class="hlt">Finite</span> <span class="hlt">element</span> analysis, as one of the valuable tools, has been implemented as an effective and noninvasive method to analyze proximal humeral fractures, providing solid evidence for management of troublesome patients. However, no review article about the applications and effects of <span class="hlt">finite</span> <span class="hlt">element</span> analysis in assessing proximal humeral fractures has been reported yet. This review article summarized the applications, contribution, and clinical significance of <span class="hlt">finite</span> <span class="hlt">element</span> analysis in assessing proximal humeral fractures. Furthermore, the limitations of <span class="hlt">finite</span> <span class="hlt">element</span> analysis, the difficulties of more realistic simulation, and the validation and also the creation of validated FE models were discussed. We concluded that although some advancements in proximal humeral fractures researches have been made by using <span class="hlt">finite</span> <span class="hlt">element</span> analysis, utility of this powerful tool for routine clinical management and adequate simulation requires more state-of-the-art studies to provide evidence and bases.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1339293-modal-substructuring-geometrically-nonlinear-finite-element-models','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1339293-modal-substructuring-geometrically-nonlinear-finite-element-models"><span>Modal Substructuring of Geometrically Nonlinear <span class="hlt">Finite-Element</span> Models</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.</p> <p>2015-12-21</p> <p>The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear <span class="hlt">finite-element</span> models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear <span class="hlt">finite-element</span> models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the <span class="hlt">finite-element</span> code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial <span class="hlt">finite-element</span> packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring <span class="hlt">element</span> to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1339293','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1339293"><span>Modal Substructuring of Geometrically Nonlinear <span class="hlt">Finite-Element</span> Models</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.</p> <p></p> <p>The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear <span class="hlt">finite-element</span> models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear <span class="hlt">finite-element</span> models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the <span class="hlt">finite-element</span> code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial <span class="hlt">finite-element</span> packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring <span class="hlt">element</span> to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_16");'>16</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li class="active"><span>18</span></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_18 --> <div id="page_19" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="361"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/88984-evaluation-finite-element-fuel-rod-analysis-code-franco','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/88984-evaluation-finite-element-fuel-rod-analysis-code-franco"><span>Evaluation of the <span class="hlt">finite</span> <span class="hlt">element</span> fuel rod analysis code (FRANCO)</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Lee, K.; Feltus, M.A.</p> <p>1994-12-31</p> <p>Knowledge of temperature distribution in a nuclear fuel rod is required to predict the behavior of fuel <span class="hlt">elements</span> during operating conditions. The thermal and mechanical properties and performance characteristics are strongly dependent on the temperature, which can vary greatly inside the fuel rod. A detailed model of fuel rod behavior can be described by various numerical methods, including the <span class="hlt">finite</span> <span class="hlt">element</span> approach. The <span class="hlt">finite</span> <span class="hlt">element</span> method has been successfully used in many engineering applications, including nuclear piping and reactor component analysis. However, fuel pin analysis has traditionally been carried out with <span class="hlt">finite</span> difference codes, with the exception of Electric Powermore » Research Institute`s FREY code, which was developed for mainframe execution. This report describes FRANCO, a <span class="hlt">finite</span> <span class="hlt">element</span> fuel rod analysis code capable of computing temperature disrtibution and mechanical deformation of a single light water reactor fuel rod.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007AIPC..908..955L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007AIPC..908..955L"><span>Sectional <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis on Viscous Pressure Forming of Sheet Metal</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Liu, Jianguang; Wang, Zhongjin; Liu, Yan</p> <p>2007-05-01</p> <p>Viscous pressure forming (VPF) is a recently developed sheet flexible-die forming process, which uses a kind of semi-solid, flowable and viscous material as pressure-carrying medium that typically applied on one side of the sheet metal or on both sides of sheet metal. Different from traditional sheet metal forming processes in which sheet metal is the unique deformation-body, VPF is a coupling process of visco-elastoplastic bulk deformation of viscous medium and elasto-plastic deformation of sheet metal. A sectional <span class="hlt">finite</span> <span class="hlt">element</span> model for the coupled deformation between visco-elastoplastic body and elasto-plastic sheet metal was proposed to analyze VPF. The resolution of the Updated <span class="hlt">Lagrangian</span> formulation is based on a static approach. By using static-explicit time integration strategy, the deformation of elasto-plastic sheet metal and visco-elastoplastic body can keep stable. The frictional contact between sheet metal and visco-elastoplastic body is treated by penalty function method. Using the proposed algorithm, sheet metal viscous pressure bulging (VPB) process is analyzed and compared with experiments. A good agreement between numerical simulation results and experimental ones proved the efficiency and stability of this algorithm.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19760006747','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19760006747"><span>A general algorithm using <span class="hlt">finite</span> <span class="hlt">element</span> method for aerodynamic configurations at low speeds</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Balasubramanian, R.</p> <p>1975-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the <span class="hlt">finite</span> <span class="hlt">element</span> algorithm. The <span class="hlt">finite</span> <span class="hlt">elements</span> are triangular with bicubic shape functions approximating the solution space. The <span class="hlt">finite</span> <span class="hlt">element</span> matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the <span class="hlt">finite</span> <span class="hlt">element</span> matrices to obtain the solution for the boundary value problem.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900000079&hterms=flower&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dflower','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900000079&hterms=flower&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dflower"><span>Assignment Of <span class="hlt">Finite</span> <span class="hlt">Elements</span> To Parallel Processors</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.</p> <p>1990-01-01</p> <p><span class="hlt">Elements</span> assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform <span class="hlt">finite-element</span> computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of <span class="hlt">elements</span> to subdomains minimizes cost of computation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920005174','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920005174"><span>Electromagnetic <span class="hlt">finite</span> <span class="hlt">elements</span> based on a four-potential variational principle</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Schuler, James J.; Felippa, Carlos A.</p> <p>1991-01-01</p> <p>Electromagnetic <span class="hlt">finite</span> <span class="hlt">elements</span> based on a variational principle that uses the electromagnetic four-potential as a primary variable are derived. This choice is used to construct <span class="hlt">elements</span> suitable for downstream coupling with mechanical and thermal <span class="hlt">finite</span> <span class="hlt">elements</span> for the analysis of electromagnetic/mechanical systems that involve superconductors. The main advantages of the four-potential as a basis for <span class="hlt">finite</span> <span class="hlt">element</span> formulation are that the number of degrees of freedom per node remains modest as the problem dimensionally increases, that jump discontinuities on interfaces are naturally accommodated, and that statics as well as dynamics may be treated without any a priori approximations. The new <span class="hlt">elements</span> are tested on an axisymmetric problem under steady state forcing conditions. The results are in excellent agreement with analytical solutions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018InvPr..34c5004B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018InvPr..34c5004B"><span>Solving ill-posed control problems by stabilized <span class="hlt">finite</span> <span class="hlt">element</span> methods: an alternative to Tikhonov regularization</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Burman, Erik; Hansbo, Peter; Larson, Mats G.</p> <p>2018-03-01</p> <p>Tikhonov regularization is one of the most commonly used methods for the regularization of ill-posed problems. In the setting of <span class="hlt">finite</span> <span class="hlt">element</span> solutions of elliptic partial differential control problems, Tikhonov regularization amounts to adding suitably weighted least squares terms of the control variable, or derivatives thereof, to the <span class="hlt">Lagrangian</span> determining the optimality system. In this note we show that the stabilization methods for discretely ill-posed problems developed in the setting of convection-dominated convection-diffusion problems, can be highly suitable for stabilizing optimal control problems, and that Tikhonov regularization will lead to less accurate discrete solutions. We consider some inverse problems for Poisson’s equation as an illustration and derive new error estimates both for the reconstruction of the solution from the measured data and reconstruction of the source term from the measured data. These estimates include both the effect of the discretization error and error in the measurements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2005AtmEn..39.7044S"><span>Evaluation of a <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> air quality model using perfluorocarbon tracers released in Texas for the BRAVO haze study</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Schichtel, Bret A.; Barna, Michael G.; Gebhart, Kristi A.; Malm, William C.</p> <p></p> <p>The Big Bend Regional Aerosol and Visibility Observational (BRAVO) study was designed to determine the sources of haze at Big Bend National Park, Texas, using a combination of source and receptor models. BRAVO included an intensive monitoring campaign from July to October 1999 that included the release of perfluorocarbon tracers from four locations at distances 230-750 km from Big Bend and measured at 24 sites. The tracer measurements near Big Bend were used to evaluate the dispersion mechanisms in the REMSAD <span class="hlt">Eulerian</span> model and the CAPITA Monte Carlo (CMC) <span class="hlt">Lagrangian</span> model used in BRAVO. Both models used 36 km MM5 wind fields as input. The CMC model also used a combination of routinely available 80 and 190 km wind fields from the National Weather Service's National Centers for Environmental Prediction (NCEP) as input. A model's performance is limited by inherent uncertainties due to errors in the tracer concentrations and a model's inability to simulate sub-resolution variability. A range in the inherent uncertainty was estimated by comparing tracer data at nearby monitoring sites. It was found that the REMSAD and CMC models, using the MM5 wind field, produced performance statistics generally within this inherent uncertainty. The CMC simulation using the NCEP wind fields could reproduce the timing of tracer impacts at Big Bend, but not the concentration values, due to a systematic underestimation. It appears that the underestimation was partly due to excessive vertical dilution from high mixing depths. The model simulations were more sensitive to the input wind fields than the models' different dispersion mechanisms. Comparisons of REMSAD to CMC tracer simulations using the MM5 wind fields had correlations between 0.75 and 0.82, depending on the tracer, but the tracer simulations using the two wind fields in the CMC model had correlations between 0.37 and 0.5.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930050001&hterms=basic+mechanics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dbasic%2Bmechanics','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930050001&hterms=basic+mechanics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dbasic%2Bmechanics"><span>Solution-adaptive <span class="hlt">finite</span> <span class="hlt">element</span> method in computational fracture mechanics</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Min, J. B.; Bass, J. M.; Spradley, L. W.</p> <p>1993-01-01</p> <p>Some recent results obtained using solution-adaptive <span class="hlt">finite</span> <span class="hlt">element</span> method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive <span class="hlt">finite</span> <span class="hlt">element</span> method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000116478','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000116478"><span>Discontinuous dual-primal mixed <span class="hlt">finite</span> <span class="hlt">elements</span> for elliptic problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo</p> <p>2000-01-01</p> <p>We propose a novel discontinuous mixed <span class="hlt">finite</span> <span class="hlt">element</span> formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial <span class="hlt">finite</span> <span class="hlt">element</span> spaces are used for the trial and test functions. The discontinuous nature of the test functions at the <span class="hlt">element</span> interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the <span class="hlt">element</span> level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19900063958&hterms=least+squares&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dleast%2Bsquares','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19900063958&hterms=least+squares&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dleast%2Bsquares"><span>Least-squares <span class="hlt">finite</span> <span class="hlt">element</span> methods for compressible Euler equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jiang, Bo-Nan; Carey, G. F.</p> <p>1990-01-01</p> <p>A method based on backward <span class="hlt">finite</span> differencing in time and a least-squares <span class="hlt">finite</span> <span class="hlt">element</span> scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear <span class="hlt">elements</span> has been implemented and proves robust. For high-order <span class="hlt">elements</span>, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree <span class="hlt">elements</span>. Finally, a conservative least-squares <span class="hlt">finite</span> <span class="hlt">element</span> method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/9220','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/9220"><span>A progress report on estuary modeling by the <span class="hlt">finite-element</span> method</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Gray, William G.</p> <p>1978-01-01</p> <p>Various schemes are investigated for <span class="hlt">finite-element</span> modeling of two-dimensional surface-water flows. The first schemes investigated combine <span class="hlt">finite-element</span> spatial discretization with split-step time stepping schemes that have been found useful in <span class="hlt">finite</span>-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these <span class="hlt">finite-element</span> schemes were found to be economically uncompetitive with <span class="hlt">finite</span>-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for <span class="hlt">finite-element</span> modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22230823-higher-order-adaptive-finite-element-methods-kohnsham-density-functional-theory','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22230823-higher-order-adaptive-finite-element-methods-kohnsham-density-functional-theory"><span>Higher-order adaptive <span class="hlt">finite-element</span> methods for Kohn–Sham density functional theory</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Motamarri, P.; Nowak, M.R.; Leiter, K.</p> <p>2013-11-15</p> <p>We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order <span class="hlt">finite-element</span> discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal <span class="hlt">finite-element</span> discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral <span class="hlt">finite-elements</span> in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposedmore » solution procedure, we investigate the computational efficiency afforded by higher-order <span class="hlt">finite-element</span> discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear <span class="hlt">finite-elements</span> can be realized, for both all-electron and local pseudopotential calculations, by using higher-order <span class="hlt">finite-element</span> discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-<span class="hlt">element</span> may be an optimal choice for the <span class="hlt">finite-element</span> discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order <span class="hlt">finite-element</span> discretizations suggests that the performance of <span class="hlt">finite-element</span> basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010CompM..46..147S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010CompM..46..147S"><span>Full <span class="hlt">Eulerian</span> simulations of biconcave neo-Hookean particles in a Poiseuille flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sugiyama, Kazuyasu; , Satoshi, II; Takeuchi, Shintaro; Takagi, Shu; Matsumoto, Yoichiro</p> <p>2010-03-01</p> <p>For a given initial configuration of a multi-component geometry represented by voxel-based data on a fixed Cartesian mesh, a full <span class="hlt">Eulerian</span> <span class="hlt">finite</span> difference method facilitates solution of dynamic interaction problems between Newtonian fluid and hyperelastic material. The solid volume fraction, and the left Cauchy-Green deformation tensor are temporally updated on the <span class="hlt">Eulerian</span> frame, respectively, to distinguish the fluid and solid phases, and to describe the solid deformation. The simulation method is applied to two- and three-dimensional motions of two biconcave neo-Hookean particles in a Poiseuille flow. Similar to the numerical study on the red blood cell motion in a circular pipe (Gong et al. in J Biomech Eng 131:074504, 2009), in which Skalak’s constitutive laws of the membrane are considered, the deformation, the relative position and orientation of a pair of particles are strongly dependent upon the initial configuration. The increase in the apparent viscosity is dependent upon the developed arrangement of the particles. The present <span class="hlt">Eulerian</span> approach is demonstrated that it has the potential to be easily extended to larger system problems involving a large number of particles of complicated geometries.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26355416','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26355416"><span>An atomic <span class="hlt">finite</span> <span class="hlt">element</span> model for biodegradable polymers. Part 1. Formulation of the <span class="hlt">finite</span> <span class="hlt">elements</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David</p> <p>2015-11-01</p> <p>Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale <span class="hlt">finite</span> <span class="hlt">element</span> method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. <span class="hlt">Finite</span> <span class="hlt">element</span> formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19720022703','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19720022703"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of elasto-plastic soils. Report no. 4: <span class="hlt">Finite</span> <span class="hlt">element</span> analysis of elasto-plastic frictional materials for application to lunar earth sciences</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Marr, W. A., Jr.