Application of Interface Technology in Nonlinear Analysis of a Stitched/RFI Composite Wing Stub Box

NASA Technical Reports Server (NTRS)

Wang, John T.; Ransom, Jonathan B.

1997-01-01

A recently developed interface technology was successfully employed in the geometrically nonlinear analysis of a full-scale stitched/RFI composite wing box loaded in bending. The technology allows mismatched finite element models to be joined in a variationally consistent manner and reduces the modeling complexity by eliminating transition meshing. In the analysis, local finite element models of nonlinearly deformed wide bays of the wing box are refined without the need for transition meshing to the surrounding coarse mesh. The COMET-AR finite element code, which has the interface technology capability, was used to perform the analyses. The COMET-AR analysis is compared to both a NASTRAN analysis and to experimental data. The interface technology solution is shown to be in good agreement with both. The viability of interface technology for coupled global/local analysis of large scale aircraft structures is demonstrated.

A general gridding, discretization, and coarsening methodology for modeling flow in porous formations with discrete geological features

NASA Astrophysics Data System (ADS)

Karimi-Fard, M.; Durlofsky, L. J.

2016-10-01

A comprehensive framework for modeling flow in porous media containing thin, discrete features, which could be high-permeability fractures or low-permeability deformation bands, is presented. The key steps of the methodology are mesh generation, fine-grid discretization, upscaling, and coarse-grid discretization. Our specialized gridding technique combines a set of intersecting triangulated surfaces by constructing approximate intersections using existing edges. This procedure creates a conforming mesh of all surfaces, which defines the internal boundaries for the volumetric mesh. The flow equations are discretized on this conforming fine mesh using an optimized two-point flux finite-volume approximation. The resulting discrete model is represented by a list of control-volumes with associated positions and pore-volumes, and a list of cell-to-cell connections with associated transmissibilities. Coarse models are then constructed by the aggregation of fine-grid cells, and the transmissibilities between adjacent coarse cells are obtained using flow-based upscaling procedures. Through appropriate computation of fracture-matrix transmissibilities, a dual-continuum representation is obtained on the coarse scale in regions with connected fracture networks. The fine and coarse discrete models generated within the framework are compatible with any connectivity-based simulator. The applicability of the methodology is illustrated for several two- and three-dimensional examples. In particular, we consider gas production from naturally fractured low-permeability formations, and transport through complex fracture networks. In all cases, highly accurate solutions are obtained with significant model reduction.

A Mesh Refinement Study on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Lyle, Karen H.; Spellman, Regina L.

2006-01-01

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0-in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at four discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Full Multigrid Flow Solver

NASA Technical Reports Server (NTRS)

Mineck, Raymond E.; Thomas, James L.; Biedron, Robert T.; Diskin, Boris

2005-01-01

FMG3D (full multigrid 3 dimensions) is a pilot computer program that solves equations of fluid flow using a finite difference representation on a structured grid. Infrastructure exists for three dimensions but the current implementation treats only two dimensions. Written in Fortran 90, FMG3D takes advantage of the recursive subroutine feature, dynamic memory allocation, and structured-programming constructs of that language. FMG3D supports multi-block grids with three types of block-to-block interfaces: periodic, C-zero, and C-infinity. For all three types, grid points must match at interfaces. For periodic and C-infinity types, derivatives of grid metrics must be continuous at interfaces. The available equation sets are as follows: scalar elliptic equations, scalar convection equations, and the pressure-Poisson formulation of the Navier-Stokes equations for an incompressible fluid. All the equation sets are implemented with nonzero forcing functions to enable the use of user-specified solutions to assist in verification and validation. The equations are solved with a full multigrid scheme using a full approximation scheme to converge the solution on each succeeding grid level. Restriction to the next coarser mesh uses direct injection for variables and full weighting for residual quantities; prolongation of the coarse grid correction from the coarse mesh to the fine mesh uses bilinear interpolation; and prolongation of the coarse grid solution uses bicubic interpolation.

Evaluation of an improved finite-element thermal stress calculation technique

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1982-01-01

A procedure for generating accurate thermal stresses with coarse finite element 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 finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element 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 finite element 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 finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-13

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

An Efficient Multiscale Finite-Element Method for Frequency-Domain Seismic Wave Propagation

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

Gao, Kai; Fu, Shubin; Chung, Eric T.

The frequency-domain seismic-wave equation, that is, the Helmholtz equation, has many important applications in seismological studies, yet is very challenging to solve, particularly for large geological models. Iterative solvers, domain decomposition, or parallel strategies can partially alleviate the computational burden, but these approaches may still encounter nontrivial difficulties in complex geological models where a sufficiently fine mesh is required to represent the fine-scale heterogeneities. We develop a novel numerical method to solve the frequency-domain acoustic wave equation on the basis of the multiscale finite-element theory. We discretize a heterogeneous model with a coarse mesh and employ carefully constructed high-order multiscalemore » basis functions to form the basis space for the coarse mesh. Solved from medium- and frequency-dependent local problems, these multiscale basis functions can effectively capture themedium’s fine-scale heterogeneity and the source’s frequency information, leading to a discrete system matrix with a much smaller dimension compared with those from conventional methods.We then obtain an accurate solution to the acoustic Helmholtz equation by solving only a small linear system instead of a large linear system constructed on the fine mesh in conventional methods.We verify our new method using several models of complicated heterogeneities, and the results show that our new multiscale method can solve the Helmholtz equation in complex models with high accuracy and extremely low computational costs.« less

Development of an adaptive hp-version finite element method for computational optimal control

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Warner, Michael S.

1994-01-01

In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response

PubMed Central

Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-01-01

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process. PMID:29027925

Multiscale Modeling of Polycrystalline NiTi Shape Memory Alloy under Various Plastic Deformation Conditions by Coupling Microstructure Evolution and Macroscopic Mechanical Response.

PubMed

Hu, Li; Jiang, Shuyong; Zhou, Tao; Tu, Jian; Shi, Laixin; Chen, Qiang; Yang, Mingbo

2017-10-13

Numerical modeling of microstructure evolution in various regions during uniaxial compression and canning compression of NiTi shape memory alloy (SMA) are studied through combined macroscopic and microscopic finite element simulation in order to investigate plastic deformation of NiTi SMA at 400 °C. In this approach, the macroscale material behavior is modeled with a relatively coarse finite element mesh, and then the corresponding deformation history in some selected regions in this mesh is extracted by the sub-model technique of finite element code ABAQUS and subsequently used as boundary conditions for the microscale simulation by means of crystal plasticity finite element method (CPFEM). Simulation results show that NiTi SMA exhibits an inhomogeneous plastic deformation at the microscale. Moreover, regions that suffered canning compression sustain more homogeneous plastic deformation by comparison with the corresponding regions subjected to uniaxial compression. The mitigation of inhomogeneous plastic deformation contributes to reducing the statistically stored dislocation (SSD) density in polycrystalline aggregation and also to reducing the difference of stress level in various regions of deformed NiTi SMA sample, and therefore sustaining large plastic deformation in the canning compression process.

Hybrid continuum-coarse-grained modeling of erythrocytes

NASA Astrophysics Data System (ADS)

Lyu, Jinming; Chen, Paul G.; Boedec, Gwenn; Leonetti, Marc; Jaeger, Marc

2018-06-01

The red blood cell (RBC) membrane is a composite structure, consisting of a phospholipid bilayer and an underlying membrane-associated cytoskeleton. Both continuum and particle-based coarse-grained RBC models make use of a set of vertices connected by edges to represent the RBC membrane, which can be seen as a triangular surface mesh for the former and a spring network for the latter. Here, we present a modeling approach combining an existing continuum vesicle model with a coarse-grained model for the cytoskeleton. Compared to other two-component approaches, our method relies on only one mesh, representing the cytoskeleton, whose velocity in the tangential direction of the membrane may be different from that of the lipid bilayer. The finitely extensible nonlinear elastic (FENE) spring force law in combination with a repulsive force defined as a power function (POW), called FENE-POW, is used to describe the elastic properties of the RBC membrane. The mechanical interaction between the lipid bilayer and the cytoskeleton is explicitly computed and incorporated into the vesicle model. Our model includes the fundamental mechanical properties of the RBC membrane, namely fluidity and bending rigidity of the lipid bilayer, and shear elasticity of the cytoskeleton while maintaining surface-area and volume conservation constraint. We present three simulation examples to demonstrate the effectiveness of this hybrid continuum-coarse-grained model for the study of RBCs in fluid flows.

A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

DOE PAGES

Tuminaro, Raymond S.; Perego, Mauro; Tezaur, Irina Kalashnikova; ...

2016-10-06

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigridmore » hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.« less

An Engineering Solution for Solving Mesh Size Effects in the Simulation of Delamination with Cohesive Zone Models

NASA Technical Reports Server (NTRS)

Turon, A.; Davila, C. G.; Camanho, P. P.; Costa, J.

2007-01-01

This paper presents a methodology to determine the parameters to be used in the constitutive equations of Cohesive Zone Models employed in the simulation of delamination in composite materials by means of decohesion finite elements. A closed-form expression is developed to define the stiffness of the cohesive layer. A novel procedure that allows the use of coarser meshes of decohesion elements in large-scale computations is also proposed. The procedure ensures that the energy dissipated by the fracture process is computed correctly. It is shown that coarse-meshed models defined using the approach proposed here yield the same results as the models with finer meshes normally used for the simulation of fracture processes.

Non-conforming finite-element formulation for cardiac electrophysiology: an effective approach to reduce the computation time of heart simulations without compromising accuracy

NASA Astrophysics Data System (ADS)

Hurtado, Daniel E.; Rojas, Guillermo

2018-04-01

Computer simulations constitute a powerful tool for studying the electrical activity of the human heart, but computational effort remains prohibitively high. In order to recover accurate conduction velocities and wavefront shapes, the mesh size in linear element (Q1) formulations cannot exceed 0.1 mm. Here we propose a novel non-conforming finite-element formulation for the non-linear cardiac electrophysiology problem that results in accurate wavefront shapes and lower mesh-dependance in the conduction velocity, while retaining the same number of global degrees of freedom as Q1 formulations. As a result, coarser discretizations of cardiac domains can be employed in simulations without significant loss of accuracy, thus reducing the overall computational effort. We demonstrate the applicability of our formulation in biventricular simulations using a coarse mesh size of ˜ 1 mm, and show that the activation wave pattern closely follows that obtained in fine-mesh simulations at a fraction of the computation time, thus improving the accuracy-efficiency trade-off of cardiac simulations.

Pathloss Calculation Using the Transmission Line Matrix and Finite Difference Time Domain Methods With Coarse Grids

DOE PAGES

Nutaro, James; Kuruganti, Teja

2017-02-24

Numerical simulations of the wave equation that are intended to provide accurate time domain solutions require a computational mesh with grid points separated by a distance less than the wavelength of the source term and initial data. However, calculations of radio signal pathloss generally do not require accurate time domain solutions. This paper describes an approach for calculating pathloss by using the finite difference time domain and transmission line matrix models of wave propagation on a grid with points separated by distances much greater than the signal wavelength. The calculated pathloss can be kept close to the true value formore » freespace propagation with an appropriate selection of initial conditions. This method can also simulate diffraction with an error governed by the ratio of the signal wavelength to the grid spacing.« less

Hybrid Multiscale Finite Volume method for multiresolution simulations of flow and reactive transport in porous media

NASA Astrophysics Data System (ADS)

Barajas-Solano, D. A.; Tartakovsky, A. M.

2017-12-01

We present a multiresolution method for the numerical simulation of flow and reactive transport in porous, heterogeneous media, based on the hybrid Multiscale Finite Volume (h-MsFV) algorithm. The h-MsFV algorithm allows us to couple high-resolution (fine scale) flow and transport models with lower resolution (coarse) models to locally refine both spatial resolution and transport models. The fine scale problem is decomposed into various "local'' problems solved independently in parallel and coordinated via a "global'' problem. This global problem is then coupled with the coarse model to strictly ensure domain-wide coarse-scale mass conservation. The proposed method provides an alternative to adaptive mesh refinement (AMR), due to its capacity to rapidly refine spatial resolution beyond what's possible with state-of-the-art AMR techniques, and the capability to locally swap transport models. We illustrate our method by applying it to groundwater flow and reactive transport of multiple species.

An engineering closure for heavily under-resolved coarse-grid CFD in large applications

NASA Astrophysics Data System (ADS)

Class, Andreas G.; Yu, Fujiang; Jordan, Thomas

2016-11-01

Even though high performance computation allows very detailed description of a wide range of scales in scientific computations, engineering simulations used for design studies commonly merely resolve the large scales thus speeding up simulation time. The coarse-grid CFD (CGCFD) methodology is developed for flows with repeated flow patterns as often observed in heat exchangers or porous structures. It is proposed to use inviscid Euler equations on a very coarse numerical mesh. This coarse mesh needs not to conform to the geometry in all details. To reinstall physics on all smaller scales cheap subgrid models are employed. Subgrid models are systematically constructed by analyzing well-resolved generic representative simulations. By varying the flow conditions in these simulations correlations are obtained. These comprehend for each individual coarse mesh cell a volume force vector and volume porosity. Moreover, for all vertices, surface porosities are derived. CGCFD is related to the immersed boundary method as both exploit volume forces and non-body conformal meshes. Yet, CGCFD differs with respect to the coarser mesh and the use of Euler equations. We will describe the methodology based on a simple test case and the application of the method to a 127 pin wire-wrap fuel bundle.

Small herbivores suppress algal accumulation on Agatti atoll, Indian Ocean

NASA Astrophysics Data System (ADS)

Cernohorsky, Nicole H.; McClanahan, Timothy R.; Babu, Idrees; Horsák, Michal

2015-12-01

Despite large herbivorous fish being generally accepted as the main group responsible for preventing algal accumulation on coral reefs, few studies have experimentally examined the relative importance of herbivore size on algal communities. This study used exclusion cages with two different mesh sizes (1 × 1 cm and 6 × 6 cm) to investigate the impact of different-sized herbivores on algal accumulation rates on the shallow (<2 m) back-reef of Agatti atoll, Lakshadweep. The fine-mesh cages excluded all visible herbivores, which had rapid and lasting effects on the benthic communities, and, after 127 d of deployment, there was a visible and significant increase in algae (mainly macroalgae) with algal volume being 13 times greater than in adjacent open areas. The coarse-mesh cages excluded larger fishes (>8 cm body depth) while allowing smaller fishes to access the plots. In contrast to the conclusions of most previous studies, the exclusion of large herbivores had no significant effect on the accumulation of benthic algae and the amount of algae present within the coarse-mesh cages was relatively consistent throughout the experimental period (around 50 % coverage and 1-2 mm height). The difference in algal accumulation between the fine-mesh and coarse-mesh cages appears to be related to the actions of small individuals from 12 herbivorous fish species (0.17 ind. m-2 and 7.7 g m-2) that were able to enter through the coarse mesh. Although restricted to a single habitat, these results suggest that when present in sufficient densities and diversity, small herbivorous fishes can prevent the accumulation of algal biomass on coral reefs.

A fast solver for the Helmholtz equation based on the generalized multiscale finite-element method

NASA Astrophysics Data System (ADS)

Fu, Shubin; Gao, Kai

2017-11-01

Conventional finite-element methods for solving the acoustic-wave Helmholtz equation in highly heterogeneous media usually require finely discretized mesh to represent the medium property variations with sufficient accuracy. Computational costs for solving the Helmholtz equation can therefore be considerably expensive for complicated and large geological models. Based on the generalized multiscale finite-element theory, we develop a novel continuous Galerkin method to solve the Helmholtz equation in acoustic media with spatially variable velocity and mass density. Instead of using conventional polynomial basis functions, we use multiscale basis functions to form the approximation space on the coarse mesh. The multiscale basis functions are obtained from multiplying the eigenfunctions of a carefully designed local spectral problem with an appropriate multiscale partition of unity. These multiscale basis functions can effectively incorporate the characteristics of heterogeneous media's fine-scale variations, thus enable us to obtain accurate solution to the Helmholtz equation without directly solving the large discrete system formed on the fine mesh. Numerical results show that our new solver can significantly reduce the dimension of the discrete Helmholtz equation system, and can also obviously reduce the computational time.

Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

NASA Astrophysics Data System (ADS)

Klimczak, Marek; Cecot, Witold

2018-01-01

We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Edge delamination of composite laminates subject to combined tension and torsional loading

NASA Technical Reports Server (NTRS)

Hooper, Steven J.

1990-01-01

Delamination is a common failure mode of laminated composite materials. Edge delamination is important since it results in reduced stiffness and strength of the laminate. The tension/torsion load condition is of particular significance to the structural integrity of composite helicopter rotor systems. Material coupons can easily be tested under this type of loading in servo-hydraulic tension/torsion test stands using techniques very similar to those used for the Edge Delamination Tensile Test (EDT) delamination specimen. Edge delamination of specimens loaded in tension was successfully analyzed by several investigators using both classical laminate theory and quasi-three dimensional (Q3D) finite element techniques. The former analysis technique can be used to predict the total strain energy release rate, while the latter technique enables the calculation of the mixed-mode strain energy release rates. The Q3D analysis is very efficient since it produces a three-dimensional solution to a two-dimensional domain. A computer program was developed which generates PATRAN commands to generate the finite element model. PATRAN is a pre- and post-processor which is commonly used with a variety of finite element programs such as MCS/NASTRAN. The program creates a sufficiently dense mesh at the delamination crack tips to support a mixed-mode fracture mechanics analysis. The program creates a coarse mesh in those regions where the gradients in the stress field are low (away from the delamination regions). A transition mesh is defined between these regions. This program is capable of generating a mesh for an arbitrarily oriented matrix crack. This program significantly reduces the modeling time required to generate these finite element meshes, thus providing a realistic tool with which to investigate the tension torsion problem.

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

NASA Astrophysics Data System (ADS)

Zahr, M. J.; Persson, P.-O.

2018-07-01

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods. The proposed method aims to align inter-element boundaries with discontinuities in the solution by deforming the computational mesh. A discontinuity-aligned mesh ensures the discontinuity is represented through inter-element jumps while smooth basis functions interior to elements are only used to approximate smooth regions of the solution, thereby avoiding Gibbs' phenomena that create well-known stability issues. Therefore, very coarse high-order discretizations accurately resolve the piecewise smooth solution throughout the domain, provided the discontinuity is tracked. Central to the proposed discontinuity-tracking framework is a discrete PDE-constrained optimization formulation that simultaneously aligns the computational mesh with discontinuities in the solution and solves the discretized conservation law on this mesh. The optimization objective is taken as a combination of the deviation of the finite-dimensional solution from its element-wise average and a mesh distortion metric to simultaneously penalize Gibbs' phenomena and distorted meshes. It will be shown that our objective function satisfies two critical properties that are required for this discontinuity-tracking framework to be practical: (1) possesses a local minima at a discontinuity-aligned mesh and (2) decreases monotonically to this minimum in a neighborhood of radius approximately h / 2, whereas other popular discontinuity indicators fail to satisfy the latter. Another important contribution of this work is the observation that traditional reduced space PDE-constrained optimization solvers that repeatedly solve the conservation law at various mesh configurations are not viable in this context since severe overshoot and undershoot in the solution, i.e., Gibbs' phenomena, may make it impossible to solve the discrete conservation law on non-aligned meshes. Therefore, we advocate a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh. The merit of the proposed method is demonstrated on a number of one- and two-dimensional model problems including the L2 projection of discontinuous functions, Burgers' equation with a discontinuous source term, transonic flow through a nozzle, and supersonic flow around a bluff body. We demonstrate optimal O (h p + 1) convergence rates in the L1 norm for up to polynomial order p = 6 and show that accurate solutions can be obtained on extremely coarse meshes.

On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem

NASA Astrophysics Data System (ADS)

Søe-Knudsen, Alf; Sorokin, Sergey

2011-06-01

This rapid communication is concerned with justification of the 'rule of thumb', which is well known to the community of users of the finite element (FE) method in dynamics, for the accuracy assessment of the wave finite element (WFE) method. An explicit formula linking the size of a window in the dispersion diagram, where the WFE method is trustworthy, with the coarseness of a FE mesh employed is derived. It is obtained by the comparison of the exact Pochhammer-Chree solution for an elastic rod having the circular cross-section with its WFE approximations. It is shown that the WFE power flow predictions are also valid within this window.

Mesh size effects on assessments of planktonic hydrozoan abundance and assemblage structure

NASA Astrophysics Data System (ADS)

Nogueira Júnior, Miodeli; Pukanski, Luis Eduardo de M.; Souza-Conceição, José M.

2015-04-01

The choice of appropriate mesh-size is paramount to accurately quantify planktonic assemblages, however there is no such information available for hydrozoans. Here planktonic hydrozoan abundance and assemblage structure were compared using 200 and 500 μm meshes at Babitonga estuary (S Brazil), throughout a year cycle. Species richness and Shannon-Wiener diversity were higher in the 200 μm mesh, while evenness was typically higher in the 500 μm. Assemblage structure was significantly different between meshes (PERMANOVA, P < 0.05; n = 72 pairs of samples) both regarding taxa and size composition. These discrepancies are due to significant underestimation of small hydromedusae by the coarse mesh, like Obelia spp., young Liriope tetraphylla, Podocoryna loyola and others. Yet, larger taxa like Eucheilota maculata and adult L. tetraphylla were more abundant in the coarse mesh on some occasions and others such as Blackfordia virginica and Muggiaea kochi were similarly represented in both meshes. Overall collection efficiency of the coarse mesh (CE500) was 14.4%, with monthly averages between 1.6% and 43.0%, in July (winter) and January (summer) respectively. Differences between the meshes were size-dependent; CE500 was ~ 0.3% for hydrozoans sizing < 0.5 mm, ~ 21% for those between 1 and 2 mm, ~ 56% for those between 2 and 4 mm, and nearly 100% for larger ones, reaching up to 312% for hydrozoans > 8 mm in October. These results suggest that both meshes have their drawbacks and the best choice would depend on the objectives of each study. Nevertheless species richness, total abundances and most taxa were better represented by the 200 μm mesh, suggesting that it is more appropriate to quantitatively sample planktonic hydrozoan assemblages.

Three dimensional unstructured multigrid for the Euler equations

NASA Technical Reports Server (NTRS)

Mavriplis, D. J.

1991-01-01

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

DOE PAGES

Svyatsky, Daniil; Lipnikov, Konstantin

2017-03-18

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

A second-order accurate finite volume scheme with the discrete maximum principle for solving Richards’ equation on unstructured meshes

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

Svyatsky, Daniil; Lipnikov, Konstantin

Richards’s equation describes steady-state or transient flow in a variably saturated medium. For a medium having multiple layers of soils that are not aligned with coordinate axes, a mesh fitted to these layers is no longer orthogonal and the classical two-point flux approximation finite volume scheme is no longer accurate. Here, we propose new second-order accurate nonlinear finite volume (NFV) schemes for the head and pressure formulations of Richards’ equation. We prove that the discrete maximum principles hold for both formulations at steady-state which mimics similar properties of the continuum solution. The second-order accuracy is achieved using high-order upwind algorithmsmore » for the relative permeability. Numerical simulations of water infiltration into a dry soil show significant advantage of the second-order NFV schemes over the first-order NFV schemes even on coarse meshes. Since explicit calculation of the Jacobian matrix becomes prohibitively expensive for high-order schemes due to build-in reconstruction and slope limiting algorithms, we study numerically the preconditioning strategy introduced recently in Lipnikov et al. (2016) that uses a stable approximation of the continuum Jacobian. Lastly, numerical simulations show that the new preconditioner reduces computational cost up to 2–3 times in comparison with the conventional preconditioners.« less

Parallel three-dimensional magnetotelluric inversion using adaptive finite-element method. Part I: theory and synthetic study

NASA Astrophysics Data System (ADS)

Grayver, Alexander V.

2015-07-01

This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated that the adaptive mesh refinement can be particularly efficient in resolving complex shapes. The implemented inversion scheme was able to resolve a hemisphere object with sufficient resolution starting from a coarse discretization and refining mesh adaptively in a fully automatic process. The code is able to harness the computational power of modern distributed platforms and is shown to work with models consisting of millions of degrees of freedom. Significant computational savings were achieved by using locally refined decoupled meshes.

Convergence analysis of two-node CMFD method for two-group neutron diffusion eigenvalue problem

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

Jeong, Yongjin; Park, Jinsu; Lee, Hyun Chul

2015-12-01

In this paper, the nonlinear coarse-mesh finite difference method with two-node local problem (CMFD2N) is proven to be unconditionally stable for neutron diffusion eigenvalue problems. The explicit current correction factor (CCF) is derived based on the two-node analytic nodal method (ANM2N), and a Fourier stability analysis is applied to the linearized algorithm. It is shown that the analytic convergence rate obtained by the Fourier analysis compares very well with the numerically measured convergence rate. It is also shown that the theoretical convergence rate is only governed by the converged second harmonic buckling and the mesh size. It is also notedmore » that the convergence rate of the CCF of the CMFD2N algorithm is dependent on the mesh size, but not on the total problem size. This is contrary to expectation for eigenvalue problem. The novel points of this paper are the analytical derivation of the convergence rate of the CMFD2N algorithm for eigenvalue problem, and the convergence analysis based on the analytic derivations.« less

Fog Harvesting with Harps.

PubMed

Shi, Weiwei; Anderson, Mark J; Tulkoff, Joshua B; Kennedy, Brook S; Boreyko, Jonathan B

2018-04-11

Fog harvesting is a useful technique for obtaining fresh water in arid climates. The wire meshes currently utilized for fog harvesting suffer from dual constraints: coarse meshes cannot efficiently capture microscopic fog droplets, whereas fine meshes suffer from clogging issues. Here, we design and fabricate fog harvesters comprising an array of vertical wires, which we call "fog harps". Under controlled laboratory conditions, the fog-harvesting rates for fog harps with three different wire diameters were compared to conventional meshes of equivalent dimensions. As expected for the mesh structures, the mid-sized wires exhibited the largest fog collection rate, with a drop-off in performance for the fine or coarse meshes. In contrast, the fog-harvesting rate continually increased with decreasing wire diameter for the fog harps due to efficient droplet shedding that prevented clogging. This resulted in a 3-fold enhancement in the fog-harvesting rate for the harp design compared to an equivalent mesh.

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement.

PubMed

Garcia-Cantero, Juan J; Brito, Juan P; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells' overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma's morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes.

Comparison of Several Dissipation Algorithms for Central Difference Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Radespiel, R.; Turkel, E.

1997-01-01

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

Hybrid discrete ordinates and characteristics method for solving the linear Boltzmann equation

NASA Astrophysics Data System (ADS)

Yi, Ce

With the ability of computer hardware and software increasing rapidly, deterministic methods to solve the linear Boltzmann equation (LBE) have attracted some attention for computational applications in both the nuclear engineering and medical physics fields. Among various deterministic methods, the discrete ordinates method (SN) and the method of characteristics (MOC) are two of the most widely used methods. The SN method is the traditional approach to solve the LBE for its stability and efficiency. While the MOC has some advantages in treating complicated geometries. However, in 3-D problems requiring a dense discretization grid in phase space (i.e., a large number of spatial meshes, directions, or energy groups), both methods could suffer from the need for large amounts of memory and computation time. In our study, we developed a new hybrid algorithm by combing the two methods into one code, TITAN. The hybrid approach is specifically designed for application to problems containing low scattering regions. A new serial 3-D time-independent transport code has been developed. Under the hybrid approach, the preferred method can be applied in different regions (blocks) within the same problem model. Since the characteristics method is numerically more efficient in low scattering media, the hybrid approach uses a block-oriented characteristics solver in low scattering regions, and a block-oriented SN solver in the remainder of the physical model. In the TITAN code, a physical problem model is divided into a number of coarse meshes (blocks) in Cartesian geometry. Either the characteristics solver or the SN solver can be chosen to solve the LBE within a coarse mesh. A coarse mesh can be filled with fine meshes or characteristic rays depending on the solver assigned to the coarse mesh. Furthermore, with its object-oriented programming paradigm and layered code structure, TITAN allows different individual spatial meshing schemes and angular quadrature sets for each coarse mesh. Two quadrature types (level-symmetric and Legendre-Chebyshev quadrature) along with the ordinate splitting techniques (rectangular splitting and PN-TN splitting) are implemented. In the S N solver, we apply a memory-efficient 'front-line' style paradigm to handle the fine mesh interface fluxes. In the characteristics solver, we have developed a novel 'backward' ray-tracing approach, in which a bi-linear interpolation procedure is used on the incoming boundaries of a coarse mesh. A CPU-efficient scattering kernel is shared in both solvers within the source iteration scheme. Angular and spatial projection techniques are developed to transfer the angular fluxes on the interfaces of coarse meshes with different discretization grids. The performance of the hybrid algorithm is tested in a number of benchmark problems in both nuclear engineering and medical physics fields. Among them are the Kobayashi benchmark problems and a computational tomography (CT) device model. We also developed an extra sweep procedure with the fictitious quadrature technique to calculate angular fluxes along directions of interest. The technique is applied in a single photon emission computed tomography (SPECT) phantom model to simulate the SPECT projection images. The accuracy and efficiency of the TITAN code are demonstrated in these benchmarks along with its scalability. A modified version of the characteristics solver is integrated in the PENTRAN code and tested within the parallel engine of PENTRAN. The limitations on the hybrid algorithm are also studied.

An efficient and robust 3D mesh compression based on 3D watermarking and wavelet transform

NASA Astrophysics Data System (ADS)

Zagrouba, Ezzeddine; Ben Jabra, Saoussen; Didi, Yosra

2011-06-01

The compression and watermarking of 3D meshes are very important in many areas of activity including digital cinematography, virtual reality as well as CAD design. However, most studies on 3D watermarking and 3D compression are done independently. To verify a good trade-off between protection and a fast transfer of 3D meshes, this paper proposes a new approach which combines 3D mesh compression with mesh watermarking. This combination is based on a wavelet transformation. In fact, the used compression method is decomposed to two stages: geometric encoding and topologic encoding. The proposed approach consists to insert a signature between these two stages. First, the wavelet transformation is applied to the original mesh to obtain two components: wavelets coefficients and a coarse mesh. Then, the geometric encoding is done on these two components. The obtained coarse mesh will be marked using a robust mesh watermarking scheme. This insertion into coarse mesh allows obtaining high robustness to several attacks. Finally, the topologic encoding is applied to the marked coarse mesh to obtain the compressed mesh. The combination of compression and watermarking permits to detect the presence of signature after a compression of the marked mesh. In plus, it allows transferring protected 3D meshes with the minimum size. The experiments and evaluations show that the proposed approach presents efficient results in terms of compression gain, invisibility and robustness of the signature against of many attacks.

Refreshing Music: Fog Harvesting with Harps

NASA Astrophysics Data System (ADS)

Shi, Weiwei; Anderson, Mark; Kennedy, Brook; Boreyko, Jonathan

2017-11-01

Fog harvesting is a useful technique for obtaining fresh water in arid climates. The wire meshes currently utilized for fog harvesting suffer from dual constraints: coarse meshes cannot efficiently capture fog, while fine meshes suffer from clogging issues. Here, we design a new type of fog harvester comprised of an array of vertical wires, which we call ``fog harps.'' To investigate the water collection efficiency, three fog harps were designed with different diameters (254 μm, 508 μm and 1.30 mm) but the same pitch-to-diameter ratio of 2. For comparison, three different size meshes were purchased with equivalent dimensions. As expected for the mesh structures, the mid-sized wires performed the best, with a drop-off in performance for the fine or coarse meshes. In contrast, the fog harvesting rate continually increased with decreasing wire diameter for the fog harps, due to its low hysteresis that prevented droplet clogging. This resulted in a 3-fold enhancement in the fog harvesting rate for the harp form factor compared to the mesh. The lack of a performance ceiling for the harps suggest that even greater enhancements could be achieved by scaling down to yet smaller sizes.

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

A moving mesh finite difference method for equilibrium radiation diffusion equations

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

Yang, Xiaobo, E-mail: xwindyb@126.com; Huang, Weizhang, E-mail: whuang@ku.edu; Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn

2015-10-01

An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativitymore » of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.« less

NeuroTessMesh: A Tool for the Generation and Visualization of Neuron Meshes and Adaptive On-the-Fly Refinement

PubMed Central

Garcia-Cantero, Juan J.; Brito, Juan P.; Mata, Susana; Bayona, Sofia; Pastor, Luis

2017-01-01

Gaining a better understanding of the human brain continues to be one of the greatest challenges for science, largely because of the overwhelming complexity of the brain and the difficulty of analyzing the features and behavior of dense neural networks. Regarding analysis, 3D visualization has proven to be a useful tool for the evaluation of complex systems. However, the large number of neurons in non-trivial circuits, together with their intricate geometry, makes the visualization of a neuronal scenario an extremely challenging computational problem. Previous work in this area dealt with the generation of 3D polygonal meshes that approximated the cells’ overall anatomy but did not attempt to deal with the extremely high storage and computational cost required to manage a complex scene. This paper presents NeuroTessMesh, a tool specifically designed to cope with many of the problems associated with the visualization of neural circuits that are comprised of large numbers of cells. In addition, this method facilitates the recovery and visualization of the 3D geometry of cells included in databases, such as NeuroMorpho, and provides the tools needed to approximate missing information such as the soma’s morphology. This method takes as its only input the available compact, yet incomplete, morphological tracings of the cells as acquired by neuroscientists. It uses a multiresolution approach that combines an initial, coarse mesh generation with subsequent on-the-fly adaptive mesh refinement stages using tessellation shaders. For the coarse mesh generation, a novel approach, based on the Finite Element Method, allows approximation of the 3D shape of the soma from its incomplete description. Subsequently, the adaptive refinement process performed in the graphic card generates meshes that provide good visual quality geometries at a reasonable computational cost, both in terms of memory and rendering time. All the described techniques have been integrated into NeuroTessMesh, available to the scientific community, to generate, visualize, and save the adaptive resolution meshes. PMID:28690511

An Analysis Technique/Automated Tool for Comparing and Tracking Analysis Modes of Different Finite Element Models

NASA Technical Reports Server (NTRS)

Towner, Robert L.; Band, Jonathan L.

2012-01-01

An analysis technique was developed to compare and track mode shapes for different Finite Element Models. The technique may be applied to a variety of structural dynamics analyses, including model reduction validation (comparing unreduced and reduced models), mode tracking for various parametric analyses (e.g., launch vehicle model dispersion analysis to identify sensitivities to modal gain for Guidance, Navigation, and Control), comparing models of different mesh fidelity (e.g., a coarse model for a preliminary analysis compared to a higher-fidelity model for a detailed analysis) and mode tracking for a structure with properties that change over time (e.g., a launch vehicle from liftoff through end-of-burn, with propellant being expended during the flight). Mode shapes for different models are compared and tracked using several numerical indicators, including traditional Cross-Orthogonality and Modal Assurance Criteria approaches, as well as numerical indicators obtained by comparing modal strain energy and kinetic energy distributions. This analysis technique has been used to reliably identify correlated mode shapes for complex Finite Element Models that would otherwise be difficult to compare using traditional techniques. This improved approach also utilizes an adaptive mode tracking algorithm that allows for automated tracking when working with complex models and/or comparing a large group of models.

Predicting mesh density for adaptive modelling of the global atmosphere.

PubMed

Weller, Hilary

2009-11-28

The shallow water equations are solved using a mesh of polygons on the sphere, which adapts infrequently to the predicted future solution. Infrequent mesh adaptation reduces the cost of adaptation and load-balancing and will thus allow for more accurate mapping on adaptation. We simulate the growth of a barotropically unstable jet adapting the mesh every 12 h. Using an adaptation criterion based largely on the gradient of the vorticity leads to a mesh with around 20 per cent of the cells of a uniform mesh that gives equivalent results. This is a similar proportion to previous studies of the same test case with mesh adaptation every 1-20 min. The prediction of the mesh density involves solving the shallow water equations on a coarse mesh in advance of the locally refined mesh in order to estimate where features requiring higher resolution will grow, decay or move to. The adaptation criterion consists of two parts: that resolved on the coarse mesh, and that which is not resolved and so is passively advected on the coarse mesh. This combination leads to a balance between resolving features controlled by the large-scale dynamics and maintaining fine-scale features.

Anatomically Realistic Three-Dimensional Meshes of the Pelvic Floor & Anal Canal for Finite Element Analysis

PubMed Central

Noakes, Kimberley F.; Bissett, Ian P.; Pullan, Andrew J.; Cheng, Leo K.

2014-01-01

Three anatomically realistic meshes, suitable for finite element analysis, of the pelvic floor and anal canal regions have been developed to provide a framework with which to examine the mechanics, via finite element analysis of normal function within the pelvic floor. Two cadaver-based meshes were produced using the Visible Human Project (male and female) cryosection data sets, and a third mesh was produced based on MR image data from a live subject. The Visible Man (VM) mesh included 10 different pelvic structures while the Visible Woman and MRI meshes contained 14 and 13 structures respectively. Each image set was digitized and then finite element meshes were created using an iterative fitting procedure with smoothing constraints calculated from ‘L’-curves. These weights produced accurate geometric meshes of each pelvic structure with average Root Mean Square (RMS) fitting errors of less than 1.15 mm. The Visible Human cadaveric data provided high resolution images, however, the cadaveric meshes lacked the normal dynamic form of living tissue and suffered from artifacts related to postmortem changes. The lower resolution MRI mesh was able to accurately portray structure of the living subject and paves the way for dynamic, functional modeling. PMID:18317929

MC21 analysis of the MIT PWR benchmark: Hot zero power results

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

Kelly Iii, D. J.; Aviles, B. N.; Herman, B. R.

2013-07-01

MC21 Monte Carlo results have been compared with hot zero power measurements from an operating pressurized water reactor (PWR), as specified in a new full core PWR performance benchmark from the MIT Computational Reactor Physics Group. Included in the comparisons are axially integrated full core detector measurements, axial detector profiles, control rod bank worths, and temperature coefficients. Power depressions from grid spacers are seen clearly in the MC21 results. Application of Coarse Mesh Finite Difference (CMFD) acceleration within MC21 has been accomplished, resulting in a significant reduction of inactive batches necessary to converge the fission source. CMFD acceleration has alsomore » been shown to work seamlessly with the Uniform Fission Site (UFS) variance reduction method. (authors)« less

NONLINEAR MULTIGRID SOLVER EXPLOITING AMGe COARSE SPACES WITH APPROXIMATION PROPERTIES

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

Christensen, Max La Cour; Villa, Umberto E.; Engsig-Karup, Allan P.

The paper introduces a nonlinear multigrid solver for mixed nite element discretizations based on the Full Approximation Scheme (FAS) and element-based Algebraic Multigrid (AMGe). The main motivation to use FAS for unstruc- tured problems is the guaranteed approximation property of the AMGe coarse spaces that were developed recently at Lawrence Livermore National Laboratory. These give the ability to derive stable and accurate coarse nonlinear discretization problems. The previous attempts (including ones with the original AMGe method, [5, 11]), were less successful due to lack of such good approximation properties of the coarse spaces. With coarse spaces with approximation properties, ourmore » FAS approach on un- structured meshes should be as powerful/successful as FAS on geometrically re ned meshes. For comparison, Newton's method and Picard iterations with an inner state-of-the-art linear solver is compared to FAS on a nonlinear saddle point problem with applications to porous media ow. It is demonstrated that FAS is faster than Newton's method and Picard iterations for the experiments considered here. Due to the guaranteed approximation properties of our AMGe, the coarse spaces are very accurate, providing a solver with the potential for mesh-independent convergence on general unstructured meshes.« less

The L sub 1 finite element method for pure convection problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1991-01-01

The least squares (L sub 2) finite element method is introduced for 2-D steady state pure convection problems with smooth solutions. It is proven that the L sub 2 method has the same stability estimate as the original equation, i.e., the L sub 2 method has better control of the streamline derivative. Numerical convergence rates are given to show that the L sub 2 method is almost optimal. This L sub 2 method was then used as a framework to develop an iteratively reweighted L sub 2 finite element method to obtain a least absolute residual (L sub 1) solution for problems with discontinuous solutions. This L sub 1 finite element method produces a nonoscillatory, nondiffusive and highly accurate numerical solution that has a sharp discontinuity in one element on both coarse and fine meshes. A robust reweighting strategy was also devised to obtain the L sub 1 solution in a few iterations. A number of examples solved by using triangle and bilinear elements are presented.

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE PAGES

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...

2018-01-30

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

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

Osborn, Sarah; Zulian, Patrick; Benson, Thomas

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

NASA Technical Reports Server (NTRS)

Tsiveriotis, K.; Brown, R. A.

1993-01-01

A new method is presented for the solution of free-boundary problems using Lagrangian finite element 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 elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental 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.

Slices: A Scalable Partitioner for Finite Element Meshes

NASA Technical Reports Server (NTRS)

Ding, H. Q.; Ferraro, R. D.

1995-01-01

A parallel partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The element based partitioner can handle mixtures of different element types. All algorithms adopted in the partitioner are scalable, including a communication template for unpredictable incoming messages, as shown in actual timing measurements.

Hybrid seine for full fish community collections

USGS Publications Warehouse

McKenna, James E.; Waldt, Emily M.; Abbett, Ross; David, Anthony; Snyder, James

2013-01-01

Seines are simple and effective fish collection gears, but the net mesh size influences how well the catch represents the fish communities. We designed and tested a hybrid seine with a dual-mesh bag (1/4″ and 1/8″) and compared the fish assemblage collected by each mesh. The fine-mesh net retained three times as many fish and collected more species (as many as eight), including representatives of several rare species, than did the coarser mesh. The dual-mesh bag permitted us to compare both sizes and species retained by each layer and to develop species-specific abundance correction factors, which allowed comparison of catches with the coarse-mesh seine used for earlier collections. The results indicate that a hybrid seine with coarse-mesh wings and a fine-mesh bag would enhance future studies of fish communities, especially when small-bodied fishes or early life stages are the research focus.

A software platform for continuum modeling of ion channels based on unstructured mesh

NASA Astrophysics Data System (ADS)

Tu, B.; Bai, S. Y.; Chen, M. X.; Xie, Y.; Zhang, L. B.; Lu, B. Z.

2014-01-01

Most traditional continuum molecular modeling adopted finite difference or finite volume methods which were based on a structured mesh (grid). Unstructured meshes were only occasionally used, but an increased number of applications emerge in molecular simulations. To facilitate the continuum modeling of biomolecular systems based on unstructured meshes, we are developing a software platform with tools which are particularly beneficial to those approaches. This work describes the software system specifically for the simulation of a typical, complex molecular procedure: ion transport through a three-dimensional channel system that consists of a protein and a membrane. The platform contains three parts: a meshing tool chain for ion channel systems, a parallel finite element solver for the Poisson-Nernst-Planck equations describing the electrodiffusion process of ion transport, and a visualization program for continuum molecular modeling. The meshing tool chain in the platform, which consists of a set of mesh generation tools, is able to generate high-quality surface and volume meshes for ion channel systems. The parallel finite element solver in our platform is based on the parallel adaptive finite element package PHG which wass developed by one of the authors [1]. As a featured component of the platform, a new visualization program, VCMM, has specifically been developed for continuum molecular modeling with an emphasis on providing useful facilities for unstructured mesh-based methods and for their output analysis and visualization. VCMM provides a graphic user interface and consists of three modules: a molecular module, a meshing module and a numerical module. A demonstration of the platform is provided with a study of two real proteins, the connexin 26 and hemolysin ion channels.

An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE

NASA Technical Reports Server (NTRS)

Baysal, Oktay; Lessard, Victor R.

1990-01-01

The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.

A mimetic finite difference method for the Stokes problem with elected edge bubbles

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

Lipnikov, K; Berirao, L

2009-01-01

A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this articlemore » is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.« less

On the Interconnection of Incompatible Solid Finite Element Meshes Using Multipoint Constraints

NASA Technical Reports Server (NTRS)

Fox, G. L.

1985-01-01

Incompatible meshes, i.e., meshes that physically must have a common boundary, but do not necessarily have coincident grid points, can arise in the course of a finite element analysis. For example, two substructures may have been developed at different times for different purposes and it becomes necessary to interconnect the two models. A technique that uses only multipoint constraints, i.e., MPC cards (or MPCS cards in substructuring), is presented. Since the method uses only MPC's, the procedure may apply at any stage in an analysis; no prior planning or special data is necessary.

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

Collins, Benjamin S.; Hamilton, Steven P.; Stimpson, Shane

The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solvesmore » the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.« less

High-speed GPU-based finite element simulations for NDT

NASA Astrophysics Data System (ADS)

Huthwaite, P.; Shi, F.; Van Pamel, A.; Lowe, M. J. S.

2015-03-01

The finite element method solved with explicit time increments is a general approach which can be applied to many ultrasound problems. It is widely used as a powerful tool within NDE for developing and testing inspection techniques, and can also be used in inversion processes. However, the solution technique is computationally intensive, requiring many calculations to be performed for each simulation, so traditionally speed has been an issue. For maximum speed, an implementation of the method, called Pogo [Huthwaite, J. Comp. Phys. 2014, doi: 10.1016/j.jcp.2013.10.017], has been developed to run on graphics cards, exploiting the highly parallelisable nature of the algorithm. Pogo typically demonstrates speed improvements of 60-90x over commercial CPU alternatives. Pogo is applied to three NDE examples, where the speed improvements are important: guided wave tomography, where a full 3D simulation must be run for each source transducer and every different defect size; scattering from rough cracks, where many simulations need to be run to build up a statistical model of the behaviour; and ultrasound propagation within coarse-grained materials where the mesh must be highly refined and many different cases run.

An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.

1993-01-01

We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.

Segmented Domain Decomposition Multigrid For 3-D Turbomachinery Flows

NASA Technical Reports Server (NTRS)

Celestina, M. L.; Adamczyk, J. J.; Rubin, S. G.

2001-01-01

A Segmented Domain Decomposition Multigrid (SDDMG) procedure was developed for three-dimensional viscous flow problems as they apply to turbomachinery flows. The procedure divides the computational domain into a coarse mesh comprised of uniformly spaced cells. To resolve smaller length scales such as the viscous layer near a surface, segments of the coarse mesh are subdivided into a finer mesh. This is repeated until adequate resolution of the smallest relevant length scale is obtained. Multigrid is used to communicate information between the different grid levels. To test the procedure, simulation results will be presented for a compressor and turbine cascade. These simulations are intended to show the ability of the present method to generate grid independent solutions. Comparisons with data will also be presented. These comparisons will further demonstrate the usefulness of the present work for they allow an estimate of the accuracy of the flow modeling equations independent of error attributed to numerical discretization.

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory

NASA Astrophysics Data System (ADS)

Stolk, Christiaan C.

2016-06-01

We develop a new dispersion minimizing compact finite difference scheme for the Helmholtz equation in 2 and 3 dimensions. The scheme is based on a newly developed ray theory for difference equations. A discrete Helmholtz operator and a discrete operator to be applied to the source and the wavefields are constructed. Their coefficients are piecewise polynomial functions of hk, chosen such that phase and amplitude errors are minimal. The phase errors of the scheme are very small, approximately as small as those of the 2-D quasi-stabilized FEM method and substantially smaller than those of alternatives in 3-D, assuming the same number of gridpoints per wavelength is used. In numerical experiments, accurate solutions are obtained in constant and smoothly varying media using meshes with only five to six points per wavelength and wave propagation over hundreds of wavelengths. When used as a coarse level discretization in a multigrid method the scheme can even be used with down to three points per wavelength. Tests on 3-D examples with up to 108 degrees of freedom show that with a recently developed hybrid solver, the use of coarser meshes can lead to corresponding savings in computation time, resulting in good simulation times compared to the literature.

Challenges of Representing Sub-Grid Physics in an Adaptive Mesh Refinement Atmospheric Model

NASA Astrophysics Data System (ADS)

O'Brien, T. A.; Johansen, H.; Johnson, J. N.; Rosa, D.; Benedict, J. J.; Keen, N. D.; Collins, W.; Goodfriend, E.