</p> <p>1972-01-01</p> <p>The behavior of <span class="hlt">finite</span> <span class="hlt">element</span> models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These <span class="hlt">finite</span> <span class="hlt">element</span> models are used to analyze retaining walls and footings. Methods of improving the <span class="hlt">finite</span> <span class="hlt">element</span> solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of <span class="hlt">elements</span>. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2000MSMSE...8..541K','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2000MSMSE...8..541K"><span><span class="hlt">Finite-element</span> simulation of ceramic drying processes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Keum, Y. T.; Jeong, J. H.; Auh, K. H.</p> <p>2000-07-01</p> <p>A <span class="hlt">finite-element</span> simulation for the drying process of ceramics is performed. The heat and moisture movements in green ceramics caused by the temperature gradient, moisture gradient, conduction, convection and evaporation are considered. The <span class="hlt">finite-element</span> formulation for solving the temperature and moisture distributions, which not only change the volume but also induce the hygro-thermal stress, is carried out. Employing the internally discontinuous interface <span class="hlt">elements</span>, the numerical divergence problem arising from sudden changes in heat capacity in the phase zone is solved. In order to verify the reliability of the formulation, the drying process of a coal and the wetting process of a graphite epoxy are simulated and the results are compared with the analytical solution and another investigator's result. Finally, the drying process of a ceramic electric insulator is simulated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1122309','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1122309"><span>Nonlinear Legendre Spectral <span class="hlt">Finite</span> <span class="hlt">Elements</span> for Wind Turbine Blade Dynamics: Preprint</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Wang, Q.; Sprague, M. A.; Jonkman, J.</p> <p>2014-01-01</p> <p>This paper presents a numerical implementation and examination of new wind turbine blade <span class="hlt">finite</span> <span class="hlt">element</span> model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral <span class="hlt">finite</span> <span class="hlt">element</span> method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral <span class="hlt">finite</span> <span class="hlt">elements</span> (LSFEs) are high-order <span class="hlt">finite</span> <span class="hlt">elements</span> with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order <span class="hlt">finite</span> <span class="hlt">elements</span> for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order <span class="hlt">finite</span> <span class="hlt">elements</span> where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/twri/twri6a4/','USGSPUBS'); return false;" href="https://pubs.usgs.gov/twri/twri6a4/"><span>A modular <span class="hlt">finite-element</span> model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 2: Derivation of <span class="hlt">finite-element</span> equations and comparisons with analytical solutions</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Cooley, Richard L.</p> <p>1992-01-01</p> <p>MODFE, a modular <span class="hlt">finite-element</span> model for simulating steady- or unsteady-state, area1 or axisymmetric flow of ground water in a heterogeneous anisotropic aquifer is documented in a three-part series of reports. In this report, part 2, the <span class="hlt">finite-element</span> equations are derived by minimizing a functional of the difference between the true and approximate hydraulic head, which produces equations that are equivalent to those obtained by either classical variational or Galerkin techniques. Spatial <span class="hlt">finite</span> <span class="hlt">elements</span> are triangular with linear basis functions, and temporal <span class="hlt">finite</span> <span class="hlt">elements</span> are one dimensional with linear basis functions. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining units; (3) specified recharge or discharge at points, along lines, or areally; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining units combined with aquifer dewatering, and evapotranspiration. The matrix equations produced by the <span class="hlt">finite-element</span> method are solved by the direct symmetric-Doolittle method or the iterative modified incomplete-Cholesky conjugate-gradient method. The direct method can be efficient for small- to medium-sized problems (less than about 500 nodes), and the iterative method is generally more efficient for larger-sized problems. Comparison of <span class="hlt">finite-element</span> solutions with analytical solutions for five example problems demonstrates that the <span class="hlt">finite-element</span> model can yield accurate solutions to ground-water flow problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1407723-simple-finite-element-method-linear-hyperbolic-problems','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1407723-simple-finite-element-method-linear-hyperbolic-problems"><span>A simple <span class="hlt">finite</span> <span class="hlt">element</span> method for linear hyperbolic problems</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Mu, Lin; Ye, Xiu</p> <p>2017-09-14</p> <p>Here, we introduce a simple <span class="hlt">finite</span> <span class="hlt">element</span> method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on <span class="hlt">finite</span> <span class="hlt">element</span> partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1407723-simple-finite-element-method-linear-hyperbolic-problems','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1407723-simple-finite-element-method-linear-hyperbolic-problems"><span>A simple <span class="hlt">finite</span> <span class="hlt">element</span> method for linear hyperbolic problems</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Mu, Lin; Ye, Xiu</p> <p></p> <p>Here, we introduce a simple <span class="hlt">finite</span> <span class="hlt">element</span> method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on <span class="hlt">finite</span> <span class="hlt">element</span> partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_17");'>17</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li class="active"><span>19</span></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_19 --> <div id="page_20" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="381"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940018141','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940018141"><span>Life assessment of structural components using inelastic <span class="hlt">finite</span> <span class="hlt">element</span> analyses</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Arya, Vinod K.; Halford, Gary R.</p> <p>1993-01-01</p> <p>The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such <span class="hlt">finite</span> <span class="hlt">element</span> solution technologies (in conjunction with the <span class="hlt">finite</span> <span class="hlt">element</span> program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other <span class="hlt">finite</span> <span class="hlt">element</span> programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic <span class="hlt">finite</span> <span class="hlt">element</span> solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this <span class="hlt">finite</span> <span class="hlt">element</span> solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding <span class="hlt">finite</span> <span class="hlt">element</span> analyses.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19990036230&hterms=square&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dsquare','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19990036230&hterms=square&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3Dsquare"><span>Flow Applications of the Least Squares <span class="hlt">Finite</span> <span class="hlt">Element</span> Method</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jiang, Bo-Nan</p> <p>1998-01-01</p> <p>The main thrust of the effort has been towards the development, analysis and implementation of the least-squares <span class="hlt">finite</span> <span class="hlt">element</span> method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order <span class="hlt">elements</span>, operator splitting and preconditioning, edge <span class="hlt">elements</span>, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the <span class="hlt">finite</span> difference and <span class="hlt">finite</span> volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040081034','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040081034"><span>User's Guide for ENSAERO_FE Parallel <span class="hlt">Finite</span> <span class="hlt">Element</span> Solver</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Eldred, Lloyd B.; Guruswamy, Guru P.</p> <p>1999-01-01</p> <p>A high fidelity parallel static structural analysis capability is created and interfaced to the multidisciplinary analysis package ENSAERO-MPI of Ames Research Center. This new module replaces ENSAERO's lower fidelity simple <span class="hlt">finite</span> <span class="hlt">element</span> and modal modules. Full aircraft structures may be more accurately modeled using the new <span class="hlt">finite</span> <span class="hlt">element</span> capability. Parallel computation is performed by breaking the full structure into multiple substructures. This approach is conceptually similar to ENSAERO's multizonal fluid analysis capability. The new substructure code is used to solve the structural <span class="hlt">finite</span> <span class="hlt">element</span> equations for each substructure in parallel. NASTRANKOSMIC is utilized as a front end for this code. Its full library of <span class="hlt">elements</span> can be used to create an accurate and realistic aircraft model. It is used to create the stiffness matrices for each substructure. The new parallel code then uses an iterative preconditioned conjugate gradient method to solve the global structural equations for the substructure boundary nodes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2011AIPC.1383..661N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2011AIPC.1383..661N"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis of Tube Hydroforming in Non-Symmetrical Dies</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nulkar, Abhishek V.; Gu, Randy; Murty, Pilaka</p> <p>2011-08-01</p> <p>Tube hydroforming has been studied intensively using commercial <span class="hlt">finite</span> <span class="hlt">element</span> programs. A great deal of the investigations dealt with models with symmetric cross-sections. It is known that additional constraints due to symmetry may be imposed on the model so that it is properly supported. For a non-symmetric model, these constraints become invalid and the model does not have sufficient support resulting in a singular <span class="hlt">finite</span> <span class="hlt">element</span> system. Majority of commercial codes have a limited capability in solving models with insufficient supports. Recently, new algorithms using penalty variable and air-like contact <span class="hlt">element</span> (ALCE) have been developed to solve positive semi-definite <span class="hlt">finite</span> <span class="hlt">element</span> systems such as those in contact mechanics. In this study the ALCE algorithm is first validated by comparing its result against a commercial code using a symmetric model in which a circular tube is formed to polygonal dies with symmetric shapes. Then, the study investigates the accuracy and efficiency of using ALCE in analyzing hydroforming of tubes with various cross-sections in non-symmetrical dies in 2-D <span class="hlt">finite</span> <span class="hlt">element</span> settings.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910021546','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910021546"><span>Use of edge-based <span class="hlt">finite</span> <span class="hlt">elements</span> for solving three dimensional scattering problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Chatterjee, A.; Jin, J. M.; Volakis, John L.</p> <p>1991-01-01</p> <p>Edge based <span class="hlt">finite</span> <span class="hlt">elements</span> are free from drawbacks associated with node based vectorial <span class="hlt">finite</span> <span class="hlt">elements</span> and are, therefore, ideal for solving 3-D scattering problems. The <span class="hlt">finite</span> <span class="hlt">element</span> discretization using edge <span class="hlt">elements</span> is checked by solving for the resonant frequencies of a closed inhomogeneously filled metallic cavity. Great improvements in accuracy are observed when compared to the classical node based approach with no penalty in terms of computational time and with the expected absence of spurious modes. A performance comparison between the edge based tetrahedra and rectangular brick <span class="hlt">elements</span> is carried out and tetrahedral <span class="hlt">elements</span> are found to be more accurate than rectangular bricks for a given storage intensity. A detailed formulation for the scattering problem with various approaches for terminating the <span class="hlt">finite</span> <span class="hlt">element</span> mesh is also presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19840050353&hterms=discrete+mathematics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Ddiscrete%2Bmathematics','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19840050353&hterms=discrete+mathematics&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Ddiscrete%2Bmathematics"><span>Error analysis and correction of discrete solutions from <span class="hlt">finite</span> <span class="hlt">element</span> codes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thurston, G. A.; Stein, P. A.; Knight, N. F., Jr.; Reissner, J. E.</p> <p>1984-01-01</p> <p>Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from <span class="hlt">finite</span> <span class="hlt">element</span> solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of <span class="hlt">finite</span> <span class="hlt">element</span> results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting <span class="hlt">finite</span> <span class="hlt">element</span> results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete <span class="hlt">finite</span> <span class="hlt">element</span> solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1989umas.reptQ....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1989umas.reptQ....O"><span><span class="hlt">Lagrangian</span> turbulence near walls: Structures and mixing in admissible model flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ottino, J. M.</p> <p>1989-05-01</p> <p>The general objective of work during this period was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: a perturbed Kelvin cat eyes flow, and prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: production flows capable of producing complex distributions of vorticity, and constructed flow fields, based on solutions of the Navier Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1053238','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1053238"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis of Particle Ionization within Carbon Nanotube Ion Micro Thruster</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2017-12-01</p> <p>NAVAL POSTGRADUATE SCHOOL MONTEREY, CALIFORNIA THESIS Approved for public release. Distribution is unlimited. <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> ...AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> ANALYSIS OF PARTICLE IONIZATION WITHIN CARBON NANOTUBE ION MICRO THRUSTER 5...simulation, carbon nanotube simulation, microsatellite, <span class="hlt">finite</span> <span class="hlt">element</span> analysis, electric field, particle tracing 15. NUMBER OF PAGES 55 16. PRICE</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2001APS..DFD.EC008A"><span>Chaos in an <span class="hlt">Eulerian</span> Based Model of Sickle Cell Blood Flow</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Apori, Akwasi; Harris, Wesley</p> <p>2001-11-01</p> <p>A novel <span class="hlt">Eulerian</span> model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This <span class="hlt">Eulerian</span> model was based on extending previous models of sickle cell blood flow which were limited due to their <span class="hlt">Lagrangian</span> formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.er.usgs.gov/publication/70023108','USGSPUBS'); return false;" href="https://pubs.er.usgs.gov/publication/70023108"><span>Treatment of internal sources in the <span class="hlt">finite</span>-volume ELLAM</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Healy, R.W.; ,; ,; ,; ,; ,</p> <p>2000-01-01</p> <p>The <span class="hlt">finite</span>-volume <span class="hlt">Eulerian-Lagrangian</span> localized adjoint method (FVELLAM) is a mass-conservative approach for solving the advection-dispersion equation. The method has been shown to be accurate and efficient for solving advection-dominated problems of solute transport in ground water in 1, 2, and 3 dimensions. Previous implementations of FVELLAM have had difficulty in representing internal sources because the standard assumption of lowest order Raviart-Thomas velocity field does not hold for source cells. Therefore, tracking of particles within source cells is problematic. A new approach has been developed to account for internal sources in FVELLAM. It is assumed that the source is uniformly distributed across a grid cell and that instantaneous mixing takes place within the cell, such that concentration is uniform across the cell at any time. Sub-time steps are used in the time-integration scheme to track mass outflow from the edges of the source cell. This avoids the need for tracking within the source cell. We describe the new method and compare results for a test problem with a wide range of cell Peclet numbers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2004PhyB..352..134S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2004PhyB..352..134S"><span>Analysis of <span class="hlt">finite</span>-strain equations of state for solids under high pressures</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sushil, K.; Arunesh, K.; Singh, P. K.; Sharma, B. S.</p> <p>2004-10-01</p> <p>We have reformulated equations of state (EOS) for solids based on <span class="hlt">Lagrangian</span> and <span class="hlt">Eulerian</span> strains following the method developed by Stacey [Phys. Earth Planet. Inter. 128 (2001) 179]. The expressions thus obtained are used conveniently to assess the validity of various EOS for different types of solids. The logarithmic EOS based on the Hencky measure of <span class="hlt">finite</span>-strain is also modified by including the higher terms arising from the fourth-order contribution in the Taylor series expansion of the free energy. The results are obtained for pressure (P), isothermal bulk modulus (KT) and its pressure derivative (dKT/dP) for Ne, Ar, Al, Cu, LiH and MgO solids for a wide range of compressions (V/V0) down to 0.5. The results determined from the <span class="hlt">finite</span>-strain equations are compared with those obtained from the Vinet-Rydberg equation and the Shanker equation, which are based on the interatomic potential energy functions. The results are also compared with the ab inito values reported by Hama and Suito [J. Phys.: Condens. Matter 8 (1996) 67] determined from first-principles calculations using the augmented plane wave method and the quantum statistical model. The EOS based on the K‧ <span class="hlt">finite</span>-strain theory due to Keane and Stacey are also discussed, emphasising the importance of K∞‧ , in the limit P→∞.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910004580','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910004580"><span>Examples of <span class="hlt">finite</span> <span class="hlt">element</span> mesh generation using SDRC IDEAS</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Zapp, John; Volakis, John L.</p> <p>1990-01-01</p> <p>IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, <span class="hlt">finite</span> <span class="hlt">element</span> pre/post processing, <span class="hlt">finite</span> <span class="hlt">element</span> solution, system dynamics, drafting, test data analysis, and project relational database.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://eric.ed.gov/?q=finite+AND+element&pg=2&id=EJ514373','ERIC'); return false;" href="https://eric.ed.gov/?q=finite+AND+element&pg=2&id=EJ514373"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis (FEA) in Design and Production.</span></a></p> <p><a target="_blank" href="http://www.eric.ed.gov/ERICWebPortal/search/extended.jsp?