2015-12-01

Some of the greatest potential impacts from future climate change are tied to extreme atmospheric phenomena that are inherently multiscale, including tropical cyclones and atmospheric rivers. Extremes are challenging to simulate in conventional climate models due to existing models' coarse resolutions relative to the native length-scales of these phenomena. Studying the weather systems of interest requires an atmospheric model with sufficient local resolution, and sufficient performance for long-duration climate-change simulations. To this end, we have developed a new global climate code with adaptive spatial and temporal resolution. The dynamics are formulated using a block-structured conservative finite volume approach suitable for moist non-hydrostatic atmospheric dynamics. By using both space- and time-adaptive mesh refinement, the solver focuses computational resources only where greater accuracy is needed to resolve critical phenomena. We explore different methods for parameterizing sub-grid physics, such as microphysics, macrophysics, turbulence, and radiative transfer. In particular, we contrast the simplified physics representation of Reed and Jablonowski (2012) with the more complex physics representation used in the System for Atmospheric Modeling of Khairoutdinov and Randall (2003). We also explore the use of a novel macrophysics parameterization that is designed to be explicitly scale-aware.

A chimera grid scheme. [multiple overset body-conforming mesh system for finite difference adaptation to complex aircraft configurations

NASA Technical Reports Server (NTRS)

Steger, J. L.; Dougherty, F. C.; Benek, J. A.

1983-01-01

A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.

Galerkin finite difference Laplacian operators on isolated unstructured triangular meshes by linear combinations

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.

1990-01-01

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formulae in Cartesian coordinates for the Laplacian operator on isolated unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator along with linear combinations of the residual equations are used to develop the algorithm. The algorithm was tested for a wide variety of unstructured meshes and found to give satisfactory results.

Finite Volume Algorithms for Heat Conduction

DTIC Science & Technology

2010-05-01

scalar quantity). Although (3) is relatively easy to discretize by using finite differences , its form in generalized coordinates is not. Later, we...familiar with the finite difference method for discretizing differential equations. In fact, the Newton divided difference is the numerical analog for a...expression (8) for the average derivative matches the Newton divided difference formula, so for uniform one-dimensional meshes, the finite volume and

Multiresolution molecular mechanics: Surface effects in nanoscale materials

NASA Astrophysics Data System (ADS)

Yang, Qingcheng; To, Albert C.

2017-05-01

Surface effects have been observed to contribute significantly to the mechanical response of nanoscale structures. The newly proposed energy-based coarse-grained atomistic method Multiresolution Molecular Mechanics (MMM) (Yang, To (2015), [57]) is applied to capture surface effect for nanosized structures by designing a surface summation rule SRS within the framework of MMM. Combined with previously proposed bulk summation rule SRB, the MMM summation rule SRMMM is completed. SRS and SRB are consistently formed within SRMMM for general finite element shape functions. Analogous to quadrature rules in finite element method (FEM), the key idea to the good performance of SRMMM lies in that the order or distribution of energy for coarse-grained atomistic model is mathematically derived such that the number, position and weight of quadrature-type (sampling) atoms can be determined. Mathematically, the derived energy distribution of surface area is different from that of bulk region. Physically, the difference is due to the fact that surface atoms lack neighboring bonding. As such, SRS and SRB are employed for surface and bulk domains, respectively. Two- and three-dimensional numerical examples using the respective 4-node bilinear quadrilateral, 8-node quadratic quadrilateral and 8-node hexahedral meshes are employed to verify and validate the proposed approach. It is shown that MMM with SRMMM accurately captures corner, edge and surface effects with less 0.3% degrees of freedom of the original atomistic system, compared against full atomistic simulation. The effectiveness of SRMMM with respect to high order element is also demonstrated by employing the 8-node quadratic quadrilateral to solve a beam bending problem considering surface effect. In addition, the introduced sampling error with SRMMM that is analogous to numerical integration error with quadrature rule in FEM is very small.

A Nested Modeling Scheme for High-resolution Simulation of the Aquitard Compaction in a Regional Groundwater Extraction Field

NASA Astrophysics Data System (ADS)

Aichi, M.; Tokunaga, T.

2006-12-01

In the fields that experienced both significant drawdown/land subsidence and the recovery of groundwater potential, temporal change of the effective stress in the clayey layers is not simple. Conducting consolidation tests of core samples is a straightforward approach to know the pre-consolidation stress. However, especially in the urban area, the cost of boring and the limitation of sites for boring make it difficult to carry out enough number of tests. Numerical simulation to reproduce stress history can contribute to selecting boring sites and to complement the results of the laboratory tests. To trace the effective stress profile in the clayey layers by numerical simulation, discretization in the clayey layers should be fine. At the same time, the size of the modeled domain should be large enough to calculate the effect of regional groundwater extraction. Here, we developed a new scheme to reduce memory consumption based on domain decomposition technique. A finite element model of coupled groundwater flow and land subsidence is used for the local model, and a finite difference groundwater flow model is used for the regional model. The local model is discretized to fine mesh in the clayey layers to reproduce the temporal change of pore pressure in the layers while the regional model is discretized to relatively coarse mesh to reproduce the effect of the regional groundwater extraction on the groundwater flow. We have tested this scheme by comparing the results obtained from this scheme with those from the finely gridded model for the entire calculation domain. The difference between the results of these models was small enough and our new scheme can be used for the practical problem.

Evaluation of the UnTRIM model for 3-D tidal circulation

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; ,

2001-01-01

A family of numerical models, known as the TRIM models, shares the same modeling philosophy for solving the shallow water equations. A characteristic analysis of the shallow water equations points out that the numerical instability is controlled by the gravity wave terms in the momentum equations and by the transport terms in the continuity equation. A semi-implicit finite-difference scheme has been formulated so that these terms and the vertical diffusion terms are treated implicitly and the remaining terms explicitly to control the numerical stability and the computations are carried out over a uniform finite-difference computational mesh without invoking horizontal or vertical coordinate transformations. An unstructured grid version of TRIM model is introduced, or UnTRIM (pronounces as "you trim"), which preserves these basic numerical properties and modeling philosophy, only the computations are carried out over an unstructured orthogonal grid. The unstructured grid offers the flexibilities in representing complex study areas so that fine grid resolution can be placed in regions of interest, and coarse grids are used to cover the remaining domain. Thus, the computational efforts are concentrated in areas of importance, and an overall computational saving can be achieved because the total number of grid-points is dramatically reduced. To use this modeling approach, an unstructured grid mesh must be generated to properly reflect the properties of the domain of the investigation. The new modeling flexibility in grid structure is accompanied by new challenges associated with issues of grid generation. To take full advantage of this new model flexibility, the model grid generation should be guided by insights into the physics of the problems; and the insights needed may require a higher degree of modeling skill.

Modelling Near-Surface Metallic Clutter Without the Excruciating Pain

NASA Astrophysics Data System (ADS)

Downs, C. M.; Weiss, C. J.; Bach, J.; Williams, J. T.

2016-12-01

An ongoing problem in modeling electromagnetic (EM) interactions with the near-surface and related anthropogenic metal clutter is the large difference in length scale between the clutter dimensions and their resulting EM response. For example, observational evidence shows that cables, pipes and rail lines can have a strong influence far from where they are located, even in situations where these artefacts are volumetrically insignificant over the scale of the model. This poses a significant modeling problem for understanding geohazards in urban environments, for example, because of the very fine numerical discretization required for accurate representation of an artefact embedded in a larger computational domain. We adopt a sub-grid approximation and impose a boundary condition along grid edges to capture the vanishing fields of a perfect conductor. We work in a Cartesian system where the EM fields are solved via finite volumes in the frequency domain in terms of the Lorenz gauged magnetic vector (A) and electric scalar (Phi) potentials. The electric fied is given simply by A-grad(Phi), and set identically to zero along edges of the mesh that coincide with the center of long, slender metallic conductors. A simple extension to bulky artefacts like blocks or slabs involves endowing all such edges in their interior with the same "internal" boundary condition. In essence, we apply the "perfect electric conductor" boundary condition to select edges interior to the modeling domain. We note a few minor numerical consequences of this approach, namely: the zero-E field internal boundary condition destroys the symmetry of the finite volume coefficient matrix; and, the accuracy of the representation of the conducting artefact is restricted by the relatively coarse discretization mesh. The former is overcome with the use of preconditioned bi-conjugate gradient methods instead of the quasi-minimal-residual method. Both are matrix-free iterative solvers - thus avoiding unnecessary storage- and both exhibit generally good convergence for well-posed problems. The latter is more difficult to overcome without either modifying the mesh (potentially degrading the condition number of the coefficient matrix) or with novel mesh sub-gridding. Initial results show qualitative agreement with the expected physics.

Automated Generation of Finite-Element Meshes for Aircraft Conceptual Design

NASA Technical Reports Server (NTRS)

Li, Wu; Robinson, Jay

2016-01-01

This paper presents a novel approach for automated generation of fully connected finite-element meshes for all internal structural components and skins of a given wing-body geometry model, controlled by a few conceptual-level structural layout parameters. Internal structural components include spars, ribs, frames, and bulkheads. Structural layout parameters include spar/rib locations in wing chordwise/spanwise direction and frame/bulkhead locations in longitudinal direction. A simple shell thickness optimization problem with two load conditions is used to verify versatility and robustness of the automated meshing process. The automation process is implemented in ModelCenter starting from an OpenVSP geometry and ending with a NASTRAN 200 solution. One subsonic configuration and one supersonic configuration are used for numerical verification. Two different structural layouts are constructed for each configuration and five finite-element meshes of different sizes are generated for each layout. The paper includes various comparisons of solutions of 20 thickness optimization problems, as well as discussions on how the optimal solutions are affected by the stress constraint bound and the initial guess of design variables.

A Linear-Elasticity Solver for Higher-Order Space-Time Mesh Deformation

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2018-01-01

A linear-elasticity approach is presented for the generation of meshes appropriate for a higher-order space-time discontinuous finite-element method. The equations of linear-elasticity are discretized using a higher-order, spatially-continuous, finite-element method. Given an initial finite-element mesh, and a specified boundary displacement, we solve for the mesh displacements to obtain a higher-order curvilinear mesh. Alternatively, for moving-domain problems we use the linear-elasticity approach to solve for a temporally discontinuous mesh velocity on each time-slab and recover a continuous mesh deformation by integrating the velocity. The applicability of this methodology is presented for several benchmark test cases.

Comparison of copepod collection efficiencies by three commonly used plankton nets: A case study in Bohai Sea, China

NASA Astrophysics Data System (ADS)

Chen, Hongju; Yu, Hao; Liu, Guangxing

2016-12-01

Selection of net with a suitable mesh size is a key concern in the quantitative assessment of zooplankton, which is crucial to understand pelagic ecosystem processes. This study compared the copepod collecting efficiency of three commonly used plankton nets, namely, the China standard coarse net (505 μm mesh), the China standard fine net (77 μm), and the WP-2 net (200 μm). The experiment was performed at six stations in the Bohai Sea during the autumn of 2012. The coarse net substantially under-sampled small individuals (body widths < 672 μm) and led to the lowest species number in each tow, whereas the fine net collected all small copepod species but failed to collect rare species. The WP-2 net appeared to be a compromise of the two other nets, collecting both small copepods and rare species. The abundance of copepods collected by the coarse net (126.4 ± 86.5 ind m-3) was one to two orders of magnitude lower than that by the WP-2 net (5802.4 ± 2595.4 ind m-3), and the value of the fine net (11117.0 ± 4563.41 ind m-3) was nearly twice that of the WP-2 net. The abundance of large copepods ( i.e., adult Calanus sinicus) in the three nets showed no significant differences, but the abundance of small copepods declined with decreasing mesh size. The difference in abundance resulted from the under-sampling of small copepods with body widths < 672 μm and < 266 μm by the coarse and WP-2 nets, respectively.

Experiments in monthly mean simulation of the atmosphere with a coarse-mesh general circulation model

NASA Technical Reports Server (NTRS)

Lutz, R. J.; Spar, J.

1978-01-01

The Hansen atmospheric model was used to compute five monthly forecasts (October 1976 through February 1977). The comparison is based on an energetics analysis, meridional and vertical profiles, error statistics, and prognostic and observed mean maps. The monthly mean model simulations suffer from several defects. There is, in general, no skill in the simulation of the monthly mean sea-level pressure field, and only marginal skill is indicated for the 850 mb temperatures and 500 mb heights. The coarse-mesh model appears to generate a less satisfactory monthly mean simulation than the finer mesh GISS model.

Subplane-based Control Rod Decusping Techniques for the 2D/1D Method in MPACT

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

Graham, Aaron M; Collins, Benjamin S; Downar, Thomas

2017-01-01

The MPACT transport code is being jointly developed by Oak Ridge National Laboratory and the University of Michigan to serve as the primary neutron transport code for the Virtual Environment for Reactor Applications Core Simulator. MPACT uses the 2D/1D method to solve the transport equation by decomposing the reactor model into a stack of 2D planes. A fine mesh flux distribution is calculated in each 2D plane using the Method of Characteristics (MOC), then the planes are coupled axially through a 1D NEM-Pmore » $$_3$$ calculation. This iterative calculation is then accelerated using the Coarse Mesh Finite Difference method. One problem that arises frequently when using the 2D/1D method is that of control rod cusping. This occurs when the tip of a control rod falls between the boundaries of an MOC plane, requiring that the rodded and unrodded regions be axially homogenized for the 2D MOC calculations. Performing a volume homogenization does not properly preserve the reaction rates, causing an error known as cusping. The most straightforward way of resolving this problem is by refining the axial mesh, but this can significantly increase the computational expense of the calculation. The other way of resolving the partially inserted rod is through the use of a decusping method. This paper presents new decusping methods implemented in MPACT that can dynamically correct the rod cusping behavior for a variety of problems.« less

Automatic construction of patient-specific finite-element mesh of the spine from IVDs and vertebra segmentations

NASA Astrophysics Data System (ADS)

Castro-Mateos, Isaac; Pozo, Jose M.; Lazary, Aron; Frangi, Alejandro F.

2016-03-01

Computational medicine aims at developing patient-specific models to help physicians in the diagnosis and treatment selection for patients. The spine, and other skeletal structures, is an articulated object, composed of rigid bones (vertebrae) and non-rigid parts (intervertebral discs (IVD), ligaments and muscles). These components are usually extracted from different image modalities, involving patient repositioning. In the case of the spine, these models require the segmentation of IVDs from MR and vertebrae from CT. In the literature, there exists a vast selection of segmentations methods, but there is a lack of approaches to align the vertebrae and IVDs. This paper presents a method to create patient-specific finite element meshes for biomechanical simulations, integrating rigid and non-rigid parts of articulated objects. First, the different parts are aligned in a complete surface model. Vertebrae extracted from CT are rigidly repositioned in between the IVDs, initially using the IVDs location and then refining the alignment using the MR image with a rigid active shape model algorithm. Finally, a mesh morphing algorithm, based on B-splines, is employed to map a template finite-element (volumetric) mesh to the patient-specific surface mesh. This morphing reduces possible misalignments and guarantees the convexity of the model elements. Results show that the accuracy of the method to align vertebrae into MR, together with IVDs, is similar to that of the human observers. Thus, this method is a step forward towards the automation of patient-specific finite element models for biomechanical simulations.

Tetrahedral and polyhedral mesh evaluation for cerebral hemodynamic simulation--a comparison.

PubMed

Spiegel, Martin; Redel, Thomas; Zhang, Y; Struffert, Tobias; Hornegger, Joachim; Grossman, Robert G; Doerfler, Arnd; Karmonik, Christof

2009-01-01

Computational fluid dynamic (CFD) based on patient-specific medical imaging data has found widespread use for visualizing and quantifying hemodynamics in cerebrovascular disease such as cerebral aneurysms or stenotic vessels. This paper focuses on optimizing mesh parameters for CFD simulation of cerebral aneurysms. Valid blood flow simulations strongly depend on the mesh quality. Meshes with a coarse spatial resolution may lead to an inaccurate flow pattern. Meshes with a large number of elements will result in unnecessarily high computation time which is undesirable should CFD be used for planning in the interventional setting. Most CFD simulations reported for these vascular pathologies have used tetrahedral meshes. We illustrate the use of polyhedral volume elements in comparison to tetrahedral meshing on two different geometries, a sidewall aneurysm of the internal carotid artery and a basilar bifurcation aneurysm. The spatial mesh resolution ranges between 5,119 and 228,118 volume elements. The evaluation of the different meshes was based on the wall shear stress previously identified as a one possible parameter for assessing aneurysm growth. Polyhedral meshes showed better accuracy, lower memory demand, shorter computational speed and faster convergence behavior (on average 369 iterations less).

A weak Galerkin least-squares finite element method for div-curl systems

NASA Astrophysics Data System (ADS)

Li, Jichun; Ye, Xiu; Zhang, Shangyou

2018-06-01

In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

Computing an upper bound on contact stress with surrogate duality

NASA Astrophysics Data System (ADS)

Xuan, Zhaocheng; Papadopoulos, Panayiotis

2016-07-01

We present a method for computing an upper bound on the contact stress of elastic bodies. The continuum model of elastic bodies with contact is first modeled as a constrained optimization problem by using finite elements. An explicit formulation of the total contact force, a fraction function with the numerator as a linear function and the denominator as a quadratic convex function, is derived with only the normalized nodal contact forces as the constrained variables in a standard simplex. Then two bounds are obtained for the sum of the nodal contact forces. The first is an explicit formulation of matrices of the finite element model, derived by maximizing the fraction function under the constraint that the sum of the normalized nodal contact forces is one. The second bound is solved by first maximizing the fraction function subject to the standard simplex and then using Dinkelbach's algorithm for fractional programming to find the maximum—since the fraction function is pseudo concave in a neighborhood of the solution. These two bounds are solved with the problem dimensions being only the number of contact nodes or node pairs, which are much smaller than the dimension for the original problem, namely, the number of degrees of freedom. Next, a scheme for constructing an upper bound on the contact stress is proposed that uses the bounds on the sum of the nodal contact forces obtained on a fine finite element mesh and the nodal contact forces obtained on a coarse finite element mesh, which are problems that can be solved at a lower computational cost. Finally, the proposed method is verified through some examples concerning both frictionless and frictional contact to demonstrate the method's feasibility, efficiency, and robustness.

Analytical and Numerical Results for an Adhesively Bonded Joint Subjected to Pure Bending

NASA Technical Reports Server (NTRS)

Smeltzer, Stanley S., III; Lundgren, Eric

2006-01-01

A one-dimensional, semi-analytical methodology that was previously developed for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit inelastic material behavior is further verified in the present paper. A summary of the first-order differential equations and applied joint loading used to determine the adhesive response from the methodology are also presented. The method was previously verified against a variety of single-lap joint configurations from the literature that subjected the joints to cases of axial tension and pure bending. Using the same joint configuration and applied bending load presented in a study by Yang, the finite element analysis software ABAQUS was used to further verify the semi-analytical method. Linear static ABAQUS results are presented for two models, one with a coarse and one with a fine element meshing, that were used to verify convergence of the finite element analyses. Close agreement between the finite element results and the semi-analytical methodology were determined for both the shear and normal stress responses of the adhesive bondline. Thus, the semi-analytical methodology was successfully verified using the ABAQUS finite element software and a single-lap joint configuration subjected to pure bending.

Method and apparatus for connecting finite element meshes and performing simulations therewith

DOEpatents

Dohrmann, Clark R.; Key, Samuel W.; Heinstein, Martin W.

2003-05-06

The present invention provides a method of connecting dissimilar finite element meshes. A first mesh, designated the master mesh, and a second mesh, designated the slave mesh, each have interface surfaces proximal the other. Each interface surface has a corresponding interface mesh comprising a plurality of interface nodes. Each slave interface node is assigned new coordinates locating the interface node on the interface surface of the master mesh. The slave interface surface is further redefined to be the projection of the slave interface mesh onto the master interface surface.

Mesoscale Fracture Analysis of Multiphase Cementitious Composites Using Peridynamics

PubMed Central

Yaghoobi, Amin; Chorzepa, Mi G.; Kim, S. Sonny; Durham, Stephan A.

2017-01-01

Concrete is a complex heterogeneous material, and thus, it is important to develop numerical modeling methods to enhance the prediction accuracy of the fracture mechanism. In this study, a two-dimensional mesoscale model is developed using a non-ordinary state-based peridynamic (NOSBPD) method. Fracture in a concrete cube specimen subjected to pure tension is studied. The presence of heterogeneous materials consisting of coarse aggregates, interfacial transition zones, air voids and cementitious matrix is characterized as particle points in a two-dimensional mesoscale model. Coarse aggregates and voids are generated using uniform probability distributions, while a statistical study is provided to comprise the effect of random distributions of constituent materials. In obtaining the steady-state response, an incremental and iterative solver is adopted for the dynamic relaxation method. Load-displacement curves and damage patterns are compared with available experimental and finite element analysis (FEA) results. Although the proposed model uses much simpler material damage models and discretization schemes, the load-displacement curves show no difference from the FEA results. Furthermore, no mesh refinement is necessary, as fracture is inherently characterized by bond breakages. Finally, a sensitivity study is conducted to understand the effect of aggregate volume fraction and porosity on the load capacity of the proposed mesoscale model. PMID:28772518

Composition of riparian litter input regulates organic matter decomposition: Implications for headwater stream functioning in a managed forest landscape.

PubMed

Lidman, Johan; Jonsson, Micael; Burrows, Ryan M; Bundschuh, Mirco; Sponseller, Ryan A

2017-02-01

Although the importance of stream condition for leaf litter decomposition has been extensively studied, little is known about how processing rates change in response to altered riparian vegetation community composition. We investigated patterns of plant litter input and decomposition across 20 boreal headwater streams that varied in proportions of riparian deciduous and coniferous trees. We measured a suite of in-stream physical and chemical characteristics, as well as the amount and type of litter inputs from riparian vegetation, and related these to decomposition rates of native (alder, birch, and spruce) and introduced (lodgepole pine) litter species incubated in coarse- and fine-mesh bags. Total litter inputs ranged more than fivefold among sites and increased with the proportion of deciduous vegetation in the riparian zone. In line with differences in initial litter quality, mean decomposition rate was highest for alder, followed by birch, spruce, and lodgepole pine (12, 55, and 68% lower rates, respectively). Further, these rates were greater in coarse-mesh bags that allow colonization by macroinvertebrates. Variance in decomposition rate among sites for different species was best explained by different sets of environmental conditions, but litter-input composition (i.e., quality) was overall highly important. On average, native litter decomposed faster in sites with higher-quality litter input and (with the exception of spruce) higher concentrations of dissolved nutrients and open canopies. By contrast, lodgepole pine decomposed more rapidly in sites receiving lower-quality litter inputs. Birch litter decomposition rate in coarse-mesh bags was best predicted by the same environmental variables as in fine-mesh bags, with additional positive influences of macroinvertebrate species richness. Hence, to facilitate energy turnover in boreal headwaters, forest management with focus on conifer production should aim at increasing the presence of native deciduous trees along streams, as they promote conditions that favor higher decomposition rates of terrestrial plant litter.

Formulation of boundary conditions for the multigrid acceleration of the Euler and Navier Stokes equations

NASA Technical Reports Server (NTRS)

Jentink, Thomas Neil; Usab, William J., Jr.

1990-01-01

An explicit, Multigrid algorithm was written to solve the Euler and Navier-Stokes equations with special consideration given to the coarse mesh boundary conditions. These are formulated in a manner consistent with the interior solution, utilizing forcing terms to prevent coarse-mesh truncation error from affecting the fine-mesh solution. A 4-Stage Hybrid Runge-Kutta Scheme is used to advance the solution in time, and Multigrid convergence is further enhanced by using local time-stepping and implicit residual smoothing. Details of the algorithm are presented along with a description of Jameson's standard Multigrid method and a new approach to formulating the Multigrid equations.

Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Bailey, David H. (Technical Monitor)

1998-01-01

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.

Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes

NASA Technical Reports Server (NTRS)

Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)

1998-01-01

In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.

Dual Formulations of Mixed Finite Element Methods with Applications

PubMed Central

Gillette, Andrew; Bajaj, Chandrajit

2011-01-01

Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail. PMID:21984841

A Domain-Decomposed Multilevel Method for Adaptively Refined Cartesian Grids with Embedded Boundaries

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2000-01-01

Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.