_pageLabel=advanced">ERIC Educational Resources Information Center</a></p> <p>Waggoner, Todd C.; And Others</p> <p>1995-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller <span class="hlt">elements</span>, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20060035967&hterms=elements+communication&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Delements%2Bcommunication','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20060035967&hterms=elements+communication&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Delements%2Bcommunication"><span>An <span class="hlt">Element</span>-Based Concurrent Partitioner for Unstructured <span class="hlt">Finite</span> <span class="hlt">Element</span> Meshes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ding, Hong Q.; Ferraro, Robert D.</p> <p>1996-01-01</p> <p>A concurrent partitioner for partitioning unstructured <span class="hlt">finite</span> <span class="hlt">element</span> meshes on distributed memory architectures is developed. The partitioner uses an <span class="hlt">element</span>-based partitioning strategy. Its main advantage over the more conventional node-based partitioning strategy is its modular programming approach to the development of parallel applications. The partitioner first partitions <span class="hlt">element</span> centroids using a recursive inertial bisection algorithm. <span class="hlt">Elements</span> and nodes then migrate according to the partitioned centroids, using a data request communication template for unpredictable incoming messages. Our scalable implementation is contrasted to a non-scalable implementation which is a straightforward parallelization of a sequential partitioner.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19830017160','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19830017160"><span>A comparative study of <span class="hlt">finite</span> <span class="hlt">element</span> and <span class="hlt">finite</span> difference methods for Cauchy-Riemann type equations</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Fix, G. J.; Rose, M. E.</p> <p>1983-01-01</p> <p>A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both <span class="hlt">finite</span> <span class="hlt">element</span> and <span class="hlt">finite</span> difference methods. Closely related arguments are shown to establish convergence estimates.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870016952','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870016952"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of flexible, rotating blades</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mcgee, Oliver G.</p> <p>1987-01-01</p> <p>A reference guide that can be used when using the <span class="hlt">finite</span> <span class="hlt">element</span> method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell <span class="hlt">elements</span>, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN <span class="hlt">elements</span> through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN <span class="hlt">elements</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1361797-plasma-transport-eulerian-amr-code"><span>Plasma transport in an <span class="hlt">Eulerian</span> AMR code</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Vold, E. L.; Rauenzahn, R. M.; Aldrich, C. H.; ...</p> <p>2017-04-04</p> <p>A plasma transport model has been implemented in an <span class="hlt">Eulerian</span> AMR radiation-hydrodynamics code, xRage, which includes plasma viscosity in the momentum tensor, viscous dissipation in the energy equations, and binary species mixing with consistent species mass and energy fluxes driven by concentration gradients, ion and electron baro-diffusion terms and temperature gradient forces. The physics basis, computational issues, numeric options, and results from several test problems are discussed. The transport coefficients are found to be relatively insensitive to the kinetic correction factors when the concentrations are expressed with the molar fractions and the ion mass differences are large. The contributions tomore » flow dynamics from plasma viscosity and mass diffusion were found to increase significantly as scale lengths decrease in an inertial confinement fusion relevant Kelvin-Helmholtz instability mix layer. The mixing scale lengths in the test case are on the order of 100 μm and smaller for viscous effects to appear and 10 μm or less for significant ion species diffusion, evident over durations on the order of nanoseconds. The temperature gradient driven mass flux is seen to deplete a high Z tracer ion at the ion shock front. The plasma transport model provides the generation of the atomic mix per unit of interfacial area between two species with no free parameters. The evolution of the total atomic mix then depends also on an accurate resolution or estimate of the interfacial area between the species mixing by plasma transport. High resolution simulations or a more <span class="hlt">Lagrangian</span>-like treatment of species interfaces may be required to distinguish plasma transport and numerical diffusion in an <span class="hlt">Eulerian</span> computation of complex and dynamically evolving mix regions.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1042064','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1042064"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling of Scattering from Underwater Proud and Buried Military Munitions</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2017-02-28</p> <p>FINAL REPORT <span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling of Scattering from Underwater Proud and Buried Military Munitions SERDP Project MR-2408 JULY 2017...solution and the red dash-dot line repre- sents the coupled <span class="hlt">finite</span> -boundary <span class="hlt">element</span> solution. . . . . . . . . . . . . . . . . . 11 3 The scattering...dot line represents the coupled <span class="hlt">finite</span> -boundary <span class="hlt">element</span> solution. . . . . . . . 11 i 4 The scattering amplitude as a function of the receiver angle for</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016AIPC.1769j0006F','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016AIPC.1769j0006F"><span>Calibration of 3D ALE <span class="hlt">finite</span> <span class="hlt">element</span> model from experiments on friction stir welding of lap joints</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Fourment, Lionel; Gastebois, Sabrina; Dubourg, Laurent</p> <p>2016-10-01</p> <p>In order to support the design of such a complex process like Friction Stir Welding (FSW) for the aeronautic industry, numerical simulation software requires (1) developing an efficient and accurate <span class="hlt">Finite</span> <span class="hlt">Element</span> (F.E.) formulation that allows predicting welding defects, (2) properly modeling the thermo-mechanical complexity of the FSW process and (3) calibrating the F.E. model from accurate measurements from FSW experiments. This work uses a parallel ALE formulation developed in the Forge® F.E. code to model the different possible defects (flashes and worm holes), while pin and shoulder threads are modeled by a new friction law at the tool / material interface. FSW experiments require using a complex tool with scroll on shoulder, which is instrumented for providing sensitive thermal data close to the joint. Calibration of unknown material thermal coefficients, constitutive equations parameters and friction model from measured forces, torques and temperatures is carried out using two F.E. models, <span class="hlt">Eulerian</span> and ALE, to reach a satisfactory agreement assessed by the proper sensitivity of the simulation to process parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=20060037058&hterms=elements+communication&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Delements%2Bcommunication','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=20060037058&hterms=elements+communication&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D70%26Ntt%3Delements%2Bcommunication"><span>Slices: A Scalable Partitioner for <span class="hlt">Finite</span> <span class="hlt">Element</span> Meshes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ding, H. Q.; Ferraro, R. D.</p> <p>1995-01-01</p> <p>A parallel partitioner for partitioning unstructured <span class="hlt">finite</span> <span class="hlt">element</span> meshes on distributed memory architectures is developed. The <span class="hlt">element</span> based partitioner can handle mixtures of different <span class="hlt">element</span> types. All algorithms adopted in the partitioner are scalable, including a communication template for unpredictable incoming messages, as shown in actual timing measurements.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_18");'>18</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li class="active"><span>20</span></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_20 --> <div id="page_21" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="401"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013CompM..52..607C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013CompM..52..607C"><span>Modelling of tunnelling processes and rock cutting tool wear with the particle <span class="hlt">finite</span> <span class="hlt">element</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Carbonell, Josep Maria; Oñate, Eugenio; Suárez, Benjamín</p> <p>2013-09-01</p> <p>Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are growing, and so safety and security demands do. New engineering tools are needed to perform a safer planning and design. This work presents the advances in the particle <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM) for the modelling and the analysis of tunneling processes including the wear of the cutting tools. The PFEM has its foundation on the <span class="hlt">Lagrangian</span> description of the motion of a continuum built from a set of particles with known physical properties. The method uses a remeshing process combined with the alpha-shape technique to detect the contacting surfaces and a <span class="hlt">finite</span> <span class="hlt">element</span> method for the mechanical computations. A contact procedure has been developed for the PFEM which is combined with a constitutive model for predicting the excavation front and the wear of cutting tools. The material parameters govern the coupling of frictional contact and wear between the interacting domains at the excavation front. The PFEM allows predicting several parameters which are relevant for estimating the performance of a tunnelling boring machine such as wear in the cutting tools, the pressure distribution on the face of the boring machine and the vibrations produced in the machinery and the adjacent soil/rock. The final aim is to help in the design of the excavating tools and in the planning of the tunnelling operations. The applications presented show that the PFEM is a promising technique for the analysis of tunnelling problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22591337-finite-element-analysis-two-disk-rotor-system','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22591337-finite-element-analysis-two-disk-rotor-system"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of two disk rotor system</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Dixit, Harsh Kumar</p> <p></p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam <span class="hlt">element</span> and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the <span class="hlt">finite</span> <span class="hlt">element</span> equations of rotary system. Consequently, Campbell diagram is plotted for finding amore » relationship between natural whirl frequencies and rotation of the rotor.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19980211456','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19980211456"><span>A 2-D Interface <span class="hlt">Element</span> for Coupled Analysis of Independently Modeled 3-D <span class="hlt">Finite</span> <span class="hlt">Element</span> Subdomains</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kandil, Osama A.</p> <p>1998-01-01</p> <p>Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed <span class="hlt">finite</span> <span class="hlt">element</span> models within <span class="hlt">finite</span> <span class="hlt">element</span> models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface <span class="hlt">element</span> is based on an alternate variational principle often used in deriving hybrid <span class="hlt">finite</span> <span class="hlt">elements</span>. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose <span class="hlt">finite</span> <span class="hlt">element</span> codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface <span class="hlt">element</span> includes the one-dimensional line interface <span class="hlt">element</span> and two-dimensional surface interface <span class="hlt">element</span>. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface <span class="hlt">element</span> technology; however, only limited applications are available for the surface interface <span class="hlt">element</span>. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface <span class="hlt">elements</span> and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26826855','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26826855"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Rivera, Michael K; Ecke, Robert E</p> <p>2016-01-01</p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale ri. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in terms of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1351187','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1351187"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Rivera, Michael K.; Ecke, Robert E.</p> <p></p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1351187-lagrangian-statistics-weakly-forced-two-dimensional-turbulence"><span><span class="hlt">Lagrangian</span> statistics in weakly forced two-dimensional turbulence</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Rivera, Michael K.; Ecke, Robert E.</p> <p>2016-01-14</p> <p>Measurements of <span class="hlt">Lagrangian</span> single-point and multiple-point statistics in a quasi-two-dimensional stratified layer system are reported. The system consists of a layer of salt water over an immiscible layer of Fluorinert and is forced electromagnetically so that mean-squared vorticity is injected at a well-defined spatial scale r i. Simultaneous cascades develop in which enstrophy flows predominately to small scales whereas energy cascades, on average, to larger scales. <span class="hlt">Lagrangian</span> correlations and one- and two-point displacements are measured for random initial conditions and for initial positions within topological centers and saddles. Some of the behavior of these quantities can be understood in termsmore » of the trapping characteristics of long-lived centers, the slow motion near strong saddles, and the rapid fluctuations outside of either centers or saddles. We also present statistics of <span class="hlt">Lagrangian</span> velocity fluctuations using energy spectra in frequency space and structure functions in real space. We compare with complementary <span class="hlt">Eulerian</span> velocity statistics. We find that simultaneous inverse energy and enstrophy ranges present in spectra are not directly echoed in real-space moments of velocity difference. Nevertheless, the spectral ranges line up well with features of moment ratios, indicating that although the moments are not exhibiting unambiguous scaling, the behavior of the probability distribution functions is changing over short ranges of length scales. Furthermore, implications for understanding weakly forced 2D turbulence with simultaneous inverse and direct cascades are discussed.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19950004782','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19950004782"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of a composite wheelchair wheel design</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ortega, Rene</p> <p>1994-01-01</p> <p>The <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a composite wheelchair wheel design is presented. The design is the result of a technology utilization request. The designer's intent is to soften the riding feeling by incorporating a mechanism attaching the wheel rim to the spokes that would allow considerable deflection upon compressive loads. A <span class="hlt">finite</span> <span class="hlt">element</span> analysis was conducted to verify proper structural function. Displacement and stress results are presented and conclusions are provided.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1311297-weak-galerkin-generalized-multiscale-finite-element-method','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1311297-weak-galerkin-generalized-multiscale-finite-element-method"><span>A weak Galerkin generalized multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Mu, Lin; Wang, Junping; Ye, Xiu</p> <p>2016-03-31</p> <p>In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) <span class="hlt">finite</span> <span class="hlt">element</span> method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method. Convergence analysis and numerical experiments are obtained for the special case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1311297','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/1311297"><span>A weak Galerkin generalized multiscale <span class="hlt">finite</span> <span class="hlt">element</span> method</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Mu, Lin; Wang, Junping; Ye, Xiu</p> <p></p> <p>In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) <span class="hlt">finite</span> <span class="hlt">element</span> method for the elliptic problems with rapidly oscillating or high contrast coefficients. This general WG-GMS method features in high order accuracy on general meshes and can work with multiscale basis derived by different numerical schemes. A special case is studied under this WG-GMS framework in which the multiscale basis functions are obtained by solving local problem with the weak Galerkin <span class="hlt">finite</span> <span class="hlt">element</span> method. Convergence analysis and numerical experiments are obtained for the special case.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870004578','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870004578"><span>Development of non-linear <span class="hlt">finite</span> <span class="hlt">element</span> computer code</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Becker, E. B.; Miller, T.</p> <p>1985-01-01</p> <p>Recent work has shown that the use of separable symmetric functions of the principal stretches can adequately describe the response of certain propellant materials and, further, that a data reduction scheme gives a convenient way of obtaining the values of the functions from experimental data. Based on representation of the energy, a computational scheme was developed that allows <span class="hlt">finite</span> <span class="hlt">element</span> analysis of boundary value problems of arbitrary shape and loading. The computational procedure was implemental in a three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> code, TEXLESP-S, which is documented herein.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19900013812','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19900013812"><span>Fourier analysis of <span class="hlt">finite</span> <span class="hlt">element</span> preconditioned collocation schemes</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Deville, Michel O.; Mund, Ernest H.</p> <p>1990-01-01</p> <p>The spectrum of the iteration operator of some <span class="hlt">finite</span> <span class="hlt">element</span> preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of <span class="hlt">finite</span> <span class="hlt">element</span> preconditioning schemes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015MS%26E...95a2046P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015MS%26E...95a2046P"><span>Modelling bucket excavation by <span class="hlt">finite</span> <span class="hlt">element</span></span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Pecingina, O. M.</p> <p>2015-11-01</p> <p>Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path <span class="hlt">elements</span> and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of <span class="hlt">finite</span> <span class="hlt">element</span> method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with <span class="hlt">finite</span> <span class="hlt">element</span> analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to <span class="hlt">finite</span> <span class="hlt">element</span> study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1991umas.rept.....O','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1991umas.rept.....O"><span><span class="hlt">Lagrangian</span> turbulence: Structures and mixing in admissible model flows</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ottino, Julio M.</p> <p>1991-12-01</p> <p>The goal of our research was to bridge the gap between modern ideas from dynamical systems and chaos and more traditional approaches to turbulence. In order to reach this objective we conducted theoretical and computational work on two systems: (1) a perturbed-Kelvin cat eyes flow, and (2) prototype solutions of the Navier-Stokes equations near solid walls. The main results obtained are two-fold: we have been able to produce flows capable of producing complex distributions of vorticity, and we have been able to construct flowfields, based on solutions of the Navier-Stokes equations, which are capable of displaying both <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> turbulence. These results exemplify typical mechanisms of mixing enhancement in transitional flows.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20040086466','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20040086466"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Model Development and Validation for Aircraft Fuselage Structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Buehrle, Ralph D.; Fleming, Gary A.; Pappa, Richard S.; Grosveld, Ferdinand W.</p> <p>2000-01-01</p> <p>The ability to extend the valid frequency range for <span class="hlt">finite</span> <span class="hlt">element</span> based structural dynamic predictions using detailed models of the structural components and attachment interfaces is examined for several stiffened aircraft fuselage structures. This extended dynamic prediction capability is needed for the integration of mid-frequency noise control technology. Beam, plate and solid <span class="hlt">element</span> models of the stiffener components are evaluated. Attachment models between the stiffener and panel skin range from a line along the rivets of the physical structure to a constraint over the entire contact surface. The <span class="hlt">finite</span> <span class="hlt">element</span> models are validated using experimental modal analysis results. The increased frequency range results in a corresponding increase in the number of modes, modal density and spatial resolution requirements. In this study, conventional modal tests using accelerometers are complemented with Scanning Laser Doppler Velocimetry and Electro-Optic Holography measurements to further resolve the spatial response characteristics. Whenever possible, component and subassembly modal tests are used to validate the <span class="hlt">finite</span> <span class="hlt">element</span> models at lower levels of assembly. Normal mode predictions for different <span class="hlt">finite</span> <span class="hlt">element</span> representations of components and assemblies are compared with experimental results to assess the most accurate techniques for modeling aircraft fuselage type structures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4801678','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4801678"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Simulation of Articular Contact Mechanics with Quadratic Tetrahedral <span class="hlt">Elements</span></span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Maas, Steve A.; Ellis, Benjamin J.; Rawlins, David S.; Weiss, Jeffrey A.</p> <p>2016-01-01</p> <p>Although it is easier to generate <span class="hlt">finite</span> <span class="hlt">element</span> discretizations with tetrahedral <span class="hlt">elements</span>, trilinear hexahedral (HEX8) <span class="hlt">elements</span> are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) <span class="hlt">elements</span>, limited availability of quadratic tetrahedron <span class="hlt">elements</span> in combination with effective contact algorithms, and the perceived increased computational expense of quadratic <span class="hlt">finite</span> <span class="hlt">elements</span>. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral <span class="hlt">elements</span> in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic <span class="hlt">elements</span> affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 <span class="hlt">element</span> demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 <span class="hlt">elements</span> for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral <span class="hlt">elements</span> was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 <span class="hlt">elements</span> provide viable alternatives to HEX8 <span class="hlt">elements</span> for simulation of articular contact mechanics. PMID:26900037</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/26900037','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/26900037"><span><span class="hlt">Finite</span> <span class="hlt">element</span> simulation of articular contact mechanics with quadratic tetrahedral <span class="hlt">elements</span>.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A</p> <p>2016-03-21</p> <p>Although it is easier to generate <span class="hlt">finite</span> <span class="hlt">element</span> discretizations with tetrahedral <span class="hlt">elements</span>, trilinear hexahedral (HEX8) <span class="hlt">elements</span> are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) <span class="hlt">elements</span>, limited availability of quadratic tetrahedron <span class="hlt">elements</span> in combination with effective contact algorithms, and the perceived increased computational expense of quadratic <span class="hlt">finite</span> <span class="hlt">elements</span>. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral <span class="hlt">elements</span> in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic <span class="hlt">elements</span> affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 <span class="hlt">element</span> demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 <span class="hlt">elements</span> for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral <span class="hlt">elements</span> was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 <span class="hlt">elements</span> provide viable alternatives to HEX8 <span class="hlt">elements</span> for simulation of articular contact mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19860023571','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19860023571"><span>Supercomputer implementation of <span class="hlt">finite</span> <span class="hlt">element</span> algorithms for high speed compressible flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, E. A.; Ramakrishnan, R.</p> <p>1986-01-01</p> <p>Prediction of compressible flow phenomena using the <span class="hlt">finite</span> <span class="hlt">element</span> method is of recent origin and considerable interest. Two shock capturing <span class="hlt">finite</span> <span class="hlt">element</span> formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the <span class="hlt">finite</span> <span class="hlt">element</span> formulations on the NASA Langley VPS-32. The vectorization scheme results in <span class="hlt">finite</span> <span class="hlt">element</span> programs that use vectors of length of the order of the number of nodes or <span class="hlt">elements</span>. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the <span class="hlt">finite</span> <span class="hlt">element</span> procedures for realistic problems that require hundreds of thousands of nodes.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/22212764-phase-space-finite-elements-least-squares-solution-transport-equation','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/22212764-phase-space-finite-elements-least-squares-solution-transport-equation"><span>Phase-space <span class="hlt">finite</span> <span class="hlt">elements</span> in a least-squares solution of the transport equation</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Drumm, C.; Fan, W.; Pautz, S.</p> <p>2013-07-01</p> <p>The linear Boltzmann transport equation is solved using a least-squares <span class="hlt">finite</span> <span class="hlt">element</span> approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular <span class="hlt">finite</span> <span class="hlt">elements</span> approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular <span class="hlt">finite</span> <span class="hlt">elements</span>: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial <span class="hlt">finite-elements</span> machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam <span class="hlt">elements</span>, also building upon the spatial <span class="hlt">finite</span> <span class="hlt">elements</span> capabilities. The methods described here can make use of either continuous or discontinuous <span class="hlt">finite</span> <span class="hlt">elements</span> in space, angle and/or energy, with the use of continuous <span class="hlt">finite</span> <span class="hlt">elements</span> resulting in a smaller problem size and the use of discontinuous <span class="hlt">finite</span> <span class="hlt">elements</span> resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous <span class="hlt">finite</span> <span class="hlt">elements</span>, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space <span class="hlt">finite</span> <span class="hlt">elements</span> capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015PhDT.......114R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015PhDT.......114R"><span><span class="hlt">Lagrangian</span> Fluid <span class="hlt">Element</span> Tracking and Estimation of Local Displacement Speeds in Turbulent Premixed Flames</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ramji, Sarah Ann</p> <p></p> <p>Improved understanding of turbulence-flame interactions in premixed combustion can be achieved using fully 3D time-resolved multi-kHz multi-scalar experimental measurements. These interactions may be represented by the evolution of various <span class="hlt">Lagrangian</span> quantities described by theoretical <span class="hlt">Lagrangian</span> Fluid <span class="hlt">Elements</span> (LFEs). The data used in this work came from two experimental campaigns that used simultaneous T-PIV and OH/CH2O PLIF, at Sandia National Labs and the Air Force Research Lab at Wright-Patterson. In this thesis, an algorithm to accurately track LFEs through this 4D experimental space has been developed and verified by cross-correlation with the T-PIV seed particle fields. A novel method to measure the local instantaneous displacement speed in 3D has been developed, using this algorithm to track control masses of fluid that interact with the flame front. Statistics of the displacement speed have been presented, and the effects of local turbulence and flame topological properties on the displacement speed have been studied.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19810022964','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19810022964"><span>Exact <span class="hlt">finite</span> <span class="hlt">elements</span> for conduction and convection</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.</p> <p>1981-01-01</p> <p>An approach for developing exact one dimensional conduction-convection <span class="hlt">finite</span> <span class="hlt">elements</span> is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional <span class="hlt">elements</span> offer advantages over <span class="hlt">elements</span> based on approximate interpolation functions.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_19");'>19</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li class="active"><span>21</span></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_21 --> <div id="page_22" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="421"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20100008495','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20100008495"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Models and Properties of a Stiffened Floor-Equipped Composite Cylinder</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.</p> <p>2010-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> models were developed of a floor-equipped, frame and stringer stiffened composite cylinder including a coarse <span class="hlt">finite</span> <span class="hlt">element</span> model of the structural components, a coarse <span class="hlt">finite</span> <span class="hlt">element</span> model of the acoustic cavities above and below the beam-supported plywood floor, and two dense models consisting of only the structural components. The report summarizes the geometry, the <span class="hlt">element</span> properties, the material and mechanical properties, the beam cross-section characteristics, the beam <span class="hlt">element</span> representations and the boundary conditions of the composite cylinder models. The expressions used to calculate the group speeds for the cylinder components are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930016034','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930016034"><span>Using a multifrontal sparse solver in a high performance, <span class="hlt">finite</span> <span class="hlt">element</span> code</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>King, Scott D.; Lucas, Robert; Raefsky, Arthur</p> <p>1990-01-01</p> <p>We consider the performance of the <span class="hlt">finite</span> <span class="hlt">element</span> method on a vector supercomputer. The computationally intensive parts of the <span class="hlt">finite</span> <span class="hlt">element</span> method are typically the individual <span class="hlt">element</span> forms and the solution of the global stiffness matrix both of which are vectorized in high performance codes. To further increase throughput, new algorithms are needed. We compare a multifrontal sparse solver to a traditional skyline solver in a <span class="hlt">finite</span> <span class="hlt">element</span> code on a vector supercomputer. The multifrontal solver uses the Multiple-Minimum Degree reordering heuristic to reduce the number of operations required to factor a sparse matrix and full matrix computational kernels (e.g., BLAS3) to enhance vector performance. The net result in an order-of-magnitude reduction in run time for a <span class="hlt">finite</span> <span class="hlt">element</span> application on one processor of a Cray X-MP.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/11477778','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/11477778"><span><span class="hlt">Finite</span> <span class="hlt">element</span> simulation of piezoelectric transformers.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Tsuchiya, T; Kagawa, Y; Wakatsuki, N; Okamura, H</p> <p>2001-07-01</p> <p>Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The <span class="hlt">finite</span> <span class="hlt">element</span> approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010AIPC.1233.1082T','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010AIPC.1233.1082T"><span>A Novel Polygonal <span class="hlt">Finite</span> <span class="hlt">Element</span> Method: Virtual Node Method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Tang, X. H.; Zheng, C.; Zhang, J. H.</p> <p>2010-05-01</p> <p>Polygonal <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM), which can construct shape functions on polygonal <span class="hlt">elements</span>, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal <span class="hlt">finite</span> <span class="hlt">element</span> method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of <span class="hlt">finite</span> <span class="hlt">element</span> method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node <span class="hlt">elements</span> in the accuracy test.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012APS..DPPJP8110C"><span>Asymptotic-preserving <span class="hlt">Lagrangian</span> approach for modeling anisotropic transport in magnetized plasmas for arbitrary magnetic fields</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Chacon, Luis; Del-Castillo-Negrete, Diego; Hauck, Cory</p> <p>2012-10-01</p> <p>Modeling electron transport in magnetized plasmas is extremely challenging due to the extreme anisotropy between parallel (to the magnetic field) and perpendicular directions (χ/χ˜10^10 in fusion plasmas). Recently, a <span class="hlt">Lagrangian</span> Green's function approach, developed for the purely parallel transport case,footnotetextD. del-Castillo-Negrete, L. Chac'on, PRL, 106, 195004 (2011)^,footnotetextD. del-Castillo-Negrete, L. Chac'on, Phys. Plasmas, 19, 056112 (2012) has been extended to the anisotropic transport case in the tokamak-ordering limit with constant density.footnotetextL. Chac'on, D. del-Castillo-Negrete, C. Hauck, JCP, submitted (2012) An operator-split algorithm is proposed that allows one to treat <span class="hlt">Eulerian</span> and <span class="hlt">Lagrangian</span> components separately. The approach is shown to feature bounded numerical errors for arbitrary χ/χ ratios, which renders it asymptotic-preserving. In this poster, we will present the generalization of the <span class="hlt">Lagrangian</span> approach to arbitrary magnetic fields. We will demonstrate the potential of the approach with various challenging configurations, including the case of transport across a magnetic island in cylindrical geometry.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20080022946','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20080022946"><span>Comparison of ALE and SPH Simulations of Vertical Drop Tests of a Composite Fuselage Section into Water</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Jackson, Karen E.; Fuchs, Yvonne T.</p> <p>2008-01-01</p> <p>Simulation of multi-terrain impact has been identified as an important research area for improved prediction of rotorcraft crashworthiness within the NASA Subsonic Rotary Wing Aeronautics Program on Rotorcraft Crashworthiness. As part of this effort, two vertical drop tests were conducted of a 5-ft-diameter composite fuselage section into water. For the first test, the fuselage section was impacted in a baseline configuration without energy absorbers. For the second test, the fuselage section was retrofitted with a composite honeycomb energy absorber. Both tests were conducted at a nominal velocity of 25-ft/s. A detailed <span class="hlt">finite</span> <span class="hlt">element</span> model was developed to represent each test article and water impact was simulated using both Arbitrary <span class="hlt">Lagrangian</span> <span class="hlt">Eulerian</span> (ALE) and Smooth Particle Hydrodynamics (SPH) approaches in LS-DYNA, a nonlinear, explicit transient dynamic <span class="hlt">finite</span> <span class="hlt">element</span> code. Analytical predictions were correlated with experimental data for both test configurations. In addition, studies were performed to evaluate the influence of mesh density on test-analysis correlation.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19960014820','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19960014820"><span>Efficient <span class="hlt">finite</span> <span class="hlt">element</span> simulation of slot spirals, slot radomes and microwave structures</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gong, J.; Volakis, J. L.</p> <p>1995-01-01</p> <p>This progress report contains the following two documents: (1) 'Efficient <span class="hlt">Finite</span> <span class="hlt">Element</span> Simulation of Slot Antennas using Prismatic <span class="hlt">Elements</span>' - A hybrid <span class="hlt">finite</span> <span class="hlt">element</span>-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic <span class="hlt">elements</span> are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for <span class="hlt">Finite</span> <span class="hlt">Element</span> Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain <span class="hlt">finite</span> <span class="hlt">element</span> simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20050204125','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20050204125"><span><span class="hlt">Finite</span> Macro-<span class="hlt">Element</span> Mesh Deformation in a Structured Multi-Block Navier-Stokes Code</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bartels, Robert E.