Stress-intensity factors for small surface and corner cracks in plates

NASA Technical Reports Server (NTRS)

Raju, I. S.; Atluri, S. N.; Newman, J. C., Jr.

1988-01-01

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Meshing of a Spiral Bevel Gearset with 3D Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, George D.; Handschuh, Robert

1996-01-01

Recent advances in spiral bevel gear geometry and finite element technology make it practical to conduct a structural analysis and analytically roll the gearset through mesh. With the advent of user specific programming linked to 3D solid modelers and mesh generators, model generation has become greatly automated. Contact algorithms available in general purpose finite element codes eliminate the need for the use and alignment of gap elements. Once the gearset is placed in mesh, user subroutines attached to the FE code easily roll the gearset through mesh. The method is described in detail. Preliminary results for a gearset segment showing the progression of the contact lineload is given as the gears roll through mesh.

ESCHER: An interactive mesh-generating editor for preparing finite-element input

NASA Technical Reports Server (NTRS)

Oakes, W. R., Jr.

1984-01-01

ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.

Electromagnetic plasma simulation in realistic geometries

NASA Astrophysics Data System (ADS)

Brandon, S.; Ambrosiano, J. J.; Nielsen, D.

1991-08-01

Particle-in-Cell (PIC) calculations have become an indispensable tool to model the nonlinear collective behavior of charged particle species in electromagnetic fields. Traditional finite difference codes, such as CONDOR (2-D) and ARGUS (3-D), are used extensively to design experiments and develop new concepts. A wide variety of physical processes can be modeled simply and efficiently by these codes. However, experiments have become more complex. Geometrical shapes and length scales are becoming increasingly more difficult to model. Spatial resolution requirements for the electromagnetic calculation force large grids and small time steps. Many hours of CRAY YMP time may be required to complete 2-D calculation -- many more for 3-D calculations. In principle, the number of mesh points and particles need only to be increased until all relevant physical processes are resolved. In practice, the size of a calculation is limited by the computer budget. As a result, experimental design is being limited by the ability to calculate, not by the experimenters ingenuity or understanding of the physical processes involved. Several approaches to meet these computational demands are being pursued. Traditional PIC codes continue to be the major design tools. These codes are being actively maintained, optimized, and extended to handle large and more complex problems. Two new formulations are being explored to relax the geometrical constraints of the finite difference codes. A modified finite volume test code, TALUS, uses a data structure compatible with that of standard finite difference meshes. This allows a basic conformal boundary/variable grid capability to be retrofitted to CONDOR. We are also pursuing an unstructured grid finite element code, MadMax. The unstructured mesh approach provides maximum flexibility in the geometrical model while also allowing local mesh refinement.

Automated finite element meshing of the lumbar spine: Verification and validation with 18 specimen-specific models.

PubMed

Campbell, J Q; Coombs, D J; Rao, M; Rullkoetter, P J; Petrella, A J

2016-09-06

The purpose of this study was to seek broad verification and validation of human lumbar spine finite element models created using a previously published automated algorithm. The automated algorithm takes segmented CT scans of lumbar vertebrae, automatically identifies important landmarks and contact surfaces, and creates a finite element model. Mesh convergence was evaluated by examining changes in key output variables in response to mesh density. Semi-direct validation was performed by comparing experimental results for a single specimen to the automated finite element model results for that specimen with calibrated material properties from a prior study. Indirect validation was based on a comparison of results from automated finite element models of 18 individual specimens, all using one set of generalized material properties, to a range of data from the literature. A total of 216 simulations were run and compared to 186 experimental data ranges in all six primary bending modes up to 7.8Nm with follower loads up to 1000N. Mesh convergence results showed less than a 5% difference in key variables when the original mesh density was doubled. The semi-direct validation results showed that the automated method produced results comparable to manual finite element modeling methods. The indirect validation results showed a wide range of outcomes due to variations in the geometry alone. The studies showed that the automated models can be used to reliably evaluate lumbar spine biomechanics, specifically within our intended context of use: in pure bending modes, under relatively low non-injurious simulated in vivo loads, to predict torque rotation response, disc pressures, and facet forces. Copyright © 2016 Elsevier Ltd. All rights reserved.

Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks

NASA Astrophysics Data System (ADS)

Kurguzov, V. D.

2016-12-01

The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.

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

Wiley, J.C.

The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.

Influence of local meshing size on stress intensity factor of orthopedic lag screw

NASA Astrophysics Data System (ADS)

Husain, M. N.; Daud, R.; Basaruddin, K. S.; Mat, F.; Bajuri, M. Y.; Arifin, A. K.

2017-09-01

Linear elastic fracture mechanics (LEFM) concept is generally used to study the influence of crack on the performance of structures. In order to study the LEFM concept on damaged structure, the usage of finite element analysis software is implemented to do the simulation of the structure. Mesh generation is one of the most crucial procedures in finite element method. For the structure that crack or damaged, it is very important to determine the accurate local meshing size at the crack tip of the crack itself in order to get the accurate value of stress intensity factor, KI. Pre crack will be introduced to the lag screw based on the von mises' stress result that had been performed in previous research. This paper shows the influence of local mesh arrangement on numerical value of the stress intensity factor, KI obtained by the displacement method. This study aims to simulate the effect of local meshing which is the singularity region on stress intensity factor, KI to the critical point of failure in screw. Five different set of wedges meshing size are introduced during the simulation of finite element analysis. The number of wedges used to simulate this research is 8, 10, 14, 16 and 20. There are three set of numerical equations used to validate the results which are brown and srawley, gross and brown and Tada equation. The result obtained from the finite element software (ANSYS APDL) has a positive agreement with the numerical analysis which is Brown and Srawley compared to other numerical formula. Radius of first row size of 0.014 and singularity element with 14 numbers of wedges is proved to be the best local meshing for this study.

Experiments with explicit filtering for LES using a finite-difference method

NASA Technical Reports Server (NTRS)

Lund, T. S.; Kaltenbach, H. J.

1995-01-01

The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture most of the energy-containing eddies, and if explicit filtering is used, the mesh must be enlarged so that these motions are passed by the filter. Given the high cost of explicit filtering, the following interesting question arises. Since the mesh must be expanded in order to perform the explicit filter, might it be better to take advantage of the increased resolution and simply perform an unfiltered simulation on the larger mesh? The cost of the two approaches is roughly the same, but the philosophy is rather different. In the filtered simulation, resolution is sacrificed in order to minimize the various forms of numerical error. In the unfiltered simulation, the errors are left intact, but they are concentrated at very small scales that could be dynamically unimportant from a LES perspective. Very little is known about this tradeoff and the objective of this work is to study this relationship in high Reynolds number channel flow simulations using a second-order finite-difference method.

Numerical evaluation of moiré pattern in touch sensor module with electrode mesh structure in oblique view

NASA Astrophysics Data System (ADS)

Pournoury, M.; Zamiri, A.; Kim, T. Y.; Yurlov, V.; Oh, K.

2016-03-01

Capacitive touch sensor screen with the metal materials has recently become qualified for substitution of ITO; however several obstacles still have to be solved. One of the most important issues is moiré phenomenon. The visibility problem of the metal-mesh, in touch sensor module (TSM) is numerically considered in this paper. Based on human eye contract sensitivity function (CSF), moiré pattern of TSM electrode mesh structure is simulated with MATLAB software for 8 inch screen display in oblique view. Standard deviation of the generated moiré by the superposition of electrode mesh and screen image is calculated to find the optimal parameters which provide the minimum moiré visibility. To create the screen pixel array and mesh electrode, rectangular function is used. The filtered image, in frequency domain, is obtained by multiplication of Fourier transform of the finite mesh pattern (product of screen pixel and mesh electrode) with the calculated CSF function for three different observer distances (L=200, 300 and 400 mm). It is observed that the discrepancy between analytical and numerical results is less than 0.6% for 400 mm viewer distance. Moreover, in the case of oblique view due to considering the thickness of the finite film between mesh electrodes and screen, different points of minimum standard deviation of moiré pattern are predicted compared to normal view.

The Influence of Shredder Feeding on Fungal Activity in a Nutrient-Enriched Stream and an Unaltered Stream

NASA Astrophysics Data System (ADS)

Chung, N.; Suberkopp, K.

2005-05-01

The effect of shredder feeding on aquatic hyphomycete communities associated with submerged leaves was studied in two southern Appalachian headwater streams in North Carolina. Coarse and fine mesh litter bags containing red maple (Acer rubrum) leaves were placed in the nutrient-enriched stream and in the reference stream and were retrieved monthly. Both shredder feeding and nutrient enrichment enhanced breakdown rates. The breakdown rates of leaves in coarse mesh bags in the reference stream (k = 0.0275) and fine mesh bags in the nutrient enriched stream (k = 0.0272) were not significantly different, suggesting that the shredding effect on litter breakdown was offset by higher fungal activity as a result of nutrient enrichment. Fungal sporulation rates and biomass (based on ergosterol concentrations) were higher in the nutrient enriched than in the reference stream, but neither fungal biomass nor sporulation rate was affected by shredder feeding. Species richness was higher in the nutrient-enriched than in the reference stream. The enrichment with nutrients altered fungal community composition more than shredder feeding.

Approaches to the automatic generation and control of finite element meshes

NASA Technical Reports Server (NTRS)

Shephard, Mark S.

1987-01-01

The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.

Pre- and postprocessing techniques for determining goodness of computational meshes

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Westermann, T.; Bass, J. M.

1993-01-01

Research in error estimation, mesh conditioning, and solution enhancement for finite element, finite difference, and finite volume methods has been incorporated into AUDITOR, a modern, user-friendly code, which operates on 2D and 3D unstructured neutral files to improve the accuracy and reliability of computational results. Residual error estimation capabilities provide local and global estimates of solution error in the energy norm. Higher order results for derived quantities may be extracted from initial solutions. Within the X-MOTIF graphical user interface, extensive visualization capabilities support critical evaluation of results in linear elasticity, steady state heat transfer, and both compressible and incompressible fluid dynamics.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

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

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Minimizing finite-volume discretization errors on polyhedral meshes

NASA Astrophysics Data System (ADS)

Mouly, Quentin; Evrard, Fabien; van Wachem, Berend; Denner, Fabian

2017-11-01

Tetrahedral meshes are widely used in CFD to simulate flows in and around complex geometries, as automatic generation tools now allow tetrahedral meshes to represent arbitrary domains in a relatively accessible manner. Polyhedral meshes, however, are an increasingly popular alternative. While tetrahedron have at most four neighbours, the higher number of neighbours per polyhedral cell leads to a more accurate evaluation of gradients, essential for the numerical resolution of PDEs. The use of polyhedral meshes, nonetheless, introduces discretization errors for finite-volume methods: skewness and non-orthogonality, which occur with all sorts of unstructured meshes, as well as errors due to non-planar faces, specific to polygonal faces with more than three vertices. Indeed, polyhedral mesh generation algorithms cannot, in general, guarantee to produce meshes free of non-planar faces. The presented work focuses on the quantification and optimization of discretization errors on polyhedral meshes in the context of finite-volume methods. A quasi-Newton method is employed to optimize the relevant mesh quality measures. Various meshes are optimized and CFD results of cases with known solutions are presented to assess the improvements the optimization approach can provide.

Coarse mesh and one-cell block inversion based diffusion synthetic acceleration

NASA Astrophysics Data System (ADS)

Kim, Kang-Seog

DSA (Diffusion Synthetic Acceleration) has been developed to accelerate the SN transport iteration. We have developed solution techniques for the diffusion equations of FLBLD (Fully Lumped Bilinear Discontinuous), SCB (Simple Comer Balance) and UCB (Upstream Corner Balance) modified 4-step DSA in x-y geometry. Our first multi-level method includes a block Gauss-Seidel iteration for the discontinuous diffusion equation, uses the continuous diffusion equation derived from the asymptotic analysis, and avoids void cell calculation. We implemented this multi-level procedure and performed model problem calculations. The results showed that the FLBLD, SCB and UCB modified 4-step DSA schemes with this multi-level technique are unconditionally stable and rapidly convergent. We suggested a simplified multi-level technique for FLBLD, SCB and UCB modified 4-step DSA. This new procedure does not include iterations on the diffusion calculation or the residual calculation. Fourier analysis results showed that this new procedure was as rapidly convergent as conventional modified 4-step DSA. We developed new DSA procedures coupled with 1-CI (Cell Block Inversion) transport which can be easily parallelized. We showed that 1-CI based DSA schemes preceded by SI (Source Iteration) are efficient and rapidly convergent for LD (Linear Discontinuous) and LLD (Lumped Linear Discontinuous) in slab geometry and for BLD (Bilinear Discontinuous) and FLBLD in x-y geometry. For 1-CI based DSA without SI in slab geometry, the results showed that this procedure is very efficient and effective for all cases. We also showed that 1-CI based DSA in x-y geometry was not effective for thin mesh spacings, but is effective and rapidly convergent for intermediate and thick mesh spacings. We demonstrated that the diffusion equation discretized on a coarse mesh could be employed to accelerate the transport equation. Our results showed that coarse mesh DSA is unconditionally stable and is as rapidly convergent as fine mesh DSA in slab geometry. For x-y geometry our coarse mesh DSA is very effective for thin and intermediate mesh spacings independent of the scattering ratio, but is not effective for purely scattering problems and high aspect ratio zoning. However, if the scattering ratio is less than about 0.95, this procedure is very effective for all mesh spacing.

The transmission of stress to grafted bone inside a titanium mesh cage used in anterior column reconstruction after total spondylectomy: a finite-element analysis.

PubMed

Akamaru, Tomoyuki; Kawahara, Norio; Sakamoto, Jiro; Yoshida, Akira; Murakami, Hideki; Hato, Taizo; Awamori, Serina; Oda, Juhachi; Tomita, Katsuro

2005-12-15

A finite-element study of posterior alone or anterior/posterior combined instrumentation following total spondylectomy and replacement with a titanium mesh cage used as an anterior strut. To compare the effect of posterior instrumentation versus anterior/posterior instrumentation on transmission of the stress to grafted bone inside a titanium mesh cage following total spondylectomy. The most recent reconstruction techniques following total spondylectomy for malignant spinal tumor include a titanium mesh cage filled with autologous bone as an anterior strut. The need for additional anterior instrumentation with posterior pedicle screws and rods is controversial. Transmission of the mechanical stress to grafted bone inside a titanium mesh cage is important for fusion and remodeling. To our knowledge, there are no published reports comparing the load-sharing properties of the different reconstruction methods following total spondylectomy. A 3-dimensional finite-element model of the reconstructed spine (T10-L4) following total spondylectomy at T12 was constructed. A Harms titanium mesh cage (DePuy Spine, Raynham, MA) was positioned as an anterior replacement, and 3 types of the reconstruction methods were compared: (1) multilevel posterior instrumentation (MPI) (i.e., posterior pedicle screws and rods at T10-L2 without anterior instrumentation); (2) MPI with anterior instrumentation (MPAI) (i.e., MPAI [Kaneda SR; DePuy Spine] at T11-L1); and (3) short posterior and anterior instrumentation (SPAI) (i.e., posterior pedicle screws and rods with anterior instrumentation at T11-L1). The mechanical energy stress distribution exerted inside the titanium mesh cage was evaluated and compared by finite-element analysis for the 3 different reconstruction methods. Simulated forces were applied to give axial compression, flexion, extension, and lateral bending. In flexion mode, the energy stress distribution in MPI was higher than 3.0 x 10 MPa in 73.0% of the total volume inside the titanium mesh cage, while 38.0% in MPAI, and 43.3% in SPAI. In axial compression and extension modes, there were no remarkable differences for each reconstruction method. In left-bending mode, there was little stress energy in the cancellous bone inside the titanium mesh cage in MPAI and SPAI. This experiment shows that from the viewpoint of stress shielding, the reconstruction method, using additional anterior instrumentation with posterior pedicle screws (MPAI and SPAI), stress shields the cancellous bone inside the titanium mesh cage to a higher degree than does the system using posterior pedicle screw fixation alone (MPI). Thus, a reconstruction method with no anterior fixation should be better at allowing stress for remodeling of the bone graft inside the titanium mesh cage.

A voxel-based finite element model for the prediction of bladder deformation

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

Chai Xiangfei; Herk, Marcel van; Hulshof, Maarten C. C. M.

2012-01-15

Purpose: A finite element (FE) bladder model was previously developed to predict bladder deformation caused by bladder filling change. However, two factors prevent a wide application of FE models: (1) the labor required to construct a FE model with high quality mesh and (2) long computation time needed to construct the FE model and solve the FE equations. In this work, we address these issues by constructing a low-resolution voxel-based FE bladder model directly from the binary segmentation images and compare the accuracy and computational efficiency of the voxel-based model used to simulate bladder deformation with those of a classicalmore » FE model with a tetrahedral mesh. Methods: For ten healthy volunteers, a series of MRI scans of the pelvic region was recorded at regular intervals of 10 min over 1 h. For this series of scans, the bladder volume gradually increased while rectal volume remained constant. All pelvic structures were defined from a reference image for each volunteer, including bladder wall, small bowel, prostate (male), uterus (female), rectum, pelvic bone, spine, and the rest of the body. Four separate FE models were constructed from these structures: one with a tetrahedral mesh (used in previous study), one with a uniform hexahedral mesh, one with a nonuniform hexahedral mesh, and one with a low-resolution nonuniform hexahedral mesh. Appropriate material properties were assigned to all structures and uniform pressure was applied to the inner bladder wall to simulate bladder deformation from urine inflow. Performance of the hexahedral meshes was evaluated against the performance of the standard tetrahedral mesh by comparing the accuracy of bladder shape prediction and computational efficiency. Results: FE model with a hexahedral mesh can be quickly and automatically constructed. No substantial differences were observed between the simulation results of the tetrahedral mesh and hexahedral meshes (<1% difference in mean dice similarity coefficient to manual contours and <0.02 cm difference in mean standard deviation of residual errors). The average equation solving time (without manual intervention) for the first two types of hexahedral meshes increased to 2.3 h and 2.6 h compared to the 1.1 h needed for the tetrahedral mesh, however, the low-resolution nonuniform hexahedral mesh dramatically decreased the equation solving time to 3 min without reducing accuracy. Conclusions: Voxel-based mesh generation allows fast, automatic, and robust creation of finite element bladder models directly from binary segmentation images without user intervention. Even the low-resolution voxel-based hexahedral mesh yields comparable accuracy in bladder shape prediction and more than 20 times faster in computational speed compared to the tetrahedral mesh. This approach makes it more feasible and accessible to apply FE method to model bladder deformation in adaptive radiotherapy.« less

Buckling analysis of Big Dee Vacuum Vessel

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

Lightner, S.; Gallix, R.

1983-12-01

A simplified three-dimensional shell buckling analysis of the GA Technologies Inc., Big Dee Vacuum Vessel (V/V) was performed using the finite element program TRICO. A coarse-mesh linear elastic model, which accommodated the support boundary conditions, was used to determine the buckling mode shape under a uniform external pressure. Using this buckling mode shape, refined models were used to calculate the linear buckling load (P/sub crit/) more accurately. Several different designs of the Big Dee V/V were considered in this analysis. The supports for the V/V were equally-spaced radial pins at the outer diameter of the mid-plane. For all the casesmore » considered, the buckling mode was axisymmetric in the toroidal direction. Therefore, it was possible to use only a small angular sector of a toric shell for the refined analysis. P/sub crit/ for the Big Dee is about 60 atm for a uniform external pressure. Also investigated in this analysis were the effects of geometrical imperfections and non-uniform pressure distributions.« less

A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS

NASA Technical Reports Server (NTRS)

Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.

1993-01-01

Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

Charged particle tracking through electrostatic wire meshes using the finite element method

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

Devlin, L. J.; Karamyshev, O.; Welsch, C. P., E-mail: carsten.welsch@cockcroft.ac.uk

Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed.more » The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.« less

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

Free Mesh Method: fundamental conception, algorithms and accuracy study

PubMed Central

YAGAWA, Genki

2011-01-01

The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy. PMID:21558752

The aggregated unfitted finite element method for elliptic problems

NASA Astrophysics Data System (ADS)

Badia, Santiago; Verdugo, Francesc; Martín, Alberto F.

2018-07-01

Unfitted finite element 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 finite element spaces based on a cell aggregation technique. The presented method, called aggregated unfitted finite element method, is easy to implement, and can be used, in contrast to previous works, in Galerkin approximations of coercive problems with conforming Lagrangian finite element spaces. The mathematical analysis of the new method states that the condition number of the resulting linear system matrix scales as in standard finite elements for body-fitted meshes, without being affected by small cut cells, and that the method leads to the optimal finite element convergence order. These theoretical results are confirmed with 2D and 3D numerical experiments.

Nanoengineering Testbed for Nanosolar Cell and Piezoelectric Compounds

DTIC Science & Technology

2012-02-29

element mesh. The third model was a 3D finite element mesh that included complete geometric representation of Berkovich tip. This model allows for a...height of the specimen. These simulations suggest the proper specimen size to approximate a body of semi-infinite extent for a given indentation depth...tip nanoindentation model was the third and final finite element mesh created for analysis and comparison. The material model and the finite element

Blasim: A computational tool to assess ice impact damage on engine blades

NASA Astrophysics Data System (ADS)

Reddy, E. S.; Abumeri, G. H.; Chamis, C. C.

1993-04-01

A portable computer called BLASIM was developed at NASA LeRC to assess ice impact damage on aircraft engine blades. In addition to ice impact analyses, the code also contains static, dynamic, resonance margin, and supersonic flutter analysis capabilities. Solid, hollow, superhybrid, and composite blades are supported. An optional preprocessor (input generator) was also developed to interactively generate input for BLASIM. The blade geometry can be defined using a series of airfoils at discrete input stations or by a finite element grid. The code employs a coarse, fixed finite element mesh containing triangular plate finite elements to minimize program execution time. Ice piece is modeled using an equivalent spherical objective that has a high velocity opposite that of the aircraft and parallel to the engine axis. For local impact damage assessment, the impact load is considered as a distributed force acting over a region around the impact point. The average radial strain of the finite elements along the leading edge is used as a measure of the local damage. To estimate damage at the blade root, the impact is treated as an impulse and a combined stress failure criteria is employed. Parametric studies of local and root ice impact damage, and post-impact dynamics are discussed for solid and composite blades.

Controlling the energy of defects and interfaces in the amplitude expansion of the phase-field crystal model

NASA Astrophysics Data System (ADS)

Salvalaglio, Marco; Backofen, Rainer; Voigt, Axel; Elder, Ken R.

2017-08-01

One of the major difficulties in employing phase-field crystal (PFC) modeling and the associated amplitude (APFC) formulation is the ability to tune model parameters to match experimental quantities. In this work, we address the problem of tuning the defect core and interface energies in the APFC formulation. We show that the addition of a single term to the free-energy functional can be used to increase the solid-liquid interface and defect energies in a well-controlled fashion, without any major change to other features. The influence of the newly added term is explored in two-dimensional triangular and honeycomb structures as well as bcc and fcc lattices in three dimensions. In addition, a finite-element method (FEM) is developed for the model that incorporates a mesh refinement scheme. The combination of the FEM and mesh refinement to simulate amplitude expansion with a new energy term provides a method of controlling microscopic features such as defect and interface energies while simultaneously delivering a coarse-grained examination of the system.

Rib fractures under anterior-posterior dynamic loads: experimental and finite-element study.

PubMed

Li, Zuoping; Kindig, Matthew W; Kerrigan, Jason R; Untaroiu, Costin D; Subit, Damien; Crandall, Jeff R; Kent, Richard W

2010-01-19

The purpose of this study was to investigate whether using a finite-element (FE) mesh composed entirely of hexahedral elements to model cortical and trabecular bone (all-hex model) would provide more accurate simulations than those with variable thickness shell elements for cortical bone and hexahedral elements for trabecular bone (hex-shell model) in the modeling human ribs. First, quasi-static non-injurious and dynamic injurious experiments were performed using the second, fourth, and tenth human thoracic ribs to record the structural behavior and fracture tolerance of individual ribs under anterior-posterior bending loads. Then, all-hex and hex-shell FE models for the three ribs were developed using an octree-based and multi-block hex meshing approach, respectively. Material properties of cortical bone were optimized using dynamic experimental data and the hex-shell model of the fourth rib and trabecular bone properties were taken from the literature. Overall, the reaction force-displacement relationship predicted by both all-hex and hex-shell models with nodes in the offset middle-cortical surfaces compared well with those measured experimentally for all the three ribs. With the exception of fracture locations, the predictions from all-hex and offset hex-shell models of the second and fourth ribs agreed better with experimental data than those from the tenth rib models in terms of reaction force at fracture (difference <15.4%), ultimate failure displacement and time (difference <7.3%), and cortical bone strains. The hex-shell models with shell nodes in outer cortical surfaces increased static reaction forces up to 16.6%, compared to offset hex-shell models. These results indicated that both all-hex and hex-shell modeling strategies were applicable for simulating rib responses and bone fractures for the loading conditions considered, but coarse hex-shell models with constant or variable shell thickness were more computationally efficient and therefore preferred. Copyright 2009 Elsevier Ltd. All rights reserved.

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

NASA Technical Reports Server (NTRS)

Oezdemir, T.; Volakis, John L.

1993-01-01

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity

NASA Technical Reports Server (NTRS)

Baker, John G.; Van Meter, James R.

2005-01-01

A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.

Research on Finite Element Model Generating Method of General Gear Based on Parametric Modelling

NASA Astrophysics Data System (ADS)

Lei, Yulong; Yan, Bo; Fu, Yao; Chen, Wei; Hou, Liguo

2017-06-01

Aiming at the problems of low efficiency and poor quality of gear meshing in the current mainstream finite element software, through the establishment of universal gear three-dimensional model, and explore the rules of unit and node arrangement. In this paper, a finite element model generation method of universal gear based on parameterization is proposed. Visual Basic program is used to realize the finite element meshing, give the material properties, and set the boundary / load conditions and other pre-processing work. The dynamic meshing analysis of the gears is carried out with the method proposed in this pape, and compared with the calculated values to verify the correctness of the method. The method greatly shortens the workload of gear finite element pre-processing, improves the quality of gear mesh, and provides a new idea for the FEM pre-processing.

Computational procedure for finite difference solution of one-dimensional heat conduction problems reduces computer time

NASA Technical Reports Server (NTRS)

Iida, H. T.

1966-01-01

Computational procedure reduces the numerical effort whenever the method of finite differences is used to solve ablation problems for which the surface recession is large relative to the initial slab thickness. The number of numerical operations required for a given maximum space mesh size is reduced.

The sensitivity of biological finite element models to the resolution of surface geometry: a case study of crocodilian crania

PubMed Central

Evans, Alistair R.; McHenry, Colin R.

2015-01-01

The reliability of finite element analysis (FEA) in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context. PMID:26056620

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

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

Prokopenko, Andrey; Tuminaro, Raymond S.

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

An algebraic multigrid method for Q2-Q1 mixed discretizations of the Navier-Stokes equations

DOE PAGES

Prokopenko, Andrey; Tuminaro, Raymond S.

2016-07-01

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily co-located at mesh points. Speci cally, we investigate a Q 2-Q 1 mixed finite element discretization of the incompressible Navier-Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees-of-freedom (dofs) are defined at spatial locations where there are no corresponding pressure dofs. Thus, AMG approaches lever- aging this co-located structure are not applicable. This paper instead proposes an automatic AMG coarsening that mimics certain pressure/velocitymore » dof relationships of the Q 2-Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity dofs resembles that on the nest grid. To define coefficients within the inter-grid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier-Stokes problems.« less

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

Boundary and Interface Conditions for High Order Finite Difference Methods Applied to the Euler and Navier-Strokes Equations

NASA Technical Reports Server (NTRS)

Nordstrom, Jan; Carpenter, Mark H.

1998-01-01

Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.

The mimetic finite difference method for the Landau–Lifshitz equation

DOE PAGES

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

2017-01-01

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

The mimetic finite difference method for the Landau–Lifshitz equation

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

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Large Eddy simulation of compressible flows with a low-numerical dissipation patch-based adaptive mesh refinement method

NASA Astrophysics Data System (ADS)

Pantano, Carlos

2005-11-01

We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

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

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

In-memory integration of existing software components for parallel adaptive unstructured mesh workflows

DOE PAGES

Smith, Cameron W.; Granzow, Brian; Diamond, Gerrett; ...

2017-01-01

Unstructured mesh methods, like finite elements and finite volumes, support the effective analysis of complex physical behaviors modeled by partial differential equations over general threedimensional domains. The most reliable and efficient methods apply adaptive procedures with a-posteriori error estimators that indicate where and how the mesh is to be modified. Although adaptive meshes can have two to three orders of magnitude fewer elements than a more uniform mesh for the same level of accuracy, there are many complex simulations where the meshes required are so large that they can only be solved on massively parallel systems.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

Three Dimensional Grid Generation for Complex Configurations - Recent Progress

DTIC Science & Technology

1988-03-01

Navier/Stokes finite difference calculations currently of interest. It has been amply demonstrated that the viability of a numerical solution depends...such as advanced fighters or logistic transports, where a multiblock mesh, for example, is necessary. There exist numerous reports and books on the...MESHES I 3.10 ADAPTIVE GRID SCHEMES 10 3.11 REFERENCES 12 4. CONTRIBUTIONS 13 4.1 SOLICITATION AND OVERVIEW 13 4.2 LESSONS LEARNED IN THE MESH

The application of finite volume methods for modelling three-dimensional incompressible flow on an unstructured mesh

NASA Astrophysics Data System (ADS)

Lonsdale, R. D.; Webster, R.

This paper demonstrates the application of a simple finite volume approach to a finite element mesh, combining the economy of the former with the geometrical flexibility of the latter. The procedure is used to model a three-dimensional flow on a mesh of linear eight-node brick (hexahedra). Simulations are performed for a wide range of flow problems, some in excess of 94,000 nodes. The resulting computer code ASTEC that incorporates these procedures is described.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

Improvement of finite element meshes - Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1989-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffnes matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.

Improvement in finite element meshes: Heat transfer in an infinite cylinder

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.

1988-01-01

An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffness matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

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

Lim, Hojun; Owen, Steven J.; Abdeljawad, Fadi F.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct linkmore » between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.« less

A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions

NASA Astrophysics Data System (ADS)

Reimer, Ashton S.; Cheviakov, Alexei F.

2013-03-01

A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers. Catalogue identifier: AENQ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AENQ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GNU General Public License v3.0 No. of lines in distributed program, including test data, etc.: 102793 No. of bytes in distributed program, including test data, etc.: 369378 Distribution format: tar.gz Programming language: Matlab 2010a. Computer: PC, Macintosh. Operating system: Windows, OSX, Linux. RAM: 8 GB (8, 589, 934, 592 bytes) Classification: 4.3. Nature of problem: To solve the Poisson problem in a standard domain with “patchy surface”-type (strongly heterogeneous) Neumann/Dirichlet boundary conditions. Solution method: Finite difference with mesh refinement. Restrictions: Spherical domain in 3D; rectangular domain or a disk in 2D. Unusual features: Choice between mldivide/iterative solver for the solution of large system of linear algebraic equations that arise. Full user control of Neumann/Dirichlet boundary conditions and mesh refinement. Running time: Depending on the number of points taken and the geometry of the domain, the routine may take from less than a second to several hours to execute.

3D Tensorial Elastodynamics for Isotropic Media on Vertically Deformed Meshes

NASA Astrophysics Data System (ADS)

Shragge, J. C.

2017-12-01

Solutions of the 3D elastodynamic wave equation are sometimes required in industrial and academic applications of elastic reverse-time migration (E-RTM) and full waveform inversion (E-FWI) that involve vertically deformed meshes. Examples include incorporating irregular free-surface topography and handling internal boundaries (e.g., water bottom) directly into the computational meshes. In 3D E-RTM and E-FWI applications, the number of forward modeling simulations can number in the tens of thousands (per iteration), which necessitates the development of stable, accurate and efficient 3D elastodynamics solvers. For topographic scenarios, most finite-difference solution approaches use a change-of-variable strategy that has a number of associated computational challenges, including difficulties in handling of the free-surface boundary condition. In this study, I follow a tensorial approach and use a generalized family of analytic transforms to develop a set of analytic equations for 3D elastodynamics that directly incorporates vertical grid deformations. Importantly, this analytic approach allows for the specification of an analytic free-surface boundary condition appropriate for vertically deformed meshes. These equations are both straightforward and efficient to solve using a velocity-stress formulation with finite-difference (MFD) operators implemented on a fully staggered grid. Moreover, I demonstrate that the use of mimetic finite difference (MFD) methods allows stable, accurate, and efficient numerical solutions to be simulated for typical topographic scenarios. Examples demonstrate that high-quality elastic wavefields can be generated for topographic surfaces exhibiting significant topographic relief.

A fully consistent and conservative vertically adaptive coordinate system for SLIM 3D v0.4 with an application to the thermocline oscillations of Lake Tanganyika

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Legat, Vincent; Vallaeys, Valentin; Naithani, Jaya; Thiery, Wim; Remacle, Jean-François; Deleersnijder, Eric

2018-03-01

The discontinuous Galerkin (DG) finite element method is well suited for the modelling, with a relatively small number of elements, of three-dimensional flows exhibiting strong velocity or density gradients. Its performance can be highly enhanced by having recourse to r-adaptivity. Here, a vertical adaptive mesh method is developed for DG finite elements. This method, originally designed for finite difference schemes, is based on the vertical diffusion of the mesh nodes, with the diffusivity controlled by the density jumps at the mesh element interfaces. The mesh vertical movement is determined by means of a conservative arbitrary Lagrangian-Eulerian (ALE) formulation. Though conservativity is naturally achieved, tracer consistency is obtained by a suitable construction of the mesh vertical velocity field, which is defined in such a way that it is fully compatible with the tracer and continuity equations at a discrete level. The vertically adaptive mesh approach is implemented in the three-dimensional version of the geophysical and environmental flow Second-generation Louvain-la-Neuve Ice-ocean Model (SLIM 3D; www.climate.be/slim). Idealised benchmarks, aimed at simulating the oscillations of a sharp thermocline, are dealt with. Then, the relevance of the vertical adaptivity technique is assessed by simulating thermocline oscillations of Lake Tanganyika. The results are compared to measured vertical profiles of temperature, showing similar stratification and outcropping events.

A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-cartesian grids

NASA Astrophysics Data System (ADS)

Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.

2018-01-01

We present a mass-conservative full approximation storage (FAS) multigrid solver for cell-centered finite difference methods on block-structured, locally cartesian grids. The algorithm is essentially a standard adaptive FAS (AFAS) scheme, but with a simple modification that comes in the form of a mass-conservative correction to the coarse-level force. This correction is facilitated by the creation of a zombie variable, analogous to a ghost variable, but defined on the coarse grid and lying under the fine grid refinement patch. We show that a number of different types of fine-level ghost cell interpolation strategies could be used in our framework, including low-order linear interpolation. In our approach, the smoother, prolongation, and restriction operations need never be aware of the mass conservation conditions at the coarse-fine interface. To maintain global mass conservation, we need only modify the usual FAS algorithm by correcting the coarse-level force function at points adjacent to the coarse-fine interface. We demonstrate through simulations that the solver converges geometrically, at a rate that is h-independent, and we show the generality of the solver, applying it to several nonlinear, time-dependent, and multi-dimensional problems. In several tests, we show that second-order asymptotic (h → 0) convergence is observed for the discretizations, provided that (1) at least linear interpolation of the ghost variables is employed, and (2) the mass conservation corrections are applied to the coarse-level force term.

Recovery of macroinvertebrates by screening in the field: a comparison between coarse (1.18 mm) and fine (0.60 mm) mesh sieves

USGS Publications Warehouse

Dukerschein, J.T.; Gent, R.; Sauer, J.

1996-01-01

We evaluated the potential loss of target benthic macroinvertebrates from coarse-mesh field wash down of samples through a 1.18-mm mesh sieve nested on a 0.60-mm mesh sieve. Visible target organisms (midges, mayflies, and fingernail clams) in the 1.18-mm mesh sieve were removed from the sample and enumerated in the field. The entire contents of both sieves were preserved for subsequent laboratory enumeration under 4X magnification. Percent recoveries from each treatment were based on total intact organisms found in all sieves. Percent recovery for fingernail clams found in the field (31%) was lower than for mayflies (79%) and midges (88%). Laboratory enumeration of organisms retained by the 1.18-mm sieve yielded additional fingernail clams (to total 74% recovered in the field and lab), mayflies (to total 89%), and midges (to total 91%). If the 1.18-mm sieve is used alone in the field, it is adequate to monitor mayflies, midges >1 cm, and adult fingernail clams greater than or equal to 5.0 mm shell length.

Influence of mesh density, cortical thickness and material properties on human rib fracture prediction.

PubMed

Li, Zuoping; Kindig, Matthew W; Subit, Damien; Kent, Richard W

2010-11-01

The purpose of this paper was to investigate the sensitivity of the structural responses and bone fractures of the ribs to mesh density, cortical thickness, and material properties so as to provide guidelines for the development of finite element (FE) thorax models used in impact biomechanics. Subject-specific FE models of the second, fourth, sixth and tenth ribs were developed to reproduce dynamic failure experiments. Sensitivity studies were then conducted to quantify the effects of variations in mesh density, cortical thickness, and material parameters on the model-predicted reaction force-displacement relationship, cortical strains, and bone fracture locations for all four ribs. Overall, it was demonstrated that rib FE models consisting of 2000-3000 trabecular hexahedral elements (weighted element length 2-3mm) and associated quadrilateral cortical shell elements with variable thickness more closely predicted the rib structural responses and bone fracture force-failure displacement relationships observed in the experiments (except the fracture locations), compared to models with constant cortical thickness. Further increases in mesh density increased computational cost but did not markedly improve model predictions. A ±30% change in the major material parameters of cortical bone lead to a -16.7 to 33.3% change in fracture displacement and -22.5 to +19.1% change in the fracture force. The results in this study suggest that human rib structural responses can be modeled in an accurate and computationally efficient way using (a) a coarse mesh of 2000-3000 solid elements, (b) cortical shells elements with variable thickness distribution and (c) a rate-dependent elastic-plastic material model. Copyright © 2010 IPEM. Published by Elsevier Ltd. All rights reserved.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

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

Ortega, Mario Ivan; Drumm, Clifton R.

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

A structure-exploiting numbering algorithm for finite elements on extruded meshes, and its performance evaluation in Firedrake

NASA Astrophysics Data System (ADS)

Bercea, Gheorghe-Teodor; McRae, Andrew T. T.; Ham, David A.; Mitchell, Lawrence; Rathgeber, Florian; Nardi, Luigi; Luporini, Fabio; Kelly, Paul H. J.

2016-10-01

We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10-20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.

An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations

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

Key, S.W.; Heinstein, M.W.; Stone, C.M.

1997-12-31

Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element 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 finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element 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 finite element (a four-node tetrahedral finite elementmore » enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.« less

Application of closed-form solutions to a mesh point field in silicon solar cells

NASA Technical Reports Server (NTRS)

Lamorte, M. F.

1985-01-01

A computer simulation method is discussed that provides for equivalent simulation accuracy, but that exhibits significantly lower CPU running time per bias point compared to other techniques. This new method is applied to a mesh point field as is customary in numerical integration (NI) techniques. The assumption of a linear approximation for the dependent variable, which is typically used in the finite difference and finite element NI methods, is not required. Instead, the set of device transport equations is applied to, and the closed-form solutions obtained for, each mesh point. The mesh point field is generated so that the coefficients in the set of transport equations exhibit small changes between adjacent mesh points. Application of this method to high-efficiency silicon solar cells is described; and the method by which Auger recombination, ambipolar considerations, built-in and induced electric fields, bandgap narrowing, carrier confinement, and carrier diffusivities are treated. Bandgap narrowing has been investigated using Fermi-Dirac statistics, and these results show that bandgap narrowing is more pronounced and that it is temperature-dependent in contrast to the results based on Boltzmann statistics.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element 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 element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Effect of boundary representation on viscous, separated flows in a discontinuous-Galerkin Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Nelson, Daniel A.; Jacobs, Gustaaf B.; Kopriva, David A.

2016-08-01

The effect of curved-boundary representation on the physics of the separated flow over a NACA 65(1)-412 airfoil is thoroughly investigated. A method is presented to approximate curved boundaries with a high-order discontinuous-Galerkin spectral element method for the solution of the Navier-Stokes equations. Multiblock quadrilateral element meshes are constructed with the grid generation software GridPro. The boundary of a NACA 65(1)-412 airfoil, defined by a cubic natural spline, is piecewise-approximated by isoparametric polynomial interpolants that represent the edges of boundary-fitted elements. Direct numerical simulation of the airfoil is performed on a coarse mesh and fine mesh with polynomial orders ranging from four to twelve. The accuracy of the curve fitting is investigated by comparing the flows computed on curved-sided meshes with those given by straight-sided meshes. Straight-sided meshes yield irregular wakes, whereas curved-sided meshes produce a regular Karman street wake. Straight-sided meshes also produce lower lift and higher viscous drag as compared with curved-sided meshes. When the mesh is refined by reducing the sizes of the elements, the lift decrease and viscous drag increase are less pronounced. The differences in the aerodynamic performance between the straight-sided meshes and the curved-sided meshes are concluded to be the result of artificial surface roughness introduced by the piecewise-linear boundary approximation provided by the straight-sided meshes.

A methodology for quadrilateral finite element mesh coarsening

DOE PAGES

Staten, Matthew L.; Benzley, Steven; Scott, Michael

2008-03-27

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedralmore » meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. Finally, this method appears to be extensible to hexahedral meshes in three dimensions.« less

A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation [A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation: 3D Meshes of Microstructurally Small Crack Growth

DOE PAGES

Spear, Ashley D.; Hochhalter, Jacob D.; Cerrone, Albert R.; ...

2016-04-27

In an effort to reproduce computationally the observed evolution of microstructurally small fatigue cracks (MSFCs), a method is presented for generating conformal, finite-element (FE), volume meshes from 3D measurements of MSFC propagation. The resulting volume meshes contain traction-free surfaces that conform to incrementally measured 3D crack shapes. Grain morphologies measured using near-field high-energy X-ray diffraction microscopy are also represented within the FE volume meshes. Proof-of-concept simulations are performed to demonstrate the utility of the mesh-generation method. The proof-of-concept simulations employ a crystal-plasticity constitutive model and are performed using the conformal FE meshes corresponding to successive crack-growth increments. Although the simulationsmore » for each crack increment are currently independent of one another, they need not be, and transfer of material-state information among successive crack-increment meshes is discussed. The mesh-generation method was developed using post-mortem measurements, yet it is general enough that it can be applied to in-situ measurements of 3D MSFC propagation.« less

A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation [A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation: 3D Meshes of Microstructurally Small Crack Growth

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

Spear, Ashley D.; Hochhalter, Jacob D.; Cerrone, Albert R.

In an effort to reproduce computationally the observed evolution of microstructurally small fatigue cracks (MSFCs), a method is presented for generating conformal, finite-element (FE), volume meshes from 3D measurements of MSFC propagation. The resulting volume meshes contain traction-free surfaces that conform to incrementally measured 3D crack shapes. Grain morphologies measured using near-field high-energy X-ray diffraction microscopy are also represented within the FE volume meshes. Proof-of-concept simulations are performed to demonstrate the utility of the mesh-generation method. The proof-of-concept simulations employ a crystal-plasticity constitutive model and are performed using the conformal FE meshes corresponding to successive crack-growth increments. Although the simulationsmore » for each crack increment are currently independent of one another, they need not be, and transfer of material-state information among successive crack-increment meshes is discussed. The mesh-generation method was developed using post-mortem measurements, yet it is general enough that it can be applied to in-situ measurements of 3D MSFC propagation.« less

Construction of hexahedral finite element mesh capturing realistic geometries of a petroleum reserve

DOE PAGES

Park, Byoung Yoon; Roberts, Barry L.; Sobolik, Steven R.

2017-07-27

The three-dimensional finite element mesh capturing realistic geometries of the Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh consists of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time while maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill,more » Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for various civil and geological structures.« less

Construction of hexahedral finite element mesh capturing realistic geometries of a petroleum reserve

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

Park, Byoung Yoon; Roberts, Barry L.; Sobolik, Steven R.

The three-dimensional finite element mesh capturing realistic geometries of the Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh consists of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time while maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill,more » Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for various civil and geological structures.« less

Array-based Hierarchical Mesh Generation in Parallel

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2015-11-03

In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less

Towards Improved Finite Element Modelling of the Interaction of Elastic Waves with Complex Defect Geometries

NASA Astrophysics Data System (ADS)

Rajagopal, P.; Drozdz, M.; Lowe, M. J. S.

2009-03-01

A solution to the problem of improving the finite element (FE) modeling of elastic wave-defect interaction is sought by reconsidering the conventional opinion on meshing strategy. The standard approach using uniform square elements imposes severe limitations in representing complex defect outlines but this is thought to improve when the mesh is made finer. Free meshing algorithms available widely in commercial packages of late can cope with difficult features well but they are thought to cause scattering by the irregular mesh itself. This paper examines whether the benefits offered by free meshing in representing defects better outweigh the inaccuracies due to mesh scattering. If using the standard mesh, the questions whether mesh refinement leads to improved results and whether a practical strategy can be constructed are considered.

Numerical benchmarking of a Coarse-Mesh Transport (COMET) Method for medical physics applications

NASA Astrophysics Data System (ADS)

Blackburn, Megan Satterfield

2009-12-01

Radiation therapy has become a very import method for treating cancer patients. Thus, it is extremely important to accurately determine the location of energy deposition during these treatments, maximizing dose to the tumor region and minimizing it to healthy tissue. A Coarse-Mesh Transport Method (COMET) has been developed at the Georgia Institute of Technology in the Computational Reactor and Medical Physics Group for use very successfully with neutron transport to analyze whole-core criticality. COMET works by decomposing a large, heterogeneous system into a set of smaller fixed source problems. For each unique local problem that exists, a solution is obtained that we call a response function. These response functions are pre-computed and stored in a library for future use. The overall solution to the global problem can then be found by a linear superposition of these local problems. This method has now been extended to the transport of photons and electrons for use in medical physics problems to determine energy deposition from radiation therapy treatments. The main goal of this work was to develop benchmarks for testing in order to evaluate the COMET code to determine its strengths and weaknesses for these medical physics applications. For response function calculations, legendre polynomial expansions are necessary for space, angle, polar angle, and azimuthal angle. An initial sensitivity study was done to determine the best orders for future testing. After the expansion orders were found, three simple benchmarks were tested: a water phantom, a simplified lung phantom, and a non-clinical slab phantom. Each of these benchmarks was decomposed into 1cm x 1cm and 0.5cm x 0.5cm coarse meshes. Three more clinically relevant problems were developed from patient CT scans. These benchmarks modeled a lung patient, a prostate patient, and a beam re-entry situation. As before, the problems were divided into 1cm x 1cm, 0.5cm x 0.5cm, and 0.25cm x 0.25cm coarse mesh cases. Multiple beam energies were also tested for each case. The COMET solutions for each case were compared to a reference solution obtained by pure Monte Carlo results from EGSnrc. When comparing the COMET results to the reference cases, a pattern of differences appeared in each phantom case. It was found that better results were obtained for lower energy incident photon beams as well as for larger mesh sizes. Possible changes may need to be made with the expansion orders used for energy and angle to better model high energy secondary electrons. Heterogeneity also did not pose a problem for the COMET methodology. Heterogeneous results were found in a comparable amount of time to the homogeneous water phantom. The COMET results were typically found in minutes to hours of computational time, whereas the reference cases typically required hundreds or thousands of hours. A second sensitivity study was also performed on a more stringent problem and with smaller coarse meshes. Previously, the same expansion order was used for each incident photon beam energy so better comparisons could be made. From this second study, it was found that it is optimal to have different expansion orders based on the incident beam energy. Recommendations for future work with this method include more testing on higher expansion orders or possible code modification to better handle secondary electrons. The method also needs to handle more clinically relevant beam descriptions with an energy and angular distribution associated with it.

Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)

2002-01-01

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Triangle geometry processing for surface modeling and cartesian grid generation

DOEpatents

Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY

2002-09-03

Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.