</p> <p>2005-01-01</p> <p>A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a <span class="hlt">finite</span> <span class="hlt">element</span> solution of either user defined or automatically generated macro-<span class="hlt">elements</span>. Macro-<span class="hlt">elements</span> are hexagonal <span class="hlt">finite</span> <span class="hlt">elements</span> created from a subset of points from the full mesh. When assembled, the <span class="hlt">finite</span> <span class="hlt">element</span> system spans the complete flow domain. Macro-<span class="hlt">element</span> moduli vary according to the distance to the nearest surface, resulting in extremely stiff <span class="hlt">elements</span> near a moving surface and very pliable <span class="hlt">elements</span> away from boundaries. Solution of the <span class="hlt">finite</span> <span class="hlt">element</span> system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the <span class="hlt">element</span> deformation. The second step is a transfinite interpolation which distributes the macro-<span class="hlt">element</span> nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018MS%26E..322d2011D','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018MS%26E..322d2011D"><span>Integral <span class="hlt">finite</span> <span class="hlt">element</span> analysis of turntable bearing with flexible rings</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng</p> <p>2018-03-01</p> <p>This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling <span class="hlt">elements</span> is determined by the <span class="hlt">finite</span> <span class="hlt">element</span> contact analysis of a single rolling <span class="hlt">element</span> and the raceway. Based on this, the nonlinear contact between the rolling <span class="hlt">elements</span> and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral <span class="hlt">finite</span> <span class="hlt">element</span> analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other <span class="hlt">finite</span> <span class="hlt">element</span> analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940029799','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940029799"><span>Analysis of random structure-acoustic interaction problems using coupled boundary <span class="hlt">element</span> and <span class="hlt">finite</span> <span class="hlt">element</span> methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mei, Chuh; Pates, Carl S., III</p> <p>1994-01-01</p> <p>A coupled boundary <span class="hlt">element</span> (BEM)-<span class="hlt">finite</span> <span class="hlt">element</span> (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary <span class="hlt">element</span> method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary <span class="hlt">element</span> results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the <span class="hlt">finite</span> <span class="hlt">element</span> method models the structure and the boundary <span class="hlt">element</span> method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1012771','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1012771"><span>A Computational Approach for Automated Posturing of a Human <span class="hlt">Finite</span> <span class="hlt">Element</span> Model</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2016-07-01</p> <p>Std. Z39.18 July 2016 Memorandum Report A Computational Approach for Automated Posturing of a Human <span class="hlt">Finite</span> <span class="hlt">Element</span> Model Justin McKee and Adam...protection by influencing the path that loading will be transferred into the body and is a major source of variability. The development of a <span class="hlt">finite</span> <span class="hlt">element</span> ...posture, human body, <span class="hlt">finite</span> <span class="hlt">element</span> , leg, spine 42 Adam Sokolow 410-306-2985Unclassified Unclassified Unclassified UU ii Approved for public release</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA609225','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA609225"><span>Predicting Rediated Noise With Power Flow <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2007-02-01</p> <p>Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19860043915&hterms=PFEM&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DPFEM','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19860043915&hterms=PFEM&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3DPFEM"><span>Probabilistic <span class="hlt">finite</span> <span class="hlt">elements</span> for transient analysis in nonlinear continua</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Liu, W. K.; Belytschko, T.; Mani, A.</p> <p>1985-01-01</p> <p>The probabilistic <span class="hlt">finite</span> <span class="hlt">element</span> method (PFEM), which is a combination of <span class="hlt">finite</span> <span class="hlt">element</span> methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in <span class="hlt">finite</span> <span class="hlt">element</span> methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.322..666R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.322..666R"><span>Mixed <span class="hlt">finite</span> <span class="hlt">element</span> - discontinuous <span class="hlt">finite</span> volume <span class="hlt">element</span> discretization of a general class of multicontinuum models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ruiz-Baier, Ricardo; Lunati, Ivan</p> <p>2016-10-01</p> <p>We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed <span class="hlt">finite</span> <span class="hlt">element</span> discretization of the momentum equations with a primal discontinuous <span class="hlt">finite</span> volume-<span class="hlt">element</span> discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant <span class="hlt">elements</span> for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous <span class="hlt">finite</span> volume <span class="hlt">elements</span> defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19820025514','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19820025514"><span>Engine dynamic analysis with general nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> codes. Part 2: Bearing <span class="hlt">element</span> implementation overall numerical characteristics and benchmaking</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.</p> <p>1982-01-01</p> <p><span class="hlt">Finite</span> <span class="hlt">element</span> codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available <span class="hlt">finite</span> <span class="hlt">element</span> codes. benchmarking the <span class="hlt">elements</span> developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of <span class="hlt">finite</span> <span class="hlt">element</span> type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/483339','SCIGOV-STC'); return false;" href="https://www.osti.gov/servlets/purl/483339"><span><span class="hlt">Finite</span> <span class="hlt">element</span> analysis of human joints</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Bossart, P.L.; Hollerbach, K.</p> <p>1996-09-01</p> <p>Our work focuses on the development of <span class="hlt">finite</span> <span class="hlt">element</span> models (FEMs) that describe the biomechanics of human joints. <span class="hlt">Finite</span> <span class="hlt">element</span> modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiringmore » data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1992JSV...152..107M','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1992JSV...152..107M"><span>A <span class="hlt">finite</span> <span class="hlt">element</span> analysis of viscoelastically damped sandwich plates</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ma, B.-A.; He, J.-F.</p> <p>1992-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> analysis associated with an asymptotic solution method for the harmonic flexural vibration of viscoelastically damped unsymmetrical sandwich plates is given. The <span class="hlt">element</span> formulation is based on generalization of the discrete Kirchhoff theory (DKT) <span class="hlt">element</span> formulation. The results obtained with the first order approximation of the asymptotic solution presented here are the same as those obtained by means of the modal strain energy (MSE) method. By taking more terms of the asymptotic solution, with successive calculations and use of the Padé approximants method, accuracy can be improved. The <span class="hlt">finite</span> <span class="hlt">element</span> computation has been verified by comparison with an analytical exact solution for rectangular plates with simply supported edges. Results for the same plates with clamped edges are also presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/servlets/purl/1079421','DOE-PATENT-XML'); return false;" href="https://www.osti.gov/servlets/purl/1079421"><span>Quadrilateral/hexahedral <span class="hlt">finite</span> <span class="hlt">element</span> mesh coarsening</span></a></p> <p><a target="_blank" href="http://www.osti.gov/doepatents">DOEpatents</a></p> <p>Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E</p> <p>2012-10-16</p> <p>A technique for coarsening a <span class="hlt">finite</span> <span class="hlt">element</span> mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh <span class="hlt">elements</span> residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20150020428','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20150020428"><span>Contact Stress Analysis of Spiral Bevel Gears Using <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Bibel, G. D.; Kumar, A; Reddy, S.; Handschuh, R.</p> <p>1995-01-01</p> <p>A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the <span class="hlt">finite</span> <span class="hlt">element</span> method. The procedure involves generating a <span class="hlt">finite</span> <span class="hlt">element</span> model by solving equations that identify tooth surface coordinates. Coordinate transformations are used to orientate the gear and pinion for gear meshing. Contact boundary conditions are simulated with gap <span class="hlt">elements</span>. A solution technique for correct orientation of the gap <span class="hlt">elements</span> is given. Example models and results are presented.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016JCoPh.322..429G','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016JCoPh.322..429G"><span>Exponential convergence through linear <span class="hlt">finite</span> <span class="hlt">element</span> discretization of stratified subdomains</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Guddati, Murthy N.; Druskin, Vladimir; Vaziri Astaneh, Ali</p> <p>2016-10-01</p> <p>Motivated by problems where the response is needed at select localized regions in a large computational domain, we devise a novel <span class="hlt">finite</span> <span class="hlt">element</span> discretization that results in exponential convergence at pre-selected points. The key features of the discretization are (a) use of midpoint integration to evaluate the contribution matrices, and (b) an unconventional mapping of the mesh into complex space. Named complex-length <span class="hlt">finite</span> <span class="hlt">element</span> method (CFEM), the technique is linked to Padé approximants that provide exponential convergence of the Dirichlet-to-Neumann maps and thus the solution at specified points in the domain. Exponential convergence facilitates drastic reduction in the number of <span class="hlt">elements</span>. This, combined with sparse computation associated with linear <span class="hlt">finite</span> <span class="hlt">elements</span>, results in significant reduction in the computational cost. The paper presents the basic ideas of the method as well as illustration of its effectiveness for a variety of problems involving Laplace, Helmholtz and elastodynamics equations.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_20");'>20</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li class="active"><span>22</span></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_22 --> <div id="page_23" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="441"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/10232856','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/10232856"><span>The effectiveness of <span class="hlt">element</span> downsizing on a three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> model of bone trabeculae in implant biomechanics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Sato, Y; Wadamoto, M; Tsuga, K; Teixeira, E R</p> <p>1999-04-01</p> <p>More validity of <span class="hlt">finite</span> <span class="hlt">element</span> analysis in implant biomechanics requires <span class="hlt">element</span> downsizing. However, excess downsizing needs computer memory and calculation time. To investigate the effectiveness of <span class="hlt">element</span> downsizing on the construction of a three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> bone trabeculae model, with different <span class="hlt">element</span> sizes (600, 300, 150 and 75 microm) models were constructed and stress induced by vertical 10 N loading was analysed. The difference in von Mises stress values between the models with 600 and 300 microm <span class="hlt">element</span> sizes was larger than that between 300 and 150 microm. On the other hand, no clear difference of stress values was detected among the models with 300, 150 and 75 microm <span class="hlt">element</span> sizes. Downsizing of <span class="hlt">elements</span> from 600 to 300 microm is suggested to be effective in the construction of a three-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> bone trabeculae model for possible saving of computer memory and calculation time in the laboratory.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19880018222','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19880018222"><span><span class="hlt">Finite</span> <span class="hlt">element</span> methodology for integrated flow-thermal-structural analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, Earl A.; Ramakrishnan, R.; Vemaganti, G. R.</p> <p>1988-01-01</p> <p>Papers entitled, An Adaptive <span class="hlt">Finite</span> <span class="hlt">Element</span> Procedure for Compressible Flows and Strong Viscous-Inviscid Interactions, and An Adaptive Remeshing Method for <span class="hlt">Finite</span> <span class="hlt">Element</span> Thermal Analysis, were presented at the June 27 to 29, 1988, meeting of the AIAA Thermophysics, Plasma Dynamics and Lasers Conference, San Antonio, Texas. The papers describe research work supported under NASA/Langley Research Grant NsG-1321, and are submitted in fulfillment of the progress report requirement on the grant for the period ending February 29, 1988.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015JCoPh.297..530B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015JCoPh.297..530B"><span>Stable <span class="hlt">finite</span> <span class="hlt">element</span> approximations of two-phase flow with soluble surfactant</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Barrett, John W.; Garcke, Harald; Nürnberg, Robert</p> <p>2015-09-01</p> <p>A parametric <span class="hlt">finite</span> <span class="hlt">element</span> approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric <span class="hlt">finite</span> <span class="hlt">element</span> approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface <span class="hlt">finite</span> <span class="hlt">element</span> method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard <span class="hlt">finite</span> <span class="hlt">element</span> approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1432978-topology-optimization-finite-strain-viscoplastic-systems-under-transient-loads-dynamic-topology-optimization-based-finite-strain-visco-plasticity','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1432978-topology-optimization-finite-strain-viscoplastic-systems-under-transient-loads-dynamic-topology-optimization-based-finite-strain-visco-plasticity"><span>Topology optimization of <span class="hlt">finite</span> strain viscoplastic systems under transient loads [Dynamic topology optimization based on <span class="hlt">finite</span> strain visco-plasticity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel</p> <p></p> <p>In this paper, a transient <span class="hlt">finite</span> strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient <span class="hlt">finite</span> strain viscoplastic effects can successfully be combined with topology optimization.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/pages/biblio/1432978-topology-optimization-finite-strain-viscoplastic-systems-under-transient-loads-dynamic-topology-optimization-based-finite-strain-visco-plasticity','SCIGOV-DOEP'); return false;" href="https://www.osti.gov/pages/biblio/1432978-topology-optimization-finite-strain-viscoplastic-systems-under-transient-loads-dynamic-topology-optimization-based-finite-strain-visco-plasticity"><span>Topology optimization of <span class="hlt">finite</span> strain viscoplastic systems under transient loads [Dynamic topology optimization based on <span class="hlt">finite</span> strain visco-plasticity</span></a></p> <p><a target="_blank" href="http://www.osti.gov/pages">DOE PAGES</a></p> <p>Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel</p> <p>2018-02-08</p> <p>In this paper, a transient <span class="hlt">finite</span> strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> <span class="hlt">element</span> formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient <span class="hlt">finite</span> strain viscoplastic effects can successfully be combined with topology optimization.« less</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19830053045&hterms=exact+differential+equation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dexact%2Bdifferential%2Bequation','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19830053045&hterms=exact+differential+equation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dexact%2Bdifferential%2Bequation"><span>Exact <span class="hlt">finite</span> <span class="hlt">elements</span> for conduction and convection</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.</p> <p>1981-01-01</p> <p>An appproach for developing exact one dimensional conduction-convection <span class="hlt">finite</span> <span class="hlt">elements</span> is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional <span class="hlt">elements</span> offer advantages over <span class="hlt">elements</span> based on approximate interpolation functions. Previously announced in STAR as N81-31507</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19800016167','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19800016167"><span>IFEMS, an Interactive <span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling System Using a CAD/CAM System</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Mckellip, S.; Schuman, T.; Lauer, S.</p> <p>1980-01-01</p> <p>A method of coupling a CAD/CAM system with a general purpose <span class="hlt">finite</span> <span class="hlt">element</span> mesh generator is described. The three computer programs which make up the interactive <span class="hlt">finite</span> <span class="hlt">element</span> graphics system are discussed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2010JMEP...19..495R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2010JMEP...19..495R"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling, Simulation, Tools, and Capabilities at Superform</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Raman, Hari; Barnes, A. J.</p> <p>2010-06-01</p> <p>Over the past thirty years Superform has been a pioneer in the SPF arena, having developed a keen understanding of the process and a range of unique forming techniques to meet varying market needs. Superform’s high-profile list of customers includes Boeing, Airbus, Aston Martin, Ford, and Rolls Royce. One of the more recent additions to Superform’s technical know-how is <span class="hlt">finite</span> <span class="hlt">element</span> modeling and simulation. <span class="hlt">Finite</span> <span class="hlt">element</span> modeling is a powerful numerical technique which when applied to SPF provides a host of benefits including accurate prediction of strain levels in a part, presence of wrinkles and predicting pressure cycles optimized for time and part thickness. This paper outlines a brief history of <span class="hlt">finite</span> <span class="hlt">element</span> modeling applied to SPF and then reviews some of the modeling tools and techniques that Superform have applied and continue to do so to successfully superplastically form complex-shaped parts. The advantages of employing modeling at the design stage are discussed and illustrated with real-world examples.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JQSRT.189..383W','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JQSRT.189..383W"><span>Discontinuous <span class="hlt">finite</span> <span class="hlt">element</span> method for vector radiative transfer</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Wang, Cun-Hai; Yi, Hong-Liang; Tan, He-Ping</p> <p>2017-03-01</p> <p>The discontinuous <span class="hlt">finite</span> <span class="hlt">element</span> method (DFEM) is applied to solve the vector radiative transfer in participating media. The derivation in a discrete form of the vector radiation governing equations is presented, in which the angular space is discretized by the discrete-ordinates approach with a local refined modification, and the spatial domain is discretized into <span class="hlt">finite</span> non-overlapped discontinuous <span class="hlt">elements</span>. The <span class="hlt">elements</span> in the whole solution domain are connected by modelling the boundary numerical flux between adjacent <span class="hlt">elements</span>, which makes the DFEM numerically stable for solving radiative transfer equations. Several various problems of vector radiative transfer are tested to verify the performance of the developed DFEM, including vector radiative transfer in a one-dimensional parallel slab containing a Mie/Rayleigh/strong forward scattering medium and a two-dimensional square medium. The fact that DFEM results agree very well with the benchmark solutions in published references shows that the developed DFEM in this paper is accurate and effective for solving vector radiative transfer problems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA166056','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA166056"><span>Development and Application of the p-version of the <span class="hlt">Finite</span> <span class="hlt">Element</span> Method.</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1985-11-21</p> <p>this property hierarchic families of <span class="hlt">finite</span> <span class="hlt">elements</span>. The h-version of the <span class="hlt">finite</span> <span class="hlt">element</span> method has been the subject of inten- sive study since the...early 1950’s and perhaps even earlier. Study of the p-version of the <span class="hlt">finite</span> <span class="hlt">element</span> method, on the other hand, began at Washington University in St...Louis in the early 1970’s and led to a more recent study of * .the h-p version. Research in the p-version (formerly called The Constraint Method) has</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25937546','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25937546"><span>Subject specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling of periprosthetic femoral fracture using <span class="hlt">element</span> deactivation to simulate bone failure.