Quasi-automatic 3D finite element model generation for individual single-rooted teeth and periodontal ligament.

PubMed

Clement, R; Schneider, J; Brambs, H-J; Wunderlich, A; Geiger, M; Sander, F G

2004-02-01

The paper demonstrates how to generate an individual 3D volume model of a human single-rooted tooth using an automatic workflow. It can be implemented into finite element simulation. In several computational steps, computed tomography data of patients are used to obtain the global coordinates of the tooth's surface. First, the large number of geometric data is processed with several self-developed algorithms for a significant reduction. The most important task is to keep geometrical information of the real tooth. The second main part includes the creation of the volume model for tooth and periodontal ligament (PDL). This is realized with a continuous free form surface of the tooth based on the remaining points. Generating such irregular objects for numerical use in biomechanical research normally requires enormous manual effort and time. The finite element mesh of the tooth, consisting of hexahedral elements, is composed of different materials: dentin, PDL and surrounding alveolar bone. It is capable of simulating tooth movement in a finite element analysis and may give valuable information for a clinical approach without the restrictions of tetrahedral elements. The mesh generator of FE software ANSYS executed the mesh process for hexahedral elements successfully.

ANSYS duplicate finite-element checker routine

NASA Technical Reports Server (NTRS)

Ortega, R.

1995-01-01

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

A full potential flow analysis with realistic wake influence for helicopter rotor airload prediction

NASA Technical Reports Server (NTRS)

Egolf, T. Alan; Sparks, S. Patrick

1987-01-01

A 3-D, quasi-steady, full potential flow solver was adapted to include realistic wake influence for the aerodynamic analysis of helicopter rotors. The method is based on a finite difference solution of the full potential equation, using an inner and outer domain procedure for the blade flowfield to accommodate wake effects. The nonlinear flow is computed in the inner domain region using a finite difference solution method. The wake is modeled by a vortex lattice using prescribed geometry techniques to allow for the inclusion of realistic rotor wakes. The key feature of the analysis is that vortices contained within the finite difference mesh (inner domain) were treated with a vortex embedding technique while the influence of the remaining portion of the wake (in the outer domain) is impressed as a boundary condition on the outer surface of the finite difference mesh. The solution procedure couples the wake influence with the inner domain solution in a consistent and efficient solution process. The method has been applied to both hover and forward flight conditions. Correlation with subsonic and transonic hover airload data is shown which demonstrates the merits of the approach.

Influence of vegetation and gravel mesh on the tertiary treatment of wastewater from a cosmetics industry.

PubMed

Vlyssides, Apostolos G; Mai, Sofia T H; Barampouti, Elli Maria P; Loukakis, Haralampos N

2009-07-01

To estimate the influence of gravel mesh (fine and coarse) and vegetation (Phragmites and Arundo) on the efficiency of a reed bed, a pilot plant was included after the wastewater treatment plant of a cosmetic industry treatment system according to a 22 factorial experimental design. The maximum biochemical oxygen demand (BOD5), chemical oxygen demand (COD) and total phosphorous (TP) reduction was observed in the reactor, where Phragmites and fine gravel were used. In the reactor with Phragmites and coarse gravel, the maximum total Kjeldahl nitrogen (TKN) and total suspended solids (TSS) reduction was observed. The maximum total solids reduction was measured in the reed bed, which was filled with Arundo and coarse gravel. Conclusively, the treatment of a cosmetic industry's wastewater by reed beds as a tertiary treatment method is quite effective.

An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

NASA Astrophysics Data System (ADS)

Zhou, Feng; Chen, Guoxian; Huang, Yuefei; Yang, Jerry Zhijian; Feng, Hui

2013-04-01

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shock-capturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

PubMed

Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

2018-06-01

Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

Spectral/ hp element methods: Recent developments, applications, and perspectives

NASA Astrophysics Data System (ADS)

Xu, Hui; Cantwell, Chris D.; Monteserin, Carlos; Eskilsson, Claes; Engsig-Karup, Allan P.; Sherwin, Spencer J.

2018-02-01

The spectral/ hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation is based upon orthogonal polynomials, such as Legendre or Chebychev polynomials, modified to accommodate a C 0 - continuous expansion. Computationally and theoretically, by increasing the polynomial order p, high-precision solutions and fast convergence can be obtained and, in particular, under certain regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/ hp element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/ hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/ hp element method in more complex science and engineering applications are discussed.

Implementation of a Smeared Crack Band Model in a Micromechanics Framework

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Bednarcyk, Brett A.; Waas, Anthony M.; Arnold, Steven M.

2012-01-01

The smeared crack band theory is implemented within the generalized method of cells and high-fidelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data (where available), and an equivalent finite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single fiber is modeled with generalized method of cells and high-fidelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple fiber repeating unit cell. The generalized method of cells and high-fidelity generalized method of cells models are validated against a very refined finite element model.

Progressive Failure of a Unidirectional Fiber-Reinforced Composite Using the Method of Cells: Discretization Objective Computational Results

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Bednarcyk, Brett A.; Waas, Anthony M.; Arnold, Steven M.

2012-01-01

The smeared crack band theory is implemented within the generalized method of cells and high-fidelity generalized method of cells micromechanics models to capture progressive failure within the constituents of a composite material while retaining objectivity with respect to the size of the discretization elements used in the model. An repeating unit cell containing 13 randomly arranged fibers is modeled and subjected to a combination of transverse tension/compression and transverse shear loading. The implementation is verified against experimental data (where available), and an equivalent finite element model utilizing the same implementation of the crack band theory. To evaluate the performance of the crack band theory within a repeating unit cell that is more amenable to a multiscale implementation, a single fiber is modeled with generalized method of cells and high-fidelity generalized method of cells using a relatively coarse subcell mesh which is subjected to the same loading scenarios as the multiple fiber repeating unit cell. The generalized method of cells and high-fidelity generalized method of cells models are validated against a very refined finite element model.

Mesh Convergence Requirements for Composite Damage Models

NASA Technical Reports Server (NTRS)

Davila, Carlos G.

2016-01-01

The ability of the finite element method to accurately represent the response of objects with intricate geometry and loading renders the finite element method as an extremely versatile analysis technique for structural analysis. Finite element analysis is routinely used in industry to calculate deflections, stress concentrations, natural frequencies, buckling loads, and much more. The method works by discretizing complex problems into smaller, simpler approximations that are valid over small uniform domains. For common analyses, the maximum size of the elements that can be used is often be determined by experience. However, to verify the quality of a solution, analyses with several levels of mesh refinement should be performed to ensure that the solution has converged. In recent years, the finite element method has been used to calculate the resistance of structures, and in particular that of composite structures. A number of techniques such as cohesive zone modeling, the virtual crack closure technique, and continuum damage modeling have emerged that can be used to predict cracking, delaminations, fiber failure, and other composite damage modes that lead to structural collapse. However, damage models present mesh refinement requirements that are not well understood. In this presentation, we examine different mesh refinement issues related to the representation of damage in composite materials. Damage process zone sizes and their corresponding mesh requirements will be discussed. The difficulties of modeling discontinuities and the associated need for regularization techniques will be illustrated, and some unexpected element size constraints will be presented. Finally, some of the difficulties in constructing models of composite structures capable of predicting transverse matrix cracking will be discussed. It will be shown that to predict the initiation and propagation of transverse matrix cracks, their density, and their saturation may require models that are significantly more refined than those that have been contemplated in the past.

Multitasking for flows about multiple body configurations using the chimera grid scheme

NASA Technical Reports Server (NTRS)

Dougherty, F. C.; Morgan, R. L.

1987-01-01

The multitasking of a finite-difference scheme using multiple overset meshes is described. In this chimera, or multiple overset mesh approach, a multiple body configuration is mapped using a major grid about the main component of the configuration, with minor overset meshes used to map each additional component. This type of code is well suited to multitasking. Both steady and unsteady two dimensional computations are run on parallel processors on a CRAY-X/MP 48, usually with one mesh per processor. Flow field results are compared with single processor results to demonstrate the feasibility of running multiple mesh codes on parallel processors and to show the increase in efficiency.

Toward automatic finite element analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Perucchio, Renato; Voelcker, Herbert

1987-01-01

Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element 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.

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements 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 elements 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 finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements 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.

GRAPE- TWO-DIMENSIONAL GRIDS ABOUT AIRFOILS AND OTHER SHAPES BY THE USE OF POISSON'S EQUATION

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1994-01-01

The ability to treat arbitrary boundary shapes is one of the most desirable characteristics of a method for generating grids, including those about airfoils. In a grid used for computing aerodynamic flow over an airfoil, or any other body shape, the surface of the body is usually treated as an inner boundary and often cannot be easily represented as an analytic function. The GRAPE computer program was developed to incorporate a method for generating two-dimensional finite-difference grids about airfoils and other shapes by the use of the Poisson differential equation. GRAPE can be used with any boundary shape, even one specified by tabulated points and including a limited number of sharp corners. The GRAPE program has been developed to be numerically stable and computationally fast. GRAPE can provide the aerodynamic analyst with an efficient and consistent means of grid generation. The GRAPE procedure generates a grid between an inner and an outer boundary by utilizing an iterative procedure to solve the Poisson differential equation subject to geometrical restraints. In this method, the inhomogeneous terms of the equation are automatically chosen such that two important effects are imposed on the grid. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. Along with the iterative solution to Poisson's equation, a technique of coarse-fine sequencing is employed to accelerate numerical convergence. GRAPE program control cards and input data are entered via the NAMELIST feature. Each variable has a default value such that user supplied data is kept to a minimum. Basic input data consists of the boundary specification, mesh point spacings on the boundaries, and mesh line angles at the boundaries. Output consists of a dataset containing the grid data and, if requested, a plot of the generated mesh. The GRAPE program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 135K (octal) of 60 bit words. For plotted output the commercially available DISSPLA graphics software package is required. The GRAPE program was developed in 1980.

Evaluation of Acoustic Propagation Paths into the Human Head

DTIC Science & Technology

2005-07-25

paths. A 3D finite-element solid mesh was constructed using a digital image database of an adult male head. Finite-element analysis was used to model the...air-borne sound pressure amplitude) via the alternate propagation paths. A 3D finite-element solid mesh was constructed using a digital image database ... database of an adult male head Coupled acoustic-mechanical finite-element analysis (FEA) was used to model the wave propagation through the fluid-solid

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element 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 finite elements. 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 finite elements that is based on a much sparser system than the original high-order finite element 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.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Manual for automatic generation of finite element models of spiral bevel gears in mesh

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Reddy, S.; Kumar, A.

1994-01-01

The goal of this research is to develop computer programs that generate finite element models suitable for doing 3D contact analysis of faced milled spiral bevel gears in mesh. A pinion tooth and a gear tooth are created and put in mesh. There are two programs: Points.f and Pat.f to perform the analysis. Points.f is based on the equation of meshing for spiral bevel gears. It uses machine tool settings to solve for an N x M mesh of points on the four surfaces, pinion concave and convex, and gear concave and convex. Points.f creates the file POINTS.OUT, an ASCI file containing N x M points for each surface. (N is the number of node points along the length of the tooth, and M is nodes along the height.) Pat.f reads POINTS.OUT and creates the file tl.out. Tl.out is a series of PATRAN input commands. In addition to the mesh density on the tooth face, additional user specified variables are the number of finite elements through the thickness, and the number of finite elements along the tooth full fillet. A full fillet is assumed to exist for both the pinion and gear.

Meshed doped silicon photonic crystals for manipulating near-field thermal radiation

NASA Astrophysics Data System (ADS)

Elzouka, Mahmoud; Ndao, Sidy

2018-01-01

The ability to control and manipulate heat flow is of great interest to thermal management and thermal logic and memory devices. Particularly, near-field thermal radiation presents a unique opportunity to enhance heat transfer while being able to tailor its characteristics (e.g., spectral selectivity). However, achieving nanometric gaps, necessary for near-field, has been and remains a formidable challenge. Here, we demonstrate significant enhancement of the near-field heat transfer through meshed photonic crystals with separation gaps above 0.5 μm. Using a first-principle method, we investigate the meshed photonic structures numerically via finite-difference time-domain technique (FDTD) along with the Langevin approach. Results for doped-silicon meshed structures show significant enhancement in heat transfer; 26 times over the non-meshed corrugated structures. This is especially important for thermal management and thermal rectification applications. The results also support the premise that thermal radiation at micro scale is a bulk (rather than a surface) phenomenon; the increase in heat transfer between two meshed-corrugated surfaces compared to the flat surface (8.2) wasn't proportional to the increase in the surface area due to the corrugations (9). Results were further validated through good agreements between the resonant modes predicted from the dispersion relation (calculated using a finite-element method), and transmission factors (calculated from FDTD).

Mechanical behaviour of synthetic surgical meshes: finite element simulation of the herniated abdominal wall.

PubMed

Hernández-Gascón, B; Peña, E; Melero, H; Pascual, G; Doblaré, M; Ginebra, M P; Bellón, J M; Calvo, B

2011-11-01

The material properties of meshes used in hernia surgery contribute to the overall mechanical behaviour of the repaired abdominal wall. The mechanical response of a surgical mesh has to be defined since the haphazard orientation of an anisotropic mesh can lead to inconsistent surgical outcomes. This study was designed to characterize the mechanical behaviour of three surgical meshes (Surgipro®, Optilene® and Infinit®) and to describe a mechanical constitutive law that accurately reproduces the experimental results. Finally, through finite element simulation, the behaviour of the abdominal wall was modelled before and after surgical mesh implant. Uniaxial loading of mesh samples in two perpendicular directions revealed the isotropic response of Surgipro® and the anisotropic behaviour of Optilene® and Infinit®. A phenomenological constitutive law was used to reproduce the measured experimental curves. To analyze the mechanical effect of the meshes once implanted in the abdomen, finite element simulation of the healthy and partially herniated repaired rabbit abdominal wall served to reproduce wall behaviour before and after mesh implant. In all cases, maximal displacements were lower and maximal principal stresses higher in the implanted abdomen than the intact wall model. Despite the fact that no mesh showed a behaviour that perfectly matched that of abdominal muscle, the Infinit® mesh was able to best comply with the biomechanics of the abdominal wall. Copyright © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

DOE PAGES

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.; ...

2016-09-22

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Upscaling of Mixed Finite Element Discretization Problems by the Spectral AMGe Method

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

Kalchev, Delyan Z.; Lee, C. S.; Villa, U.

Here, we propose two multilevel spectral techniques for constructing coarse discretization spaces for saddle-point problems corresponding to PDEs involving a divergence constraint, with a focus on mixed finite element discretizations of scalar self-adjoint second order elliptic equations on general unstructured grids. We use element agglomeration algebraic multigrid (AMGe), which employs coarse elements that can have nonstandard shape since they are agglomerates of fine-grid elements. The coarse basis associated with each agglomerated coarse element is constructed by solving local eigenvalue problems and local mixed finite element problems. This construction leads to stable upscaled coarse spaces and guarantees the inf-sup compatibility ofmore » the upscaled discretization. Also, the approximation properties of these upscaled spaces improve by adding more local eigenfunctions to the coarse spaces. The higher accuracy comes at the cost of additional computational effort, as the sparsity of the resulting upscaled coarse discretization (referred to as operator complexity) deteriorates when we introduce additional functions in the coarse space. We also provide an efficient solver for the coarse (upscaled) saddle-point system by employing hybridization, which leads to a symmetric positive definite (s.p.d.) reduced system for the Lagrange multipliers, and to solve the latter s.p.d. system, we use our previously developed spectral AMGe solver. Numerical experiments, in both two and three dimensions, are provided to illustrate the efficiency of the proposed upscaling technique.« less

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

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 finite element 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 finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element 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 finite element 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.

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

A finite element method with overlapping meshes for free-boundary axisymmetric plasma equilibria in realistic geometries

NASA Astrophysics Data System (ADS)

Heumann, Holger; Rapetti, Francesca

2017-04-01

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.

Reducing numerical costs for core wide nuclear reactor CFD simulations by the Coarse-Grid-CFD

NASA Astrophysics Data System (ADS)

Viellieber, Mathias; Class, Andreas G.

2013-11-01

Traditionally complete nuclear reactor core simulations are performed with subchannel analysis codes, that rely on experimental and empirical input. The Coarse-Grid-CFD (CGCFD) intends to replace the experimental or empirical input with CFD data. The reactor core consists of repetitive flow patterns, allowing the general approach of creating a parametrized model for one segment and composing many of those to obtain the entire reactor simulation. The method is based on a detailed and well-resolved CFD simulation of one representative segment. From this simulation we extract so-called parametrized volumetric forces which close, an otherwise strongly under resolved, coarsely-meshed model of a complete reactor setup. While the formulation so far accounts for forces created internally in the fluid others e.g. obstruction and flow deviation through spacers and wire wraps, still need to be accounted for if the geometric details are not represented in the coarse mesh. These are modelled with an Anisotropic Porosity Formulation (APF). This work focuses on the application of the CGCFD to a complete reactor core setup and the accomplishment of the parametrization of the volumetric forces.

A Finite Difference Method for Modeling Migration of Impurities in Multilayer Systems

NASA Astrophysics Data System (ADS)

Tosa, V.; Kovacs, Katalin; Mercea, P.; Piringer, O.

2008-09-01

A finite difference method to solve the one-dimensional diffusion of impurities in a multilayer system was developed for the special case in which a partition coefficient K impose a ratio of the concentrations at the interface between two adiacent layers. The fictitious point method was applied to derive the algebraic equations for the mesh points at the interface, while for the non-uniform mesh points within the layers a combined method was used. The method was tested and then applied to calculate migration of impurities from multilayer systems into liquids or solids samples, in migration experiments performed for quality testing purposes. An application was developed in the field of impurities migrations from multilayer plastic packagings into food, a problem of increasing importance in food industry.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

DOE PAGES

Kauffman, Justin A.; Sheldon, Jason P.; Miller, Scott T.

2017-03-01

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusionmore » and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.« less

User Manual for the PROTEUS Mesh Tools

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

Smith, Micheal A.; Shemon, Emily R

2016-09-19

PROTEUS is built around a finite element representation of the geometry for visualization. In addition, the PROTEUS-SN solver was built to solve the even-parity transport equation on a finite element mesh provided as input. Similarly, PROTEUS-MOC and PROTEUS-NEMO were built to apply the method of characteristics on unstructured finite element meshes. Given the complexity of real world problems, experience has shown that using commercial mesh generator to create rather simple input geometries is overly complex and slow. As a consequence, significant effort has been put into place to create multiple codes that help assist in the mesh generation and manipulation.more » There are three input means to create a mesh in PROTEUS: UFMESH, GRID, and NEMESH. At present, the UFMESH is a simple way to generate two-dimensional Cartesian and hexagonal fuel assembly geometries. The UFmesh input allows for simple assembly mesh generation while the GRID input allows the generation of Cartesian, hexagonal, and regular triangular structured grid geometry options. The NEMESH is a way for the user to create their own mesh or convert another mesh file format into a PROTEUS input format. Given that one has an input mesh format acceptable for PROTEUS, we have constructed several tools which allow further mesh and geometry construction (i.e. mesh extrusion and merging). This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial or .merge) can be used as “mesh” input for any of the mesh tools discussed in this manual.« less

Adaptive Skin Meshes Coarsening for Biomolecular Simulation

PubMed Central

Shi, Xinwei; Koehl, Patrice

2011-01-01

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137

Seamless atmospheric modeling across the hydrostatic-nonhydrostatic scales - preliminary results using an unstructured-Voronoi mesh for weather prediction.

NASA Astrophysics Data System (ADS)

Skamarock, W. C.

2015-12-01

One of the major problems in atmospheric model applications is the representation of deep convection within the models; explicit simulation of deep convection on fine meshes performs much better than sub-grid parameterized deep convection on coarse meshes. Unfortunately, the high cost of explicit convective simulation has meant it has only been used to down-scale global simulations in weather prediction and regional climate applications, typically using traditional one-way interactive nesting technology. We have been performing real-time weather forecast tests using a global non-hydrostatic atmospheric model (the Model for Prediction Across Scales, MPAS) that employs a variable-resolution unstructured Voronoi horizontal mesh (nominally hexagons) to span hydrostatic to nonhydrostatic scales. The smoothly varying Voronoi mesh eliminates many downscaling problems encountered using traditional one- or two-way grid nesting. Our test weather forecasts cover two periods - the 2015 Spring Forecast Experiment conducted at the NOAA Storm Prediction Center during the month of May in which we used a 50-3 km mesh, and the PECAN field program examining nocturnal convection over the US during the months of June and July in which we used a 15-3 km mesh. An important aspect of this modeling system is that the model physics be scale-aware, particularly the deep convection parameterization. These MPAS simulations employ the Grell-Freitas scale-aware convection scheme. Our test forecasts show that the scheme produces a gradual transition in the deep convection, from the deep unstable convection being handled entirely by the convection scheme on the coarse mesh regions (dx > 15 km), to the deep convection being almost entirely explicit on the 3 km NA region of the meshes. We will present results illustrating the performance of critical aspects of the MPAS model in these tests.

The finite cell method for polygonal meshes: poly-FCM

NASA Astrophysics Data System (ADS)

Duczek, Sascha; Gabbert, Ulrich

2016-10-01

In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.

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

Yang, Qingcheng, E-mail: qiy9@pitt.edu; To, Albert C., E-mail: albertto@pitt.edu

Surface effects have been observed to contribute significantly to the mechanical response of nanoscale structures. The newly proposed energy-based coarse-grained atomistic method Multiresolution Molecular Mechanics (MMM) (Yang, To (2015), ) is applied to capture surface effect for nanosized structures by designing a surface summation rule SR{sup S} within the framework of MMM. Combined with previously proposed bulk summation rule SR{sup B}, the MMM summation rule SR{sup MMM} is completed. SR{sup S} and SR{sup B} are consistently formed within SR{sup MMM} for general finite element shape functions. Analogous to quadrature rules in finite element method (FEM), the key idea to themore » good performance of SR{sup MMM} lies in that the order or distribution of energy for coarse-grained atomistic model is mathematically derived such that the number, position and weight of quadrature-type (sampling) atoms can be determined. Mathematically, the derived energy distribution of surface area is different from that of bulk region. Physically, the difference is due to the fact that surface atoms lack neighboring bonding. As such, SR{sup S} and SR{sup B} are employed for surface and bulk domains, respectively. Two- and three-dimensional numerical examples using the respective 4-node bilinear quadrilateral, 8-node quadratic quadrilateral and 8-node hexahedral meshes are employed to verify and validate the proposed approach. It is shown that MMM with SR{sup MMM} accurately captures corner, edge and surface effects with less 0.3% degrees of freedom of the original atomistic system, compared against full atomistic simulation. The effectiveness of SR{sup MMM} with respect to high order element is also demonstrated by employing the 8-node quadratic quadrilateral to solve a beam bending problem considering surface effect. In addition, the introduced sampling error with SR{sup MMM} that is analogous to numerical integration error with quadrature rule in FEM is very small. - Highlights: • Surface effect captured by Multiresolution Molecular Mechanics (MMM) is presented. • A novel surface summation rule within the framework of MMM is proposed. • Surface, corner and edges effects are accuterly captured in two and three dimension. • MMM with less 0.3% degrees of freedom of atomistics reproduces atomistic results.« less

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.

1989-01-01

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

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

Strauss, H.R.

This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.

Adaptive mesh refinement for time-domain electromagnetics using vector finite elements :a feasibility study.

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

Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis

This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.

Quadrilateral/hexahedral finite element mesh coarsening

DOEpatents

Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E

2012-10-16

A technique for coarsening a finite element 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 elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.

Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D

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

Pavel Kus; Pavel Solin; David Andrs

2014-11-01

In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.