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Miles, Brad; Kolos, Elizabeth; Walter, William L; Appleyard, Richard; Shi, Angela; Li, Qing; Ruys, Andrew J</p> <p>2015-06-01</p> <p>Subject-specific <span class="hlt">finite</span> <span class="hlt">element</span> (FE) modeling methodology could predict peri-prosthetic femoral fracture (PFF) for cementless hip arthoplasty in the early postoperative period. This study develops methodology for subject-specific <span class="hlt">finite</span> <span class="hlt">element</span> modeling by using the <span class="hlt">element</span> deactivation technique to simulate bone failure and validate with experimental testing, thereby predicting peri-prosthetic femoral fracture in the early postoperative period. Material assignments for biphasic and triphasic models were undertaken. Failure modeling with the <span class="hlt">element</span> deactivation feature available in ABAQUS 6.9 was used to simulate a crack initiation and propagation in the bony tissue based upon a threshold of fracture strain. The crack mode for the biphasic models was very similar to the experimental testing crack mode, with a similar shape and path of the crack. The fracture load is sensitive to the friction coefficient at the implant-bony interface. The development of a novel technique to simulate bone failure by <span class="hlt">element</span> deactivation of subject-specific <span class="hlt">finite</span> <span class="hlt">element</span> models could aid prediction of fracture load in addition to fracture risk characterization for PFF. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.osti.gov/biblio/1253865-error-analysis-finite-element-method-poissonnernstplanck-equations','SCIGOV-STC'); return false;" href="https://www.osti.gov/biblio/1253865-error-analysis-finite-element-method-poissonnernstplanck-equations"><span>Error analysis of <span class="hlt">finite</span> <span class="hlt">element</span> method for Poisson–Nernst–Planck equations</span></a></p> <p><a target="_blank" href="http://www.osti.gov/search">DOE Office of Scientific and Technical Information (OSTI.GOV)</a></p> <p>Sun, Yuzhou; Sun, Pengtao; Zheng, Bin</p> <p></p> <p>A priori error estimates of <span class="hlt">finite</span> <span class="hlt">element</span> method for time-dependent Poisson-Nernst-Planck equations are studied in this work. We obtain the optimal error estimates in L∞(H1) and L2(H1) norms, and suboptimal error estimates in L∞(L2) norm, with linear <span class="hlt">element</span>, and optimal error estimates in L∞(L2) norm with quadratic or higher-order <span class="hlt">element</span>, for both semi- and fully discrete <span class="hlt">finite</span> <span class="hlt">element</span> approximations. Numerical experiments are also given to validate the theoretical results.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970023058','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970023058"><span>Substructure System Identification for <span class="hlt">Finite</span> <span class="hlt">Element</span> Model Updating</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Craig, Roy R., Jr.; Blades, Eric L.</p> <p>1997-01-01</p> <p>This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for <span class="hlt">Finite</span> <span class="hlt">Element</span> Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order <span class="hlt">finite</span> <span class="hlt">element</span> models.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28505811','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28505811"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Lacorata, Guglielmo; Vulpiani, Angelo</p> <p>2017-04-01</p> <p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the <span class="hlt">finite</span>-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017PhRvE..95d3106L"><span>Chaotic <span class="hlt">Lagrangian</span> models for turbulent relative dispersion</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lacorata, Guglielmo; Vulpiani, Angelo</p> <p>2017-04-01</p> <p>A deterministic multiscale dynamical system is introduced and discussed as a prototype model for relative dispersion in stationary, homogeneous, and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by <span class="hlt">Lagrangian</span> chaos. The anomalous "sweeping effect," a known drawback common to kinematic simulations, is removed through the use of quasi-<span class="hlt">Lagrangian</span> coordinates. <span class="hlt">Lagrangian</span> dispersion statistics of the model are accurately analyzed by computing the <span class="hlt">finite</span>-scale Lyapunov exponent (FSLE), which is the optimal measure of the scaling properties of dispersion. FSLE scaling exponents provide a severe test to decide whether model simulations are in agreement with theoretical expectations and/or observation. The results of our numerical experiments cover a wide range of "Reynolds numbers" and show that chaotic deterministic flows can be very efficient, and numerically low-cost, models of turbulent trajectories in stationary, homogeneous, and isotropic conditions. The mathematics of the model is relatively simple, and, in a geophysical context, potential applications may regard small-scale parametrization issues in general circulation models, mixed layer, and/or boundary layer turbulence models as well as <span class="hlt">Lagrangian</span> predictability studies.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19970017415','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19970017415"><span>Improved <span class="hlt">Finite</span> <span class="hlt">Element</span> Modeling of the Turbofan Engine Inlet Radiation Problem</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Roy, Indranil Danda; Eversman, Walter; Meyer, H. D.</p> <p>1993-01-01</p> <p>Improvements have been made in the <span class="hlt">finite</span> <span class="hlt">element</span> model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional <span class="hlt">finite</span> <span class="hlt">elements</span> in the near field and wave envelope <span class="hlt">elements</span> in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential; thereby minimizing computer storage and time requirements. The <span class="hlt">finite</span> <span class="hlt">element</span> mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a <span class="hlt">finite</span> <span class="hlt">element</span> duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the <span class="hlt">elements</span> and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional <span class="hlt">finite</span> <span class="hlt">elements</span> and wave envelope <span class="hlt">elements</span> has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19880057663&hterms=flower&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dflower','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19880057663&hterms=flower&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D80%26Ntt%3Dflower"><span>Optimal mapping of irregular <span class="hlt">finite</span> <span class="hlt">element</span> domains to parallel processors</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Flower, J.; Otto, S.; Salama, M.</p> <p>1987-01-01</p> <p>Mapping the solution domain of n-<span class="hlt">finite</span> <span class="hlt">elements</span> into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular <span class="hlt">finite</span> <span class="hlt">element</span> domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional <span class="hlt">finite</span> <span class="hlt">element</span> domain containing a singularity onto the Hypercube computer.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19760007434','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19760007434"><span>Shear-flexible <span class="hlt">finite-element</span> models of laminated composite plates and shells</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, A. K.; Mathers, M. D.</p> <p>1975-01-01</p> <p>Several <span class="hlt">finite-element</span> models are applied to the linear static, stability, and vibration analysis of laminated composite plates and shells. The study is based on linear shallow-shell theory, with the effects of shear deformation, anisotropic material behavior, and bending-extensional coupling included. Both stiffness (displacement) and mixed <span class="hlt">finite-element</span> models are considered. Discussion is focused on the effects of shear deformation and anisotropic material behavior on the accuracy and convergence of different <span class="hlt">finite-element</span> models. Numerical studies are presented which show the effects of increasing the order of the approximating polynomials, adding internal degrees of freedom, and using derivatives of generalized displacements as nodal parameters.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750','PMC'); return false;" href="https://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=4833750"><span>Investigation of particle inertial migration in high particle concentration suspension flow by multi-electrodes sensing and <span class="hlt">Eulerian-Lagrangian</span> simulation in a square microchannel</span></a></p> <p><a target="_blank" href="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pmc">PubMed Central</a></p> <p>Zhao, Tong; Liu, Kai; Takei, Masahiro</p> <p>2016-01-01</p> <p>The inertial migration of neutrally buoyant spherical particles in high particle concentration (αpi > 3%) suspension flow in a square microchannel was investigated by means of the multi-electrodes sensing method which broke through the limitation of conventional optical measurement techniques in the high particle concentration suspensions due to interference from the large particle numbers. Based on the measured particle concentrations near the wall and at the corner of the square microchannel, particle cross-sectional migration ratios are calculated to quantitatively estimate the migration degree. As a result, particle migration to four stable equilibrium positions near the centre of each face of the square microchannel is found only in the cases of low initial particle concentration up to 5.0 v/v%, while the migration phenomenon becomes partial as the initial particle concentration achieves 10.0 v/v% and disappears in the cases of the initial particle concentration αpi ≥ 15%. In order to clarify the influential mechanism of particle-particle interaction on particle migration, an <span class="hlt">Eulerian-Lagrangian</span> numerical model was proposed by employing the Lennard-Jones potential as the inter-particle potential, while the inertial lift coefficient is calculated by a pre-processed semi-analytical simulation. Moreover, based on the experimental and simulation results, a dimensionless number named migration index was proposed to evaluate the influence of the initial particle concentration on the particle migration phenomenon. The migration index less than 0.1 is found to denote obvious particle inertial migration, while a larger migration index denotes the absence of it. This index is helpful for estimation of the maximum initial particle concentration for the design of inertial microfluidic devices. PMID:27158288</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/AD1047166','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/AD1047166"><span>Using <span class="hlt">Finite</span> <span class="hlt">Element</span> Method to Estimate the Material Properties of a Bearing Cage</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>2018-02-01</p> <p>UNCLASSIFIED UNCLASSIFIED AD-E403 988 Technical Report ARMET-TR-17035 USING <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> METHOD TO ESTIMATE THE MATERIAL...TITLE AND SUBTITLE USING <span class="hlt">FINITE</span> <span class="hlt">ELEMENT</span> METHOD TO ESTIMATE THE MATERIAL PROPERTIES OF A BEARING CAGE 5a. CONTRACT NUMBER 5b. GRANT...specifications of non-metallic bearing cages are typically not supplied by the manufacturer. In order to setup a <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li class="active"><span>23</span></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_23 --> <div id="page_24" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="461"> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19920007148','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19920007148"><span>Traction free <span class="hlt">finite</span> <span class="hlt">elements</span> with the assumed stress hybrid model. M.S. Thesis, 1981</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Kafie, Kurosh</p> <p>1991-01-01</p> <p>An effective approach in the <span class="hlt">finite</span> <span class="hlt">element</span> analysis of the stress field at the traction free boundary of a solid continuum was studied. Conventional displacement and assumed stress <span class="hlt">finite</span> <span class="hlt">elements</span> were used in the determination of stress concentrations around circular and elliptical holes. Specialized hybrid <span class="hlt">elements</span> were then developed to improve the satisfaction of prescribed traction boundary conditions. Results of the stress analysis indicated that <span class="hlt">finite</span> <span class="hlt">elements</span> which exactly satisfy the free stress boundary conditions are the most accurate and efficient in such problems. A general approach for hybrid <span class="hlt">finite</span> <span class="hlt">elements</span> which incorporate traction free boundaries of arbitrary geometry was formulated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/23832095','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/23832095"><span>Establishing the 3-D <span class="hlt">finite</span> <span class="hlt">element</span> solid model of femurs in partial by volume rendering.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin</p> <p>2013-01-01</p> <p>It remains rare to report three-dimensional (3-D) <span class="hlt">finite</span> <span class="hlt">element</span> solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D <span class="hlt">finite</span> <span class="hlt">element</span> modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D <span class="hlt">finite</span> <span class="hlt">element</span> solid model of femurs in partial by volume rendering. A 3-D <span class="hlt">finite</span> <span class="hlt">element</span> model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the <span class="hlt">finite-element</span> analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D <span class="hlt">finite</span> <span class="hlt">element</span> of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D <span class="hlt">finite</span> <span class="hlt">element</span> solid model created in partial is more real and fit for <span class="hlt">finite</span> <span class="hlt">element</span> analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19740011432','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19740011432"><span>New triangular and quadrilateral plate-bending <span class="hlt">finite</span> <span class="hlt">elements</span></span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Narayanaswami, R.</p> <p>1974-01-01</p> <p>A nonconforming plate-bending <span class="hlt">finite</span> <span class="hlt">element</span> of triangular shape and associated quadrilateral <span class="hlt">elements</span> are developed. The transverse displacement is approximated within the <span class="hlt">element</span> by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20170004568','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20170004568"><span>A Decadal Inversion of CO2 Using the Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric Model (GELCA): Sensitivity to the Ground-Based Observation Network</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Shirai, T.; Ishizawa, M.; Zhuravlev, R.; Ganshin, A.; Belikov, D.; Saito, M.; Oda, T.; Valsala, V.; Gomez-Pelaez, A. J.; Langenfelds, R.; <a style="text-decoration: none; " href="javascript:void(0); " onClick="displayelement('author_20170004568'); toggleEditAbsImage('author_20170004568_show'); toggleEditAbsImage('author_20170004568_hide'); "> <img style="display:inline; width:12px; height:12px; " src="images/arrow-up.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_show"> <img style="width:12px; height:12px; display:none; " src="images/arrow-down.gif" width="12" height="12" border="0" alt="hide" id="author_20170004568_hide"></p> <p>2017-01-01</p> <p>We present an assimilation system for atmospheric carbon dioxide (CO2) using a Global <span class="hlt">Eulerian-Lagrangian</span> Coupled Atmospheric model (GELCA), and demonstrate its capability to capture the observed atmospheric CO2 mixing ratios and to estimate CO2 fluxes. With the efficient data handling scheme in GELCA, our system assimilates non-smoothed CO2 data from observational data products such as the Observation Package (ObsPack) data products as constraints on surface fluxes. We conducted sensitivity tests to examine the impact of the site selections and the prior uncertainty settings of observation on the inversion results. For these sensitivity tests, we made five different sitedata selections from the ObsPack product. In all cases, the time series of the global net CO2 flux to the atmosphere stayed close to values calculated from the growth rate of the observed global mean atmospheric CO2 mixing ratio. At regional scales, estimated seasonal CO2 fluxes were altered, depending on the CO2 data selected for assimilation. Uncertainty reductions (URs) were determined at the regional scale and compared among cases. As measures of the model-data mismatch, we used the model-data bias, root-mean-square error, and the linear correlation. For most observation sites, the model-data mismatch was reasonably small. Regarding regional flux estimates, tropical Asia was one of the regions that showed a significant impact from the observation network settings. We found that the surface fluxes in tropical Asia were the most sensitive to the use of aircraft measurements over the Pacific, and the seasonal cycle agreed better with the results of bottom-up studies when the aircraft measurements were assimilated. These results confirm the importance of these aircraft observations, especially for constraining surface fluxes in the tropics.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/27845929','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/27845929"><span>Electroencephalography (EEG) forward modeling via H(div) <span class="hlt">finite</span> <span class="hlt">element</span> sources with focal interpolation.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Pursiainen, S; Vorwerk, J; Wolters, C H</p> <p>2016-12-21</p> <p>The goal of this study is to develop focal, accurate and robust <span class="hlt">finite</span> <span class="hlt">element</span> method (FEM) based approaches which can predict the electric potential on the surface of the computational domain given its structure and internal primary source current distribution. While conducting an EEG evaluation, the placement of source currents to the geometrically complex grey matter compartment is a challenging but necessary task to avoid forward errors attributable to tissue conductivity jumps. Here, this task is approached via a mathematically rigorous formulation, in which the current field is modeled via divergence conforming H(div) basis functions. Both linear and quadratic functions are used while the potential field is discretized via the standard linear <span class="hlt">Lagrangian</span> (nodal) basis. The resulting model includes dipolar sources which are interpolated into a random set of positions and orientations utilizing two alternative approaches: the position based optimization (PBO) and the mean position/orientation (MPO) method. These results demonstrate that the present dipolar approach can reach or even surpass, at least in some respects, the accuracy of two classical reference methods, the partial integration (PI) and St. Venant (SV) approach which utilize monopolar loads instead of dipolar currents.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013EEEV...12..569Y','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013EEEV...12..569Y"><span>Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous <span class="hlt">finite</span> <span class="hlt">element</span> method</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Yang, Zailin; Wang, Yao; Hei, Baoping</p> <p>2013-12-01</p> <p>The dynamic inhomogeneous <span class="hlt">finite</span> <span class="hlt">element</span> method is studied for use in the transient analysis of onedimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general <span class="hlt">finite</span> <span class="hlt">element</span> method. A linear bar <span class="hlt">element</span> is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous <span class="hlt">finite</span> <span class="hlt">element</span> method that demonstrate its advantages are obtained through comparison with the general <span class="hlt">finite</span> <span class="hlt">element</span> method. It is found that the method can be used to solve elastic wave motion problems with a large <span class="hlt">element</span> scale and a large number of iteration steps.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19930013278','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19930013278"><span>A class of hybrid <span class="hlt">finite</span> <span class="hlt">element</span> methods for electromagnetics: A review</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Volakis, J. L.; Chatterjee, A.; Gong, J.</p> <p>1993-01-01</p> <p>Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the <span class="hlt">finite</span> <span class="hlt">element</span> method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid <span class="hlt">finite</span> <span class="hlt">element</span> methods for simulating composite scatterers, conformal microstrip antennas, and <span class="hlt">finite</span> periodic arrays. Specifically, we discuss the <span class="hlt">finite</span> <span class="hlt">element</span> method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870013796','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870013796"><span>A survey of mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Brezzi, F.</p> <p>1987-01-01</p> <p>This paper is an introduction to and an overview of mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19920057267&hterms=right+Bless+you&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dright%2BBless%2Byou','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19920057267&hterms=right+Bless+you&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D10%26Ntt%3Dright%2BBless%2Byou"><span><span class="hlt">Finite</span> <span class="hlt">element</span> method for optimal guidance of an advanced launch vehicle</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin</p> <p>1992-01-01</p> <p>A temporal <span class="hlt">finite</span> <span class="hlt">element</span> based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian <span class="hlt">finite</span> <span class="hlt">element</span> method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require <span class="hlt">element</span> quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the <span class="hlt">finite</span> <span class="hlt">element</span> method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2009CompM..43..353P','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2009CompM..43..353P"><span>Nonlinear solid <span class="hlt">finite</span> <span class="hlt">element</span> analysis of mitral valves with heterogeneous leaflet layers</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Prot, V.; Skallerud, B.</p> <p>2009-02-01</p> <p>An incompressible transversely isotropic hyperelastic material for solid <span class="hlt">finite</span> <span class="hlt">element</span> analysis of a porcine mitral valve response is described. The material model implementation is checked in single <span class="hlt">element</span> tests and compared with a membrane implementation in an out-of-plane loading test to study how the layered structures modify the stress response for a simple geometry. Three different collagen layer arrangements are used in <span class="hlt">finite</span> <span class="hlt">element</span> analysis of the mitral valve. When the leaflets are arranged in two layers with the collagen on the ventricular side, the stress in the fibre direction through the thickness in the central part of the anterior leaflet is homogenized and the peak stress is reduced. A simulation using membrane <span class="hlt">elements</span> is also carried out for comparison with the solid <span class="hlt">finite</span> <span class="hlt">element</span> results. Compared to echocardiographic measurements, the <span class="hlt">finite</span> <span class="hlt">element</span> models bulge too much in the left atrium. This may be due to evidence of active muscle fibres in some parts of the anterior leaflet, whereas our constitutive modelling is based on passive material.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/20000057395','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/20000057395"><span>Challenges in Integrating Nondestructive Evaluation and <span class="hlt">Finite</span> <span class="hlt">Element</span> Methods for Realistic Structural Analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Abdul-Aziz, Ali; Baaklini, George Y.; Zagidulin, Dmitri; Rauser, Richard W.</p> <p>2000-01-01</p> <p>Capabilities and expertise related to the development of links between nondestructive evaluation (NDE) and <span class="hlt">finite</span> <span class="hlt">element</span> analysis (FEA) at Glenn Research Center (GRC) are demonstrated. Current tools to analyze data produced by computed tomography (CT) scans are exercised to help assess the damage state in high temperature structural composite materials. A utility translator was written to convert velocity (an image processing software) STL data file to a suitable CAD-FEA type file. <span class="hlt">Finite</span> <span class="hlt">element</span> analyses are carried out with MARC, a commercial nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> code, and the analytical results are discussed. Modeling was established by building MSC/Patran (a pre and post processing <span class="hlt">finite</span> <span class="hlt">element</span> package) generated model and comparing it to a model generated by Velocity in conjunction with MSC/Patran Graphics. Modeling issues and results are discussed in this paper. The entire process that outlines the tie between the data extracted via NDE and the <span class="hlt">finite</span> <span class="hlt">element</span> modeling and analysis is fully described.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2013JGRD..11810243H','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2013JGRD..11810243H"><span>Identification and uncertainty estimation of vertical reflectivity profiles using a <span class="hlt">Lagrangian</span> approach to support quantitative precipitation measurements by weather radar</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Hazenberg, P.; Torfs, P. J. J. F.; Leijnse, H.; Delrieu, G.; Uijlenhoet, R.</p> <p>2013-09-01</p> <p>This paper presents a novel approach to estimate the vertical profile of reflectivity (VPR) from volumetric weather radar data using both a traditional <span class="hlt">Eulerian</span> as well as a newly proposed <span class="hlt">Lagrangian</span> implementation. For this latter implementation, the recently developed Rotational Carpenter Square Cluster Algorithm (RoCaSCA) is used to delineate precipitation regions at different reflectivity levels. A piecewise linear VPR is estimated for either stratiform or neither stratiform/convective precipitation. As a second aspect of this paper, a novel approach is presented which is able to account for the impact of VPR uncertainty on the estimated radar rainfall variability. Results show that implementation of the VPR identification and correction procedure has a positive impact on quantitative precipitation estimates from radar. Unfortunately, visibility problems severely limit the impact of the <span class="hlt">Lagrangian</span> implementation beyond distances of 100 km. However, by combining this procedure with the global <span class="hlt">Eulerian</span> VPR estimation procedure for a given rainfall type (stratiform and neither stratiform/convective), the quality of the quantitative precipitation estimates increases up to a distance of 150 km. Analyses of the impact of VPR uncertainty shows that this aspect accounts for a large fraction of the differences between weather radar rainfall estimates and rain gauge measurements.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2015IJCEM..16..188J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2015IJCEM..16..188J"><span>A Dual Super-<span class="hlt">Element</span> Domain Decomposition Approach for Parallel Nonlinear <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jokhio, G. A.; Izzuddin, B. A.</p> <p>2015-05-01</p> <p>This article presents a new domain decomposition method for nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> analysis introducing the concept of dual partition super-<span class="hlt">elements</span>. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-<span class="hlt">element</span>, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-<span class="hlt">element</span> along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-<span class="hlt">elements</span>. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing <span class="hlt">finite</span> <span class="hlt">element</span> analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19740036099&hterms=feng+fluid&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfeng%252C%2Bfluid','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19740036099&hterms=feng+fluid&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dfeng%252C%2Bfluid"><span>Fluid-structure <span class="hlt">finite-element</span> vibrational analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Feng, G. C.; Kiefling, L.</p> <p>1974-01-01</p> <p>A fluid <span class="hlt">finite</span> <span class="hlt">element</span> has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural <span class="hlt">elements</span>, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid <span class="hlt">elements</span> can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the <span class="hlt">element</span> formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19850014785','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19850014785"><span>On Hybrid and mixed <span class="hlt">finite</span> <span class="hlt">element</span> methods</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pian, T. H. H.</p> <p>1981-01-01</p> <p>Three versions of the assumed stress hybrid model in <span class="hlt">finite</span> <span class="hlt">element</span> methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof <span class="hlt">elements</span> for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof <span class="hlt">elements</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017APS..DFDG28009L','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017APS..DFDG28009L"><span>Scale-by-scale contributions to <span class="hlt">Lagrangian</span> particle acceleration</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Lalescu, Cristian C.; Wilczek, Michael</p> <p>2017-11-01</p> <p>Fluctuations on a wide range of scales in both space and time are characteristic of turbulence. <span class="hlt">Lagrangian</span> particles, advected by the flow, probe these fluctuations along their trajectories. In an effort to isolate the influence of the different scales on <span class="hlt">Lagrangian</span> statistics, we employ direct numerical simulations (DNS) combined with a filtering approach. Specifically, we study the acceleration statistics of tracers advected in filtered fields to characterize the smallest temporal scales of the flow. Emphasis is put on the acceleration variance as a function of filter scale, along with the scaling properties of the relevant terms of the Navier-Stokes equations. We furthermore discuss scaling ranges for higher-order moments of the tracer acceleration, as well as the influence of the choice of filter on the results. Starting from the <span class="hlt">Lagrangian</span> tracer acceleration as the short time limit of the <span class="hlt">Lagrangian</span> velocity increment, we also quantify the influence of filtering on <span class="hlt">Lagrangian</span> intermittency. Our work complements existing experimental results on intermittency and accelerations of <span class="hlt">finite</span>-sized, neutrally-buoyant particles: for the passive tracers used in our DNS, feedback effects are neglected such that the spatial averaging effect is cleanly isolated.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870020362','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870020362"><span><span class="hlt">Finite-element</span> reentry heat-transfer analysis of space shuttle Orbiter</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Ko, William L.; Quinn, Robert D.; Gong, Leslie</p> <p>1986-01-01</p> <p>A structural performance and resizing (SPAR) <span class="hlt">finite-element</span> thermal analysis computer program was used in the heat-transfer analysis of the space shuttle orbiter subjected to reentry aerodynamic heating. Three wing cross sections and one midfuselage cross section were selected for the thermal analysis. The predicted thermal protection system temperatures were found to agree well with flight-measured temperatures. The calculated aluminum structural temperatures also agreed reasonably well with the flight data from reentry to touchdown. The effects of internal radiation and of internal convection were found to be significant. The SPAR <span class="hlt">finite-element</span> solutions agreed reasonably well with those obtained from the conventional <span class="hlt">finite</span>-difference method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://www.dtic.mil/docs/citations/ADA117078','DTIC-ST'); return false;" href="http://www.dtic.mil/docs/citations/ADA117078"><span>Moving <span class="hlt">Finite</span> <span class="hlt">Elements</span> in 2-D.</span></a></p> <p><a target="_blank" href="http://www.dtic.mil/">DTIC Science & Technology</a></p> <p></p> <p>1982-06-07</p> <p>that a small number of control parameters would allow a great deal of flexibility in the type of node mobility available in specific problems while...CLEO 󈨕), Washington, DC, June 10-12, 1981.) 5. R. J. Gelinas and S. K. Doss, "The Moving <span class="hlt">Finite</span> <span class="hlt">Element</span> Method: 1-D Transient Flow Aplications ," to</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910007955','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910007955"><span>A combined <span class="hlt">finite</span> <span class="hlt">element</span>-boundary <span class="hlt">element</span> formulation for solution of axially symmetric bodies</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Collins, Jeffrey D.; Volakis, John L.</p> <p>1991-01-01</p> <p>A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the <span class="hlt">finite</span> <span class="hlt">element</span> and boundary <span class="hlt">element</span> techniques. Interior to a fictitious surface enclosing the scattering body, the <span class="hlt">finite</span> <span class="hlt">element</span> method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19750029601&hterms=Nonlinear+equations&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DNonlinear%2Bequations','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19750029601&hterms=Nonlinear+equations&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D90%26Ntt%3DNonlinear%2Bequations"><span>Application of variational and Galerkin equations to linear and nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> analysis</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Yu, Y.-Y.</p> <p>1974-01-01</p> <p>The paper discusses the application of the variational equation to nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the <span class="hlt">finite</span> <span class="hlt">element</span> formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the <span class="hlt">finite</span> <span class="hlt">element</span> formulation of two-dimensional linear elasticity and of the linear classical beam.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li class="active"><span>24</span></li> <li><a href="#" onclick='return showDiv("page_25");'>25</a></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_24 --> <div id="page_25" class="hiddenDiv"> <div class="row"> <div class="col-sm-12"> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div> </div> <div class="row"> <div class="col-sm-12"> <ol class="result-class" start="481"> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/25241111','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/25241111"><span>NiftySim: A GPU-based nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> package for simulation of soft tissue biomechanics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Johnsen, Stian F; Taylor, Zeike A; Clarkson, Matthew J; Hipwell, John; Modat, Marc; Eiben, Bjoern; Han, Lianghao; Hu, Yipeng; Mertzanidou, Thomy; Hawkes, David J; Ourselin, Sebastien</p> <p>2015-07-01</p> <p>NiftySim, an open-source <span class="hlt">finite</span> <span class="hlt">element</span> toolkit, has been designed to allow incorporation of high-performance soft tissue simulation capabilities into biomedical applications. The toolkit provides the option of execution on fast graphics processing unit (GPU) hardware, numerous constitutive models and solid-<span class="hlt">element</span> options, membrane and shell <span class="hlt">elements</span>, and contact modelling facilities, in a simple to use library. The toolkit is founded on the total <span class="hlt">Lagrangian</span> explicit dynamics (TLEDs) algorithm, which has been shown to be efficient and accurate for simulation of soft tissues. The base code is written in C[Formula: see text], and GPU execution is achieved using the nVidia CUDA framework. In most cases, interaction with the underlying solvers can be achieved through a single Simulator class, which may be embedded directly in third-party applications such as, surgical guidance systems. Advanced capabilities such as contact modelling and nonlinear constitutive models are also provided, as are more experimental technologies like reduced order modelling. A consistent description of the underlying solution algorithm, its implementation with a focus on GPU execution, and examples of the toolkit's usage in biomedical applications are provided. Efficient mapping of the TLED algorithm to parallel hardware results in very high computational performance, far exceeding that available in commercial packages. The NiftySim toolkit provides high-performance soft tissue simulation capabilities using GPU technology for biomechanical simulation research applications in medical image computing, surgical simulation, and surgical guidance applications.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19930049886&hterms=distributed+generation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Ddistributed%2Bgeneration','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19930049886&hterms=distributed+generation&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D60%26Ntt%3Ddistributed%2Bgeneration"><span>A new parallel-vector <span class="hlt">finite</span> <span class="hlt">element</span> analysis software on distributed-memory computers</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Qin, Jiangning; Nguyen, Duc T.</p> <p>1993-01-01</p> <p>A new parallel-vector <span class="hlt">finite</span> <span class="hlt">element</span> analysis software package MPFEA (Massively Parallel-vector <span class="hlt">Finite</span> <span class="hlt">Element</span> Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global <span class="hlt">finite</span> <span class="hlt">element</span> stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a <span class="hlt">finite</span> <span class="hlt">element</span> analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940009971','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940009971"><span>Development of an hp-version <span class="hlt">finite</span> <span class="hlt">element</span> method for computational optimal control</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Hodges, Dewey H.; Warner, Michael S.</p> <p>1993-01-01</p> <p>The purpose of this research effort is to develop a means to use, and to ultimately implement, hp-version <span class="hlt">finite</span> <span class="hlt">elements</span> in the numerical solution of optimal control problems. The hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version <span class="hlt">finite</span> <span class="hlt">elements</span> to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version <span class="hlt">finite</span> <span class="hlt">elements</span>, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each <span class="hlt">element</span>.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2007JSV...302..577A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2007JSV...302..577A"><span>Nonlinear dynamics of planetary gears using analytical and <span class="hlt">finite</span> <span class="hlt">element</span> models</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Ambarisha, Vijaya Kumar; Parker, Robert G.