Efficient Use of Distributed Systems for Scientific Applications

NASA Technical Reports Server (NTRS)

Taylor, Valerie; Chen, Jian; Canfield, Thomas; Richard, Jacques

2000-01-01

Distributed computing has been regarded as the future of high performance computing. Nationwide high speed networks such as vBNS are becoming widely available to interconnect high-speed computers, virtual environments, scientific instruments and large data sets. One of the major issues to be addressed with distributed systems is the development of computational tools that facilitate the efficient execution of parallel applications on such systems. These tools must exploit the heterogeneous resources (networks and compute nodes) in distributed systems. This paper presents a tool, called PART, which addresses this issue for mesh partitioning. PART takes advantage of the following heterogeneous system features: (1) processor speed; (2) number of processors; (3) local network performance; and (4) wide area network performance. Further, different finite element applications under consideration may have different computational complexities, different communication patterns, and different element types, which also must be taken into consideration when partitioning. PART uses parallel simulated annealing to partition the domain, taking into consideration network and processor heterogeneity. The results of using PART for an explicit finite element application executing on two IBM SPs (located at Argonne National Laboratory and the San Diego Supercomputer Center) indicate an increase in efficiency by up to 36% as compared to METIS, a widely used mesh partitioning tool. The input to METIS was modified to take into consideration heterogeneous processor performance; METIS does not take into consideration heterogeneous networks. The execution times for these applications were reduced by up to 30% as compared to METIS. These results are given in Figure 1 for four irregular meshes with number of elements ranging from 30,269 elements for the Barth5 mesh to 11,451 elements for the Barth4 mesh. Future work with PART entails using the tool with an integrated application requiring distributed systems. In particular this application, illustrated in the document entails an integration of finite element and fluid dynamic simulations to address the cooling of turbine blades of a gas turbine engine design. It is not uncommon to encounter high-temperature, film-cooled turbine airfoils with 1,000,000s of degrees of freedom. This results because of the complexity of the various components of the airfoils, requiring fine-grain meshing for accuracy. Additional information is contained in the original.

The Effect of Scale Dependent Discretization on the Progressive Failure of Composite Materials Using Multiscale Analyses

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

A multiscale modeling methodology, which incorporates a statistical distribution of fiber strengths into coupled micromechanics/ finite element analyses, is applied to unidirectional polymer matrix composites (PMCs) to analyze the effect of mesh discretization both at the micro- and macroscales on the predicted ultimate tensile (UTS) strength and failure behavior. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a PMC tensile specimen that initiates at the repeating unit cell (RUC) level. Three different finite element mesh densities were employed and each coupled with an appropriate RUC. Multiple simulations were performed in order to assess the effect of a statistical distribution of fiber strengths on the bulk composite failure and predicted strength. The coupled effects of both the micro- and macroscale discretizations were found to have a noticeable effect on the predicted UTS and computational efficiency of the simulations.

Developments in the Gung Ho dynamical core

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2017-04-01

Gung Ho is the new dynamical core being developed for the next generation Met Office weather and climate model, suitable for meeting the exascale challenge on emerging computer architectures. It builds upon the earlier collaborative project between the Met Office, NERC and STFC Daresbury of the same name to investigate suitable numerical methods for dynamical cores. A mixed-finite element approach is used, where different finite element spaces are used to represent various fields. This method provides a number of beneficial improvements over the current model, such a compatibility and inherent conservation on quasi-uniform unstructured meshes, whilst maintaining the accuracy and good dispersion properties of the staggered grid currently used. Furthermore, the mixed finite element approach allows a large degree of flexibility in the type of mesh, order of approximation and discretisation, providing a simple way to test alternative options to obtain the best model possible.

Modifications made to ModelMuse to add support for the Saturated-Unsaturated Transport model (SUTRA)

USGS Publications Warehouse

Winston, Richard B.

2014-01-01

This report (1) describes modifications to ModelMuse,as described in U.S. Geological Survey (USGS) Techniques and Methods (TM) 6–A29 (Winston, 2009), to add support for the Saturated-Unsaturated Transport model (SUTRA) (Voss and Provost, 2002; version of September 22, 2010) and (2) supplements USGS TM 6–A29. Modifications include changes to the main ModelMuse window where the model is designed, addition of methods for generating a finite-element mesh suitable for SUTRA, defining how some functions shouldapply when using a finite-element mesh rather than a finite-difference grid (as originally programmed in ModelMuse), and applying spatial interpolation to angles. In addition, the report describes ways of handling objects on the front view of the model and displaying data. A tabulation contains a summary of the new or modified dialog boxes.

Biomechanics Simulations Using Cubic Hermite Meshes with Extraordinary Nodes for Isogeometric Cardiac Modeling

PubMed Central

Gonzales, Matthew J.; Sturgeon, Gregory; Segars, W. Paul; McCulloch, Andrew D.

2016-01-01

Cubic Hermite hexahedral finite element meshes have some well-known advantages over linear tetrahedral finite element meshes in biomechanical and anatomic modeling using isogeometric analysis. These include faster convergence rates as well as the ability to easily model rule-based anatomic features such as cardiac fiber directions. However, it is not possible to create closed complex objects with only regular nodes; these objects require the presence of extraordinary nodes (nodes with 3 or >= 5 adjacent elements in 2D) in the mesh. The presence of extraordinary nodes requires new constraints on the derivatives of adjacent elements to maintain continuity. We have developed a new method that uses an ensemble coordinate frame at the nodes and a local-to-global mapping to maintain continuity. In this paper, we make use of this mapping to create cubic Hermite models of the human ventricles and a four-chamber heart. We also extend the methods to the finite element equations to perform biomechanics simulations using these meshes. The new methods are validated using simple test models and applied to anatomically accurate ventricular meshes with valve annuli to simulate complete cardiac cycle simulations. PMID:27182096

Mass-corrections for the conservative coupling of flow and transport on collocated meshes

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

Waluga, Christian, E-mail: waluga@ma.tum.de; Wohlmuth, Barbara; Rüde, Ulrich

2016-01-15

Buoyancy-driven flow models demand a careful treatment of the mass-balance equation to avoid spurious source and sink terms in the non-linear coupling between flow and transport. In the context of finite-elements, it is therefore commonly proposed to employ sufficiently rich pressure spaces, containing piecewise constant shape functions to obtain local or even strong mass-conservation. In three-dimensional computations, this usually requires nonconforming approaches, special meshes or higher order velocities, which make these schemes prohibitively expensive for some applications and complicate the implementation into legacy code. In this paper, we therefore propose a lean and conservatively coupled scheme based on standard stabilizedmore » linear equal-order finite elements for the Stokes part and vertex-centered finite volumes for the energy equation. We show that in a weak mass-balance it is possible to recover exact conservation properties by a local flux-correction which can be computed efficiently on the control volume boundaries of the transport mesh. We discuss implementation aspects and demonstrate the effectiveness of the flux-correction by different two- and three-dimensional examples which are motivated by geophysical applications.« less

A new multigrid formulation for high order finite difference methods on summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Weinerfelt, Per; Nordström, Jan

2018-04-01

Multigrid schemes for high order finite difference methods on summation-by-parts form are studied by comparing the effect of different interpolation operators. By using the standard linear prolongation and restriction operators, the Galerkin condition leads to inaccurate coarse grid discretizations. In this paper, an alternative class of interpolation operators that bypass this issue and preserve the summation-by-parts property on each grid level is considered. Clear improvements of the convergence rate for relevant model problems are achieved.

Treatment of late time instabilities in finite-difference EMP scattering codes

NASA Astrophysics Data System (ADS)

Simpson, L. T.; Holland, R.; Arman, S.

1982-12-01

Constraints applicable to a finite difference mesh for solution of Maxwell's equations are defined. The equations are applied in the time domain for computing electromagnetic coupling to complex structures, e.g., rectangular, cylindrical, or spherical. In a spatially varying grid, the amplitude growth of high frequency waves becomes exponential through multiple reflections from the outer boundary in cases of late-time solution. The exponential growth of the numerical noise exceeds the value of the real signal. The correction technique employs an absorbing surface and a radiating boundary, along with tailored selection of the grid mesh size. High frequency noise is removed through use of a low-pass digital filter, a linear least squares fit is made to thy low frequency filtered response, and the original, filtered, and fitted data are merged to preserve the high frequency early-time response.

Contact Stress Analysis of Spiral Bevel Gears Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A; Reddy, S.; Handschuh, R.

1995-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element 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 elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Simulation of thin slot spirals and dual circular patch antennas using the finite element method with mixed elements

NASA Technical Reports Server (NTRS)

Gong, Jian; Volakis, John L.; Nurnberger, Michael W.

1995-01-01

This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.

Moving mesh finite element simulation for phase-field modeling of brittle fracture and convergence of Newton's iteration

NASA Astrophysics Data System (ADS)

Zhang, Fei; Huang, Weizhang; Li, Xianping; Zhang, Shicheng

2018-03-01

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the decomposition of the strain tensor into tensile and compressive components is essential for the success of the phase-field modeling of brittle fracture but results in a non-smooth elastic energy and stronger nonlinearity in the governing equation. This makes the governing equation much more difficult to solve and, in particular, Newton's iteration often fails to converge. Three regularization methods are proposed to smooth out the decomposition of the strain tensor. Numerical examples of fracture propagation under quasi-static load demonstrate that all of the methods can effectively improve the convergence of Newton's iteration for relatively small values of the regularization parameter but without compromising the accuracy of the numerical solution. They also show that the moving mesh finite element method is able to adaptively concentrate the mesh elements around propagating cracks and handle multiple and complex crack systems.

Finite Element Models and Properties of a Stiffened Floor-Equipped Composite Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.

2010-01-01

Finite element models were developed of a floor-equipped, frame and stringer stiffened composite cylinder including a coarse finite element model of the structural components, a coarse finite element 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 element properties, the material and mechanical properties, the beam cross-section characteristics, the beam element representations and the boundary conditions of the composite cylinder models. The expressions used to calculate the group speeds for the cylinder components are presented.

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.

1999-01-01

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Computational performance of Free Mesh Method applied to continuum mechanics problems

PubMed Central

YAGAWA, Genki

2011-01-01

The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics. PMID:21558753

Combination of the discontinuous Galerkin method with finite differences for simulation of seismic wave propagation

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

Lisitsa, Vadim, E-mail: lisitsavv@ipgg.sbras.ru; Novosibirsk State University, Novosibirsk; Tcheverda, Vladimir

We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. Inmore » this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.« less

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

Neurosurgery simulation using non-linear finite element modeling and haptic interaction

NASA Astrophysics Data System (ADS)

Lee, Huai-Ping; Audette, Michel; Joldes, Grand R.; Enquobahrie, Andinet

2012-02-01

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 element 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 finite element method (FEM) with haptic interaction. Real-time finite element analysis is achieved by utilizing the total Lagrangian explicit dynamic (TLED) formulation and GPU acceleration of per-node and per-element 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.

An adaptive embedded mesh procedure for leading-edge vortex flows

NASA Technical Reports Server (NTRS)

Powell, Kenneth G.; Beer, Michael A.; Law, Glenn W.

1989-01-01

A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.

Connectivity-based, all-hexahedral mesh generation method and apparatus

DOEpatents

Tautges, T.J.; Mitchell, S.A.; Blacker, T.D.; Murdoch, P.

1998-06-16

The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as ``whisker chords.`` This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method. 79 figs.

Connectivity-based, all-hexahedral mesh generation method and apparatus

DOEpatents

Tautges, Timothy James; Mitchell, Scott A.; Blacker, Ted D.; Murdoch, Peter

1998-01-01

The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as "whisker chords." This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method.

Application of the discrete generalized multigroup method to ultra-fine energy mesh in infinite medium calculations

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

Gibson, N. A.; Forget, B.

2012-07-01

The Discrete Generalized Multigroup (DGM) method uses discrete Legendre orthogonal polynomials to expand the energy dependence of the multigroup neutron transport equation. This allows a solution on a fine energy mesh to be approximated for a cost comparable to a solution on a coarse energy mesh. The DGM method is applied to an ultra-fine energy mesh (14,767 groups) to avoid using self-shielding methodologies without introducing the cost usually associated with such energy discretization. Results show DGM to converge to the reference ultra-fine solution after a small number of recondensation steps for multiple infinite medium compositions. (authors)

Moving Particles Through a Finite Element Mesh

PubMed Central

Peskin, Adele P.; Hardin, Gary R.

1998-01-01

We present a new numerical technique for modeling the flow around multiple objects moving in a fluid. The method tracks the dynamic interaction between each particle and the fluid. The movements of the fluid and the object are directly coupled. A background mesh is designed to fit the geometry of the overall domain. The mesh is designed independently of the presence of the particles except in terms of how fine it must be to track particles of a given size. Each particle is represented by a geometric figure that describes its boundary. This figure overlies the mesh. Nodes are added to the mesh where the particle boundaries intersect the background mesh, increasing the number of nodes contained in each element whose boundary is intersected. These additional nodes are then used to describe and track the particle in the numerical scheme. Appropriate element shape functions are defined to approximate the solution on the elements with extra nodes. The particles are moved through the mesh by moving only the overlying nodes defining the particles. The regular finite element grid remains unchanged. In this method, the mesh does not distort as the particles move. Instead, only the placement of particle-defining nodes changes as the particles move. Element shape functions are updated as the nodes move through the elements. This method is especially suited for models of moderate numbers of moderate-size particles, where the details of the fluid-particle coupling are important. Both the complications of creating finite element meshes around appreciable numbers of particles, and extensive remeshing upon movement of the particles are simplified in this method. PMID:28009377

Contact stress analysis of spiral bevel gears using nonlinear finite element static analysis

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Kumar, A.; Reddy, S.; Handschuh, R.

1993-01-01

A procedure is presented for performing three-dimensional stress analysis of spiral bevel gears in mesh using the finite element method. The procedure involves generating a finite element 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 elements. A solution technique for correct orientation of the gap elements is given. Example models and results are presented.

Convergence of finite difference transient response computations for thin shells.

NASA Technical Reports Server (NTRS)

Sobel, L. H.; Geers, T. L.

1973-01-01

Numerical studies pertaining to the limits of applicability of the finite difference method in the solution of linear transient shell response problems are performed, and a computational procedure for the use of the method is recommended. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. This is not a serious limitation in view of natural constraints imposed by the extension of Saint Venant's principle to transient response problems. It is also found that the short wavelength limitations of thin shell (Bernoulli-Euler) theory create significant convergence difficulties in computed response to certain types of transverse excitations. These difficulties may be overcome, however, through proper selection of finite difference mesh dimensions and temporal smoothing of the excitation.

Analysis of transient, linear wave propagation in shells by the finite difference method

NASA Technical Reports Server (NTRS)

Geers, T. L.; Sobel, L. H.

1971-01-01

The applicability of the finite difference method to propagation problems in shells, and the response of a cylindrical shell with cutouts to both longitudinal and radial transient excitations are investigated. It is found that the only inherent limitation of the finite difference method is its inability to reproduce accurately response discontinuities. The short wave length limitations of thin shell theory create significant convergence difficulties may often be overcome through proper selection of finite difference mesh dimensions and temporal or spatial smoothing of the excitation. Cutouts produce moderate changes in early and intermediate time response of a cylindrical shell to axisymmetric pulse loads applied at one end. The cutouts may facilitate the undesirable late-time transfer of load-injected extensional energy into nonaxisymmetric flexural response.

Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

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

Dolbow, John; Zhang, Ziyu; Spencer, Benjamin

Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside ofmore » the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.« less

Finite element mesh refinement criteria for stress analysis

NASA Technical Reports Server (NTRS)

Kittur, Madan G.; Huston, Ronald L.

1990-01-01

This paper discusses procedures for finite-element mesh selection and refinement. The objective is to improve accuracy. The procedures are based on (1) the minimization of the stiffness matrix race (optimizing node location); (2) the use of h-version refinement (rezoning, element size reduction, and increasing the number of elements); and (3) the use of p-version refinement (increasing the order of polynomial approximation of the elements). A step-by-step procedure of mesh selection, improvement, and refinement is presented. The criteria for 'goodness' of a mesh are based on strain energy, displacement, and stress values at selected critical points of a structure. An analysis of an aircraft lug problem is presented as an example.

Electrical Resistivity Tomography using a finite element based BFGS algorithm with algebraic multigrid preconditioning

NASA Astrophysics Data System (ADS)

Codd, A. L.; Gross, L.

2018-03-01

We present a new inversion method for Electrical Resistivity Tomography which, in contrast to established approaches, minimizes the cost function prior to finite element discretization for the unknown electric conductivity and electric potential. Minimization is performed with the Broyden-Fletcher-Goldfarb-Shanno method (BFGS) in an appropriate function space. BFGS is self-preconditioning and avoids construction of the dense Hessian which is the major obstacle to solving large 3-D problems using parallel computers. In addition to the forward problem predicting the measurement from the injected current, the so-called adjoint problem also needs to be solved. For this problem a virtual current is injected through the measurement electrodes and an adjoint electric potential is obtained. The magnitude of the injected virtual current is equal to the misfit at the measurement electrodes. This new approach has the advantage that the solution process of the optimization problem remains independent to the meshes used for discretization and allows for mesh adaptation during inversion. Computation time is reduced by using superposition of pole loads for the forward and adjoint problems. A smoothed aggregation algebraic multigrid (AMG) preconditioned conjugate gradient is applied to construct the potentials for a given electric conductivity estimate and for constructing a first level BFGS preconditioner. Through the additional reuse of AMG operators and coarse grid solvers inversion time for large 3-D problems can be reduced further. We apply our new inversion method to synthetic survey data created by the resistivity profile representing the characteristics of subsurface fluid injection. We further test it on data obtained from a 2-D surface electrode survey on Heron Island, a small tropical island off the east coast of central Queensland, Australia.

On applications of chimera grid schemes to store separation

NASA Technical Reports Server (NTRS)

Cougherty, F. C.; Benek, J. A.; Steger, J. L.

1985-01-01

A finite difference scheme which uses multiple overset meshes to simulate the aerodynamics of aircraft/store interaction and store separation is described. In this chimera, or multiple mesh, scheme, a complex configuration is mapped using a major grid about the main component of the configuration, and minor overset meshes are used to map each additional component such as a store. As a first step in modeling the aerodynamics of store separation, two dimensional inviscid flow calculations were carried out in which one of the minor meshes is allowed to move with respect to the major grid. Solutions of calibrated two dimensional problems indicate that allowing one mesh to move with respect to another does not adversely affect the time accuracy of an unsteady solution. Steady, inviscid three dimensional computations demonstrate the capability to simulate complex configurations, including closely packed multiple bodies.

ImageParser: a tool for finite element generation from three-dimensional medical images

PubMed Central

Yin, HM; Sun, LZ; Wang, G; Yamada, T; Wang, J; Vannier, MW

2004-01-01

Background The finite element method (FEM) is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures) of interest (ROIs) may be irregular and fuzzy. Methods A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. Results The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. Conclusion The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information. PMID:15461787

Microstructure and mesh sensitivities of mesoscale surrogate driving force measures for transgranular fatigue cracks in polycrystals

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

Castelluccio, Gustavo M.; McDowell, David L.

The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. Our paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We also employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipatedmore » fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Furthermore, results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Furthermore, volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains.« less

Microstructure and mesh sensitivities of mesoscale surrogate driving force measures for transgranular fatigue cracks in polycrystals

DOE PAGES

Castelluccio, Gustavo M.; McDowell, David L.

2015-05-22

The number of cycles required to form and grow microstructurally small fatigue cracks in metals exhibits substantial variability, particularly for low applied strain amplitudes. This variability is commonly attributed to the heterogeneity of cyclic plastic deformation within the microstructure, and presents a challenge to minimum life design of fatigue resistant components. Our paper analyzes sources of variability that contribute to the driving force of transgranular fatigue cracks within nucleant grains. We also employ crystal plasticity finite element simulations that explicitly render the polycrystalline microstructure and Fatigue Indicator Parameters (FIPs) averaged over different volume sizes and shapes relative to the anticipatedmore » fatigue damage process zone. Volume averaging is necessary to both achieve description of a finite fatigue damage process zone and to regularize mesh dependence in simulations. Furthermore, results from constant amplitude remote applied straining are characterized in terms of the extreme value distributions of volume averaged FIPs. Grain averaged FIP values effectively mitigate mesh sensitivity, but they smear out variability within grains. Furthermore, volume averaging over bands that encompass critical transgranular slip planes appear to present the most attractive approach to mitigate mesh sensitivity while preserving variability within grains.« less

Method of modifying a volume mesh using sheet extraction

DOEpatents

Borden, Michael J [Albuquerque, NM; Shepherd, Jason F [Albuquerque, NM

2007-02-20

A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet extraction. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of determining a sheet of hexahedral mesh elements, generating nodes for merging, and merging the nodes to delete the sheet of hexahedral mesh elements and modify the volume mesh.

MPACT Theory Manual, Version 2.2.0

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

Downar, Thomas; Collins, Benjamin S.; Gehin, Jess C.

2016-06-09

This theory manual describes the three-dimensional (3-D) whole-core, pin-resolved transport calculation methodology employed in the MPACT code. To provide sub-pin level power distributions with sufficient accuracy, MPACT employs the method of characteristics (MOC) solutions in the framework of a 3-D coarse mesh finite difference (CMFD) formulation. MPACT provides a 3D MOC solution, but also a 2D/1D solution in which the 2D planar solution is provided by MOC and the axial coupling is resolved by one-dimensional (1-D) lower order (diffusion or P3) solutions. In Chapter 2 of the manual, the MOC methodology is described for calculating the regional angular and scalarmore » fluxes from the Boltzmann transport equation. In Chapter 3, the 2D/1D methodology is described, together with the description of the CMFD iteration process involving dynamic homogenization and solution of the multigroup CMFD linear system. A description of the MPACT depletion algorithm is given in Chapter 4, followed by a discussion of the subgroup and ESSM resonance processing methods in Chapter 5. The final Chapter 6 describes a simplified thermal hydraulics model in MPACT.« less

Non-Markovian closure models for large eddy simulations using the Mori-Zwanzig formalism

NASA Astrophysics Data System (ADS)

Parish, Eric J.; Duraisamy, Karthik

2017-01-01

This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from nonequilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation (GLE) are considered, and insight gained from the orthogonal dynamics equation is used as a starting point for model development. A class of subgrid models is considered which represent nonlocal behavior via a finite memory approximation [Stinis, arXiv:1211.4285 (2012)], the length of which is determined using a heuristic that is related to the spectral radius of the Jacobian of the resolved variables. The resulting models are intimately tied to the underlying numerical resolution and are capable of approximating non-Markovian effects. Numerical experiments on the Burgers equation demonstrate that the M-Z-based models can accurately predict the temporal evolution of the total kinetic energy and the total dissipation rate at varying mesh resolutions. The trajectory of each resolved mode in phase space is accurately predicted for cases where the coarse graining is moderate. Large eddy simulations (LESs) of homogeneous isotropic turbulence and the Taylor-Green Vortex show that the M-Z-based models are able to provide excellent predictions, accurately capturing the subgrid contribution to energy transfer. Last, LESs of fully developed channel flow demonstrate the applicability of M-Z-based models to nondecaying problems. It is notable that the form of the closure is not imposed by the modeler, but is rather derived from the mathematics of the coarse graining, highlighting the potential of M-Z-based techniques to define LES closures.

Gradients estimation from random points with volumetric tensor in turbulence

NASA Astrophysics Data System (ADS)

Watanabe, Tomoaki; Nagata, Koji

2017-12-01

We present an estimation method of fully-resolved/coarse-grained gradients from randomly distributed points in turbulence. The method is based on a linear approximation of spatial gradients expressed with the volumetric tensor, which is a 3 × 3 matrix determined by a geometric distribution of the points. The coarse grained gradient can be considered as a low pass filtered gradient, whose cutoff is estimated with the eigenvalues of the volumetric tensor. The present method, the volumetric tensor approximation, is tested for velocity and passive scalar gradients in incompressible planar jet and mixing layer. Comparison with a finite difference approximation on a Cartesian grid shows that the volumetric tensor approximation computes the coarse grained gradients fairly well at a moderate computational cost under various conditions of spatial distributions of points. We also show that imposing the solenoidal condition improves the accuracy of the present method for solenoidal vectors, such as a velocity vector in incompressible flows, especially when the number of the points is not large. The volumetric tensor approximation with 4 points poorly estimates the gradient because of anisotropic distribution of the points. Increasing the number of points from 4 significantly improves the accuracy. Although the coarse grained gradient changes with the cutoff length, the volumetric tensor approximation yields the coarse grained gradient whose magnitude is close to the one obtained by the finite difference. We also show that the velocity gradient estimated with the present method well captures the turbulence characteristics such as local flow topology, amplification of enstrophy and strain, and energy transfer across scales.