</p> <p>2007-05-01</p> <p>Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a <span class="hlt">finite</span> <span class="hlt">element</span> model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D <span class="hlt">finite</span> <span class="hlt">element</span> model is developed from a unique <span class="hlt">finite</span> <span class="hlt">element</span>-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the <span class="hlt">finite</span> <span class="hlt">element</span> analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and <span class="hlt">finite</span> <span class="hlt">element</span> models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JIEIC..98...37J','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JIEIC..98...37J"><span><span class="hlt">Finite</span> <span class="hlt">Element</span> Simulation of Temperature and Strain Distribution during Friction Stir Welding of AA2024 Aluminum Alloy</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Jain, Rahul; Pal, Surjya Kanta; Singh, Shiv Brat</p> <p>2017-02-01</p> <p>Friction Stir Welding (FSW) is a solid state joining process and is handy for welding aluminum alloys. <span class="hlt">Finite</span> <span class="hlt">Element</span> Method (FEM) is an important tool to predict state variables of the process but numerical simulation of FSW is highly complex due to non-linear contact interactions between tool and work piece and interdependency of displacement and temperature. In the present work, a three dimensional coupled thermo-mechanical method based on <span class="hlt">Lagrangian</span> implicit method is proposed to study the thermal history, strain distribution and thermo-mechanical process in butt welding of Aluminum alloy 2024 using DEFORM-3D software. Workpiece is defined as rigid-visco plastic material and sticking condition between tool and work piece is defined. Adaptive re-meshing is used to tackle high mesh distortion. Effect of tool rotational and welding speed on plastic strain is studied and insight is given on asymmetric nature of FSW process. Temperature distribution on the workpiece and tool is predicted and maximum temperature is found in workpiece top surface.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://ntrs.nasa.gov/search.jsp?R=19790038914&hterms=cdc&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dcdc','NASA-TRS'); return false;" href="https://ntrs.nasa.gov/search.jsp?R=19790038914&hterms=cdc&qs=Ntx%3Dmode%2Bmatchall%26Ntk%3DAll%26N%3D0%26No%3D20%26Ntt%3Dcdc"><span><span class="hlt">Finite</span> <span class="hlt">element</span> dynamic analysis on CDC STAR-100 computer</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Noor, A. K.; Lambiotte, J. J., Jr.</p> <p>1978-01-01</p> <p>Computational algorithms are presented for the <span class="hlt">finite</span> <span class="hlt">element</span> dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order <span class="hlt">finite</span> <span class="hlt">elements</span>. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell <span class="hlt">elements</span> having 80 degrees of freedom.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19720006838','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19720006838"><span><span class="hlt">Finite</span> <span class="hlt">element</span> solution of lubrication problems</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Reddi, M. M.</p> <p>1971-01-01</p> <p>A variational formulation of the transient lubrication problem is presented and the corresponding <span class="hlt">finite</span> <span class="hlt">element</span> equations derived for three and six point triangles, and, four and eight point quadrilaterals. Test solutions for a one dimensional slider bearing used in validating the computer program are given. Utility of the method is demonstrated by a solution of the shrouded step bearing.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19910011766','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19910011766"><span>A multidimensional <span class="hlt">finite</span> <span class="hlt">element</span> method for CFD</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Pepper, Darrell W.; Humphrey, Joseph W.</p> <p>1991-01-01</p> <p>A <span class="hlt">finite</span> <span class="hlt">element</span> method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) <span class="hlt">elements</span>, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19730007866','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19730007866"><span><span class="hlt">Finite</span> <span class="hlt">element</span> solution for energy conservation using a highly stable explicit integration algorithm</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Baker, A. J.; Manhardt, P. D.</p> <p>1972-01-01</p> <p>Theoretical derivation of a <span class="hlt">finite</span> <span class="hlt">element</span> solution algorithm for the transient energy conservation equation in multidimensional, stationary multi-media continua with irregular solution domain closure is considered. The complete <span class="hlt">finite</span> <span class="hlt">element</span> matrix forms for arbitrarily irregular discretizations are established, using natural coordinate function representations. The algorithm is embodied into a user-oriented computer program (COMOC) which obtains transient temperature distributions at the node points of the <span class="hlt">finite</span> <span class="hlt">element</span> discretization using a highly stable explicit integration procedure with automatic error control features. The <span class="hlt">finite</span> <span class="hlt">element</span> algorithm is shown to posses convergence with discretization for a transient sample problem. The condensed form for the specific heat <span class="hlt">element</span> matrix is shown to be preferable to the consistent form. Computed results for diverse problems illustrate the versatility of COMOC, and easily prepared output subroutines are shown to allow quick engineering assessment of solution behavior.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2008MSMSE..16c5008R','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2008MSMSE..16c5008R"><span>Dislocation dynamics in non-convex domains using <span class="hlt">finite</span> <span class="hlt">elements</span> with embedded discontinuities</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Romero, Ignacio; Segurado, Javier; LLorca, Javier</p> <p>2008-04-01</p> <p>The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional <span class="hlt">finite</span> domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the <span class="hlt">finite</span> <span class="hlt">element</span> analysis carried out to compute the image stresses on the dislocations due to the <span class="hlt">finite</span> boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the <span class="hlt">finite</span> <span class="hlt">element</span> solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a <span class="hlt">finite</span> <span class="hlt">element</span> program is detailed in the appendix.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://pubs.usgs.gov/wri/1977/0049/report.pdf','USGSPUBS'); return false;" href="https://pubs.usgs.gov/wri/1977/0049/report.pdf"><span>The use of Galerkin <span class="hlt">finite-element</span> methods to solve mass-transport equations</span></a></p> <p><a target="_blank" href="http://pubs.er.usgs.gov/pubs/index.jsp?view=adv">USGS Publications Warehouse</a></p> <p>Grove, David B.</p> <p>1977-01-01</p> <p>The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin <span class="hlt">finite-element</span> technique. These <span class="hlt">finite</span> <span class="hlt">elements</span> were superimposed over <span class="hlt">finite</span>-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the <span class="hlt">finite-element</span> methods to the <span class="hlt">finite</span>-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19940019207','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19940019207"><span>Domain decomposition methods for nonconforming <span class="hlt">finite</span> <span class="hlt">element</span> spaces of Lagrange-type</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Cowsar, Lawrence C.</p> <p>1993-01-01</p> <p>In this article, we consider the application of three popular domain decomposition methods to Lagrange-type nonconforming <span class="hlt">finite</span> <span class="hlt">element</span> discretizations of scalar, self-adjoint, second order elliptic equations. The additive Schwarz method of Dryja and Widlund, the vertex space method of Smith, and the balancing method of Mandel applied to nonconforming <span class="hlt">elements</span> are shown to converge at a rate no worse than their applications to the standard conforming piecewise linear Galerkin discretization. Essentially, the theory for the nonconforming <span class="hlt">elements</span> is inherited from the existing theory for the conforming <span class="hlt">elements</span> with only modest modification by constructing an isomorphism between the nonconforming <span class="hlt">finite</span> <span class="hlt">element</span> space and a space of continuous piecewise linear functions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/28060270','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/28060270"><span>Building <span class="hlt">Finite</span> <span class="hlt">Element</span> Models to Investigate Zebrafish Jaw Biomechanics.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>Brunt, Lucy H; Roddy, Karen A; Rayfield, Emily J; Hammond, Chrissy L</p> <p>2016-12-03</p> <p>Skeletal morphogenesis occurs through tightly regulated cell behaviors during development; many cell types alter their behavior in response to mechanical strain. Skeletal joints are subjected to dynamic mechanical loading. <span class="hlt">Finite</span> <span class="hlt">element</span> analysis (FEA) is a computational method, frequently used in engineering that can predict how a material or structure will respond to mechanical input. By dividing a whole system (in this case the zebrafish jaw skeleton) into a mesh of smaller '<span class="hlt">finite</span> <span class="hlt">elements</span>', FEA can be used to calculate the mechanical response of the structure to external loads. The results can be visualized in many ways including as a 'heat map' showing the position of maximum and minimum principal strains (a positive principal strain indicates tension while a negative indicates compression. The maximum and minimum refer the largest and smallest strain). These can be used to identify which regions of the jaw and therefore which cells are likely to be under particularly high tensional or compressional loads during jaw movement and can therefore be used to identify relationships between mechanical strain and cell behavior. This protocol describes the steps to generate <span class="hlt">Finite</span> <span class="hlt">Element</span> models from confocal image data on the musculoskeletal system, using the zebrafish lower jaw as a practical example. The protocol leads the reader through a series of steps: 1) staining of the musculoskeletal components, 2) imaging the musculoskeletal components, 3) building a 3 dimensional (3D) surface, 4) generating a mesh of <span class="hlt">Finite</span> <span class="hlt">Elements</span>, 5) solving the FEA and finally 6) validating the results by comparison to real displacements seen in movements of the fish jaw.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2017JSV...405..208N','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2017JSV...405..208N"><span>Nonlinear <span class="hlt">finite</span> <span class="hlt">element</span> analysis of liquid sloshing in complex vehicle motion scenarios</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Nicolsen, Brynne; Wang, Liang; Shabana, Ahmed</p> <p>2017-09-01</p> <p>The objective of this investigation is to develop a new total <span class="hlt">Lagrangian</span> continuum-based liquid sloshing model that can be systematically integrated with multibody system (MBS) algorithms in order to allow for studying complex motion scenarios. The new approach allows for accurately capturing the effect of the sloshing forces during curve negotiation, rapid lane change, and accelerating and braking scenarios. In these motion scenarios, the liquid experiences large displacements and significant changes in shape that can be captured effectively using the <span class="hlt">finite</span> <span class="hlt">element</span> (FE) absolute nodal coordinate formulation (ANCF). ANCF <span class="hlt">elements</span> are used in this investigation to describe complex mesh geometries, to capture the change in inertia due to the change in the fluid shape, and to accurately calculate the centrifugal forces, which for flexible bodies do not take the simple form used in rigid body dynamics. A penalty formulation is used to define the contact between the rigid tank walls and the fluid. A fully nonlinear MBS truck model that includes a suspension system and Pacejka's brush tire model is developed. Specified motion trajectories are used to examine the vehicle dynamics in three different scenarios - deceleration during straight-line motion, rapid lane change, and curve negotiation. It is demonstrated that the liquid sloshing changes the contact forces between the tires and the ground - increasing the forces on certain wheels and decreasing the forces on other wheels. In cases of extreme sloshing, this dynamic behavior can negatively impact the vehicle stability by increasing the possibility of wheel lift and vehicle rollover.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2018JCoPh.358..103B','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2018JCoPh.358..103B"><span>A second-order cell-centered <span class="hlt">Lagrangian</span> ADER-MOOD <span class="hlt">finite</span> volume scheme on multidimensional unstructured meshes for hydrodynamics</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Boscheri, Walter; Dumbser, Michael; Loubère, Raphaël; Maire, Pierre-Henri</p> <p>2018-04-01</p> <p>In this paper we develop a conservative cell-centered <span class="hlt">Lagrangian</span> <span class="hlt">finite</span> volume scheme for the solution of the hydrodynamics equations on unstructured multidimensional grids. The method is derived from the Eucclhyd scheme discussed in [47,43,45]. It is second-order accurate in space and is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves. Second-order of accuracy in time is achieved via the ADER (Arbitrary high order schemes using DERivatives) approach. A large set of numerical test cases is proposed to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior on discontinuous profiles, general robustness ensuring physical admissibility of the numerical solution, and precision where appropriate.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('https://www.ncbi.nlm.nih.gov/pubmed/29435676','PUBMED'); return false;" href="https://www.ncbi.nlm.nih.gov/pubmed/29435676"><span>Vortex dynamics and <span class="hlt">Lagrangian</span> statistics in a model for active turbulence.</span></a></p> <p><a target="_blank" href="https://www.ncbi.nlm.nih.gov/entrez/query.fcgi?DB=pubmed">PubMed</a></p> <p>James, Martin; Wilczek, Michael</p> <p>2018-02-14</p> <p>Cellular suspensions such as dense bacterial flows exhibit a turbulence-like phase under certain conditions. We study this phenomenon of "active turbulence" statistically by using numerical tools. Following Wensink et al. (Proc. Natl. Acad. Sci. U.S.A. 109, 14308 (2012)), we model active turbulence by means of a generalized Navier-Stokes equation. Two-point velocity statistics of active turbulence, both in the <span class="hlt">Eulerian</span> and the <span class="hlt">Lagrangian</span> frame, is explored. We characterize the scale-dependent features of two-point statistics in this system. Furthermore, we extend this statistical study with measurements of vortex dynamics in this system. Our observations suggest that the large-scale statistics of active turbulence is close to Gaussian with sub-Gaussian tails.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2016WRR....52.8561Z','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2016WRR....52.8561Z"><span>Bounded fractional diffusion in geological media: Definition and <span class="hlt">Lagrangian</span> approximation</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Zhang, Yong; Green, Christopher T.; LaBolle, Eric M.; Neupauer, Roseanna M.; Sun, HongGuang</p> <p>2016-11-01</p> <p>Spatiotemporal fractional-derivative models (FDMs) have been increasingly used to simulate non-Fickian diffusion, but methods have not been available to define boundary conditions for FDMs in bounded domains. This study defines boundary conditions and then develops a <span class="hlt">Lagrangian</span> solver to approximate bounded, one-dimensional fractional diffusion. Both the zero-value and nonzero-value Dirichlet, Neumann, and mixed Robin boundary conditions are defined, where the sign of Riemann-Liouville fractional derivative (capturing nonzero-value spatial-nonlocal boundary conditions with directional superdiffusion) remains consistent with the sign of the fractional-diffusive flux term in the FDMs. New <span class="hlt">Lagrangian</span> schemes are then proposed to track solute particles moving in bounded domains, where the solutions are checked against analytical or <span class="hlt">Eulerian</span> solutions available for simplified FDMs. Numerical experiments show that the particle-tracking algorithm for non-Fickian diffusion differs from Fickian diffusion in relocating the particle position around the reflective boundary, likely due to the nonlocal and nonsymmetric fractional diffusion. For a nonzero-value Neumann or Robin boundary, a source cell with a reflective face can be applied to define the release rate of random-walking particles at the specified flux boundary. Mathematical definitions of physically meaningful nonlocal boundaries combined with bounded <span class="hlt">Lagrangian</span> solvers in this study may provide the only viable techniques at present to quantify the impact of boundaries on anomalous diffusion, expanding the applicability of FDMs from infinite domains to those with any size and boundary conditions.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/2012JCoPh.231.4694A','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/2012JCoPh.231.4694A"><span>Semi-automatic sparse preconditioners for high-order <span class="hlt">finite</span> <span class="hlt">element</span> methods on non-uniform meshes</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John</p> <p>2012-05-01</p> <p>High-order <span class="hlt">finite</span> <span class="hlt">elements</span> often have a higher accuracy per degree of freedom than the classical low-order <span class="hlt">finite</span> <span class="hlt">elements</span>. However, in the context of implicit time-stepping methods, high-order <span class="hlt">finite</span> <span class="hlt">elements</span> present challenges to the construction of efficient simulations due to the high cost of inverting the denser <span class="hlt">finite</span> <span class="hlt">element</span> matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order <span class="hlt">finite</span> <span class="hlt">elements</span>. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order <span class="hlt">finite</span> <span class="hlt">elements</span> that is based on a much sparser system than the original high-order <span class="hlt">finite</span> <span class="hlt">element</span> system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://hdl.handle.net/2060/19870004652','NASA-TRS'); return false;" href="http://hdl.handle.net/2060/19870004652"><span>Mathematical aspects of <span class="hlt">finite</span> <span class="hlt">element</span> methods for incompressible viscous flows</span></a></p> <p><a target="_blank" href="http://ntrs.nasa.gov/search.jsp">NASA Technical Reports Server (NTRS)</a></p> <p>Gunzburger, M. D.</p> <p>1986-01-01</p> <p>Mathematical aspects of <span class="hlt">finite</span> <span class="hlt">element</span> methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of <span class="hlt">finite</span> <span class="hlt">element</span> spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.</p> </li> <li> <p><a target="_blank" onclick="trackOutboundLink('http://adsabs.harvard.edu/abs/1999CompM..23..482S','NASAADS'); return false;" href="http://adsabs.harvard.edu/abs/1999CompM..23..482S"><span>Extension to linear dynamics for hybrid stress <span class="hlt">finite</span> <span class="hlt">element</span> formulation based on additional displacements</span></a></p> <p><a target="_blank" href="http://adsabs.harvard.edu/abstract_service.html">NASA Astrophysics Data System (ADS)</a></p> <p>Sumihara, K.</p> <p></p> <p>Based upon legitimate variational principles, one microscopic-macroscopic <span class="hlt">finite</span> <span class="hlt">element</span> formulation for linear dynamics is presented by Hybrid Stress <span class="hlt">Finite</span> <span class="hlt">Element</span> Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core <span class="hlt">element</span> (Baby <span class="hlt">Element</span>) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid <span class="hlt">Finite</span> <span class="hlt">Element</span> Method is extended to linear dynamics with the introduction of physically meaningful higher modes.</p> </li> </ol> <div class="pull-right"> <ul class="pagination"> <li><a href="#" onclick='return showDiv("page_1");'>«</a></li> <li><a href="#" onclick='return showDiv("page_21");'>21</a></li> <li><a href="#" onclick='return showDiv("page_22");'>22</a></li> <li><a href="#" onclick='return showDiv("page_23");'>23</a></li> <li><a href="#" onclick='return showDiv("page_24");'>24</a></li> <li class="active"><span>25</span></li> <li><a href="#" onclick='return showDiv("page_25");'>»</a></li> </ul> </div> </div><!-- col-sm-12 --> </div><!-- row --> </div><!-- page_25 --> <div class="footer-extlink text-muted" style="margin-bottom:1rem; text-align:center;">Some links on this page may take you to non-federal websites. 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