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

NASA Technical Reports Server (NTRS)

Dey, C.; Dey, S. K.

1983-01-01

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight. [atmospheric general circulation experiment, convection in a float zone, and the Bridgman-Stockbarger crystal growing system

NASA Technical Reports Server (NTRS)

Roberts, G. O.; Fowlis, W. W.; Miller, T. L.

1984-01-01

Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

NASA Technical Reports Server (NTRS)

Chung, T. J. (Editor); Karr, Gerald R. (Editor)

1989-01-01

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, 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 finite elements, and mesh generation. Also discussed are mixed finite elements, 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.

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

Field Test of a Hybrid Finite-Difference and Analytic Element Regional Model.

PubMed

Abrams, D B; Haitjema, H M; Feinstein, D T; Hunt, R J

2016-01-01

Regional finite-difference models often have cell sizes that are too large to sufficiently model well-stream interactions. Here, a steady-state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell-by-cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real-world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined "benchmark" MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost-effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite-difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady-state conditions. © 2015, National Ground Water Association.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

1991-01-01

Validated results are presented for the new 3D body of revolution finite element 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 finite element 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 finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

Computer animation of modal and transient vibrations

NASA Technical Reports Server (NTRS)

Lipman, Robert R.

1987-01-01

An interactive computer graphics processor is described that is capable of generating input to animate modal and transient vibrations of finite element models on an interactive graphics system. The results from NASTRAN can be postprocessed such that a three dimensional wire-frame picture, in perspective, of the finite element mesh is drawn on the graphics display. Modal vibrations of any mode shape or transient motions over any range of steps can be animated. The finite element mesh can be color-coded by any component of displacement. Viewing parameters and the rate of vibration of the finite element model can be interactively updated while the structure is vibrating.

Momentum Advection on a Staggered Mesh

NASA Astrophysics Data System (ADS)

Benson, David J.

1992-05-01

Eulerian and ALE (arbitrary Lagrangian-Eulerian) hydrodynamics programs usually split a timestep into two parts. The first part is a Lagrangian step, which calculates the incremental motion of the material. The second part is referred to as the Eulerian step, the advection step, or the remap step, and it accounts for the transport of material between cells. In most finite difference and finite element 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.

A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation

NASA Astrophysics Data System (ADS)

Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric

2016-12-01

We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.

On the implementation of an accurate and efficient solver for convection-diffusion equations

NASA Astrophysics Data System (ADS)

Wu, Chin-Tien

In this dissertation, we examine several different aspects of computing the numerical solution of the convection-diffusion equation. The solution of this equation often exhibits sharp gradients due to Dirichlet outflow boundaries or discontinuities in boundary conditions. Because of the singular-perturbed nature of the equation, numerical solutions often have severe oscillations when grid sizes are not small enough to resolve sharp gradients. To overcome such difficulties, the streamline diffusion discretization method can be used to obtain an accurate approximate solution in regions where the solution is smooth. To increase accuracy of the solution in the regions containing layers, adaptive mesh refinement and mesh movement based on a posteriori error estimations can be employed. An error-adapted mesh refinement strategy based on a posteriori error estimations is also proposed to resolve layers. For solving the sparse linear systems that arise from discretization, goemetric multigrid (MG) and algebraic multigrid (AMG) are compared. In addition, both methods are also used as preconditioners for Krylov subspace methods. We derive some convergence results for MG with line Gauss-Seidel smoothers and bilinear interpolation. Finally, while considering adaptive mesh refinement as an integral part of the solution process, it is natural to set a stopping tolerance for the iterative linear solvers on each mesh stage so that the difference between the approximate solution obtained from iterative methods and the finite element solution is bounded by an a posteriori error bound. Here, we present two stopping criteria. The first is based on a residual-type a posteriori error estimator developed by Verfurth. The second is based on an a posteriori error estimator, using local solutions, developed by Kay and Silvester. Our numerical results show the refined mesh obtained from the iterative solution which satisfies the second criteria is similar to the refined mesh obtained from the finite element solution.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. 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 finite element 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 finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Extended bounds limiter for high-order finite-volume schemes on unstructured meshes

NASA Astrophysics Data System (ADS)

Tsoutsanis, Panagiotis

2018-06-01

This paper explores the impact of the definition of the bounds of the limiter proposed by Michalak and Ollivier-Gooch in [56] (2009), for higher-order Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) numerical schemes on unstructured meshes in the finite-volume (FV) framework. A new modification of the limiter is proposed where the bounds are redefined by utilising all the spatial information provided by all the elements in the reconstruction stencil. Numerical results obtained on smooth and discontinuous test problems of the Euler equations on unstructured meshes, highlight that the newly proposed extended bounds limiter exhibits superior performance in terms of accuracy and mesh sensitivity compared to the cell-based or vertex-based bounds implementations.

Investigation of Grid Adaptation to Reduce Computational Efforts for a 2-D Hydrogen-Fueled Dual-Mode Scramjet

NASA Astrophysics Data System (ADS)

Foo, Kam Keong

A two-dimensional dual-mode scramjet flowpath is developed and evaluated using the ANSYS Fluent density-based flow solver with various computational grids. Results are obtained for fuel-off, fuel-on non-reacting, and fuel-on reacting cases at different equivalence ratios. A one-step global chemical kinetics hydrogen-air model is used in conjunction with the eddy-dissipation model. Coarse, medium and fine computational grids are used to evaluate grid sensitivity and to investigate a lack of grid independence. Different grid adaptation strategies are performed on the coarse grid in an attempt to emulate the solutions obtained from the finer grids. The goal of this study is to investigate the feasibility of using various mesh adaptation criteria to significantly decrease computational efforts for high-speed reacting flows.

A simple finite element method for non-divergence form elliptic equation

DOE PAGES

Mu, Lin; Ye, Xiu

2017-03-01

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

A simple finite element method for non-divergence form elliptic equation

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

Mu, Lin; Ye, Xiu

Here, we develop a simple finite element method for solving second order elliptic equations in non-divergence form by combining least squares concept with discontinuous approximations. This simple method has a symmetric and positive definite system and can be easily analyzed and implemented. We could have also used general meshes with polytopal element and hanging node in the method. We prove that our finite element solution approaches to the true solution when the mesh size approaches to zero. Numerical examples are tested that demonstrate the robustness and flexibility of the method.

Solid/FEM integration at SNLA

NASA Technical Reports Server (NTRS)

Chavez, Patrick F.

1987-01-01

The effort at Sandia National Labs. on the methodologies and techniques being used to generate strict hexahedral finite element meshes from a solid model is described. The functionality of the modeler is used to decompose the solid into a set of nonintersecting meshable finite element primitives. The description of the decomposition is exported, via a Boundary Representative format, to the meshing program which uses the information for complete finite element model specification. Particular features of the program are discussed in some detail along with future plans for development which includes automation of the decomposition using artificial intelligence techniques.

Stress distribution in the temporo-mandibular joint discs during jaw closing: a high-resolution three-dimensional finite-element model analysis.

PubMed

Savoldelli, Charles; Bouchard, Pierre-Olivier; Loudad, Raounak; Baque, Patrick; Tillier, Yannick

2012-07-01

This study aims at analysing the stresses distribution in the temporomandibular joint (TMJ) using a complete high-resolution finite element model (FE Model). This model is used here to analyse the stresses distribution in the discs during a closing jaw cycle. In the end, this model enables the prediction of the stress evolution in the TMJ disc submitted to various loadings induced by mandibular trauma, surgery or parafunction. The geometric data for the model were obtained from MRI and CT scans images of a healthy male patient. Surface and volume meshes were successively obtained using a 3D image segmentation software (AMIRA(®)). Bone components of skull and mandible, both of joint discs, temporomandibular capsules and ligaments and dental arches were meshed as separate bodies. The volume meshes were transferred to the FE analysis software (FORGE(®)). Material properties were assigned for each region. Boundary conditions for closing jaw simulations were represented by different load directions of jaws muscles. The von Mises stresses distribution in both joint discs during closing conditions was analyzed. The pattern of von Mises stresses in the TMJ discs is non-symmetric and changed continuously during jaw movement. Maximal stress is reached on the surface disc in areas in contact with others bodies. The three-dimension finite element model of masticatory system will make it possible to simulate different conditions that appear to be important in the cascade of events leading to joint damage.

Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure

NASA Technical Reports Server (NTRS)

Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.

1992-01-01

Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.

Finite element meshing approached as a global minimization process

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

WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.

2000-03-01

The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within amore » charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested before this project ended. The primary complexity in the extension was in the connectivity problem formulation. Defining all of the interparticle interactions that occur in three-dimensions and expressing them in mathematical relationships is very difficult.« less

A weak Galerkin generalized multiscale finite element method

DOE PAGES

Mu, Lin; Wang, Junping; Ye, Xiu

2016-03-31

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element 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 finite element method. Convergence analysis and numerical experiments are obtained for the special case.

A weak Galerkin generalized multiscale finite element method

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

Mu, Lin; Wang, Junping; Ye, Xiu

In this study, we propose a general framework for weak Galerkin generalized multiscale (WG-GMS) finite element 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 finite element method. Convergence analysis and numerical experiments are obtained for the special case.

Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2012-01-01

The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.

Ab initio velocity-field curves in monoclinic β-Ga2O3

NASA Astrophysics Data System (ADS)

Ghosh, Krishnendu; Singisetti, Uttam

2017-07-01

We investigate the high-field transport in monoclinic β-Ga2O3 using a combination of ab initio calculations and full band Monte Carlo (FBMC) simulation. Scattering rate calculation and the final state selection in the FBMC simulation use complete wave-vector (both electron and phonon) and crystal direction dependent electron phonon interaction (EPI) elements. We propose and implement a semi-coarse version of the Wannier-Fourier interpolation method [Giustino et al., Phys. Rev. B 76, 165108 (2007)] for short-range non-polar optical phonon (EPI) elements in order to ease the computational requirement in FBMC simulation. During the interpolation of the EPI, the inverse Fourier sum over the real-space electronic grids is done on a coarse mesh while the unitary rotations are done on a fine mesh. This paper reports the high field transport in monoclinic β-Ga2O3 with deep insight into the contribution of electron-phonon interactions and velocity-field characteristics for electric fields ranging up to 450 kV/cm in different crystal directions. A peak velocity of 2 × 107 cm/s is estimated at an electric field of 200 kV/cm.

A vortex wake capturing method for potential flow calculations

NASA Technical Reports Server (NTRS)

Murman, E. M.; Stremel, P. M.

1982-01-01

A method is presented for modifying finite difference solutions of the potential equation to include the calculation of non-planar vortex wake features. The approach is an adaptation of Baker's 'cloud in cell' algorithm developed for the stream function-vorticity equations. The vortex wake is tracked in a Lagrangian frame of reference as a group of discrete vortex filaments. These are distributed to the Eulerian mesh system on which the velocity is calculated by a finite difference solution of the potential equation. An artificial viscosity introduced by the finite difference equations removes the singular nature of the vortex filaments. Computed examples are given for the two-dimensional time dependent roll-up of vortex wakes generated by wings with different spanwise loading distributions.

Procedure for Tooth Contact Analysis of a Face Gear Meshing With a Spur Gear Using Finite Element Analysis

NASA Technical Reports Server (NTRS)

Bibel, George; Lewicki, David G. (Technical Monitor)

2002-01-01

A procedure was developed to perform tooth contact analysis between a face gear meshing with a spur pinion using finite element analysis. The face gear surface points from a previous analysis were used to create a connected tooth solid model without gaps or overlaps. The face gear surface points were used to create a five tooth face gear Patran model (with rim) using Patran PCL commands. These commands were saved in a series of session files suitable for Patran input. A four tooth spur gear that meshes with the face gear was designed and constructed with Patran PCL commands. These commands were also saved in a session files suitable for Patran input. The orientation of the spur gear required for meshing with the face gear was determined. The required rotations and translations are described and built into the session file for the spur gear. The Abaqus commands for three-dimensional meshing were determined and verified for a simplified model containing one spur tooth and one face gear tooth. The boundary conditions, loads, and weak spring constraints were determined to make the simplified model work. The load steps and load increments to establish contact and obtain a realistic load was determined for the simplified two tooth model. Contact patterns give some insight into required mesh density. Building the two gears in two different local coordinate systems and rotating the local coordinate systems was verified as an easy way to roll the gearset through mesh. Due to limitation of swap space, disk space and time constraints of the summer period, the larger model was not completed.

Floating shock fitting via Lagrangian adaptive meshes

NASA Technical Reports Server (NTRS)

Vanrosendale, John

1994-01-01

In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.

2001-01-01

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Mathematical Aspects of Finite Element Methods for Incompressible Viscous Flows.

DTIC Science & Technology

1986-09-01

respectively. Here h is a parameter which is usually related to the size of the grid associated with the finite element partitioning of Q. Then one... grid and of not at least performing serious mesh refinement studies. It also points out the usefulness of rigorous results concerning the stability...overconstrained the .1% approximate velocity field. However, by employing different grids for the ’z pressure and velocity fields, the linear-constant

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai; Fu, Shubin; Gibson, Richard L.

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

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

Gao, Kai, E-mail: kaigao87@gmail.com; Fu, Shubin, E-mail: shubinfu89@gmail.com; Gibson, Richard L., E-mail: gibson@tamu.edu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE PAGES

Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

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

Park, Byoung Yoon; Roberts, Barry L.

The three-dimensional finite element mesh capturing realistic geometries of Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh is consisting of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time with maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill,more » Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for not only various civil and geological structures but also biological applications such as artificial limbs.« less

Anisotropic mesh adaptation for marine ice-sheet modelling

NASA Astrophysics Data System (ADS)

Gillet-Chaulet, Fabien; Tavard, Laure; Merino, Nacho; Peyaud, Vincent; Brondex, Julien; Durand, Gael; Gagliardini, Olivier

2017-04-01

Improving forecasts of ice-sheets contribution to sea-level rise requires, amongst others, to correctly model the dynamics of the grounding line (GL), i.e. the line where the ice detaches from its underlying bed and goes afloat on the ocean. Many numerical studies, including the intercomparison exercises MISMIP and MISMIP3D, have shown that grid refinement in the GL vicinity is a key component to obtain reliable results. Improving model accuracy while maintaining the computational cost affordable has then been an important target for the development of marine icesheet models. Adaptive mesh refinement (AMR) is a method where the accuracy of the solution is controlled by spatially adapting the mesh size. It has become popular in models using the finite element method as they naturally deal with unstructured meshes, but block-structured AMR has also been successfully applied to model GL dynamics. The main difficulty with AMR is to find efficient and reliable estimators of the numerical error to control the mesh size. Here, we use the estimator proposed by Frey and Alauzet (2015). Based on the interpolation error, it has been found effective in practice to control the numerical error, and has some flexibility, such as its ability to combine metrics for different variables, that makes it attractive. Routines to compute the anisotropic metric defining the mesh size have been implemented in the finite element ice flow model Elmer/Ice (Gagliardini et al., 2013). The mesh adaptation is performed using the freely available library MMG (Dapogny et al., 2014) called from Elmer/Ice. Using a setup based on the inter-comparison exercise MISMIP+ (Asay-Davis et al., 2016), we study the accuracy of the solution when the mesh is adapted using various variables (ice thickness, velocity, basal drag, …). We show that combining these variables allows to reduce the number of mesh nodes by more than one order of magnitude, for the same numerical accuracy, when compared to uniform mesh refinement. For transient solutions where the GL is moving, we have implemented an algorithm where the computation is reiterated allowing to anticipate the GL displacement and to adapt the mesh to the transient solution. We discuss the performance and robustness of this algorithm.

Mesh refinement strategy for optimal control problems

NASA Astrophysics Data System (ADS)

Paiva, L. T.; Fontes, F. A. C. C.

2013-10-01

Direct methods are becoming the most used technique to solve nonlinear optimal control problems. Regular time meshes having equidistant spacing are frequently used. However, in some cases these meshes cannot cope accurately with nonlinear behavior. One way to improve the solution is to select a new mesh with a greater number of nodes. Another way, involves adaptive mesh refinement. In this case, the mesh nodes have non equidistant spacing which allow a non uniform nodes collocation. In the method presented in this paper, a time mesh refinement strategy based on the local error is developed. After computing a solution in a coarse mesh, the local error is evaluated, which gives information about the subintervals of time domain where refinement is needed. This procedure is repeated until the local error reaches a user-specified threshold. The technique is applied to solve the car-like vehicle problem aiming minimum consumption. The approach developed in this paper leads to results with greater accuracy and yet with lower overall computational time as compared to using a time meshes having equidistant spacing.

Personal computer study of finite-difference methods for the transonic small disturbance equation

NASA Technical Reports Server (NTRS)

Bland, Samuel R.

1989-01-01

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Auto-adaptive finite element meshes

NASA Technical Reports Server (NTRS)

Richter, Roland; Leyland, Penelope

1995-01-01

Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.

Benchmark measurements and calculations of a 3-dimensional neutron streaming experiment

NASA Astrophysics Data System (ADS)

Barnett, D. A., Jr.

1991-02-01

An experimental assembly known as the Dog-Legged Void assembly was constructed to measure the effect of neutron streaming in iron and void regions. The primary purpose of the measurements was to provide benchmark data against which various neutron transport calculation tools could be compared. The measurements included neutron flux spectra at four places and integral measurements at two places in the iron streaming path as well as integral measurements along several axial traverses. These data have been used in the verification of Oak Ridge National Laboratory's three-dimensional discrete ordinates code, TORT. For a base case calculation using one-half inch mesh spacing, finite difference spatial differencing, an S(sub 16) quadrature and P(sub 1) cross sections in the MUFT multigroup structure, the calculated solution agreed to within 18 percent with the spectral measurements and to within 24 percent of the integral measurements. Variations on the base case using a fewgroup energy structure and P(sub 1) and P(sub 3) cross sections showed similar agreement. Calculations using a linear nodal spatial differencing scheme and fewgroup cross sections also showed similar agreement. For the same mesh size, the nodal method was seen to require 2.2 times as much CPU time as the finite difference method. A nodal calculation using a typical mesh spacing of 2 inches, which had approximately 32 times fewer mesh cells than the base case, agreed with the measurements to within 34 percent and yet required on 8 percent of the CPU time.

A Finite Element Method for Simulation of Compressible Cavitating Flows

NASA Astrophysics Data System (ADS)

Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

2016-11-01

This work focuses on a novel approach for finite element 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 finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian 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.

Prediction of contact path and load sharing in spiral bevel gears

NASA Technical Reports Server (NTRS)

Bibel, George D.; Tiku, Karuna; Kumar, Ashok

1994-01-01

A procedure is presented to perform a contact analysis of spiral bevel gears in order to predict the contact path and the load sharing as the gears roll through mesh. The approach utilizes recent advances in automated contact methods for nonlinear finite element analysis. A sector of the pinion and gear is modeled consisting of three pinion teeth and four gear teeth in mesh. Calculation of the contact force and stresses through the gear meshing cycle are demonstrated. Summary of the results are presented using three dimensional plots and tables. Issues relating to solution convergence and requirements for running large finite element analysis on a supercomputer are discussed.

A finite-difference method for the variable coefficient Poisson equation on hierarchical Cartesian meshes

NASA Astrophysics Data System (ADS)

Raeli, Alice; Bergmann, Michel; Iollo, Angelo

2018-02-01

We consider problems governed by a linear elliptic equation with varying coefficients across internal interfaces. The solution and its normal derivative can undergo significant variations through these internal boundaries. We present a compact finite-difference scheme on a tree-based adaptive grid that can be efficiently solved using a natively parallel data structure. The main idea is to optimize the truncation error of the discretization scheme as a function of the local grid configuration to achieve second-order accuracy. Numerical illustrations are presented in two and three-dimensional configurations.

Grid adaption using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Grid adaptation using chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1994-01-01

The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.

Grid adaptation using Chimera composite overlapping meshes

NASA Technical Reports Server (NTRS)

Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen

1993-01-01

The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.

Impact of Variable-Resolution Meshes on Regional Climate Simulations

NASA Astrophysics Data System (ADS)

Fowler, L. D.; Skamarock, W. C.; Bruyere, C. L.

2014-12-01

The Model for Prediction Across Scales (MPAS) is currently being used for seasonal-scale simulations on globally-uniform and regionally-refined meshes. Our ongoing research aims at analyzing simulations of tropical convective activity and tropical cyclone development during one hurricane season over the North Atlantic Ocean, contrasting statistics obtained with a variable-resolution mesh against those obtained with a quasi-uniform mesh. Analyses focus on the spatial distribution, frequency, and intensity of convective and grid-scale precipitations, and their relative contributions to the total precipitation as a function of the horizontal scale. Multi-month simulations initialized on May 1st 2005 using ERA-Interim re-analyses indicate that MPAS performs satisfactorily as a regional climate model for different combinations of horizontal resolutions and transitions between the coarse and refined meshes. Results highlight seamless transitions for convection, cloud microphysics, radiation, and land-surface processes between the quasi-uniform and locally- refined meshes, despite the fact that the physics parameterizations were not developed for variable resolution meshes. Our goal of analyzing the performance of MPAS is twofold. First, we want to establish that MPAS can be successfully used as a regional climate model, bypassing the need for nesting and nudging techniques at the edges of the computational domain as done in traditional regional climate modeling. Second, we want to assess the performance of our convective and cloud microphysics parameterizations as the horizontal resolution varies between the lower-resolution quasi-uniform and higher-resolution locally-refined areas of the global domain.

Impact of Variable-Resolution Meshes on Regional Climate Simulations

NASA Astrophysics Data System (ADS)

Fowler, L. D.; Skamarock, W. C.; Bruyere, C. L.

2013-12-01

The Model for Prediction Across Scales (MPAS) is currently being used for seasonal-scale simulations on globally-uniform and regionally-refined meshes. Our ongoing research aims at analyzing simulations of tropical convective activity and tropical cyclone development during one hurricane season over the North Atlantic Ocean, contrasting statistics obtained with a variable-resolution mesh against those obtained with a quasi-uniform mesh. Analyses focus on the spatial distribution, frequency, and intensity of convective and grid-scale precipitations, and their relative contributions to the total precipitation as a function of the horizontal scale. Multi-month simulations initialized on May 1st 2005 using NCEP/NCAR re-analyses indicate that MPAS performs satisfactorily as a regional climate model for different combinations of horizontal resolutions and transitions between the coarse and refined meshes. Results highlight seamless transitions for convection, cloud microphysics, radiation, and land-surface processes between the quasi-uniform and locally-refined meshes, despite the fact that the physics parameterizations were not developed for variable resolution meshes. Our goal of analyzing the performance of MPAS is twofold. First, we want to establish that MPAS can be successfully used as a regional climate model, bypassing the need for nesting and nudging techniques at the edges of the computational domain as done in traditional regional climate modeling. Second, we want to assess the performance of our convective and cloud microphysics parameterizations as the horizontal resolution varies between the lower-resolution quasi-uniform and higher-resolution locally-refined areas of the global domain.

Incorporating inductances in tissue-scale models of cardiac electrophysiology

NASA Astrophysics Data System (ADS)

Rossi, Simone; Griffith, Boyce E.

2017-09-01

In standard models of cardiac electrophysiology, including the bidomain and monodomain models, local perturbations can propagate at infinite speed. We address this unrealistic property by developing a hyperbolic bidomain model that is based on a generalization of Ohm's law with a Cattaneo-type model for the fluxes. Further, we obtain a hyperbolic monodomain model in the case that the intracellular and extracellular conductivity tensors have the same anisotropy ratio. In one spatial dimension, the hyperbolic monodomain model is equivalent to a cable model that includes axial inductances, and the relaxation times of the Cattaneo fluxes are strictly related to these inductances. A purely linear analysis shows that the inductances are negligible, but models of cardiac electrophysiology are highly nonlinear, and linear predictions may not capture the fully nonlinear dynamics. In fact, contrary to the linear analysis, we show that for simple nonlinear ionic models, an increase in conduction velocity is obtained for small and moderate values of the relaxation time. A similar behavior is also demonstrated with biophysically detailed ionic models. Using the Fenton-Karma model along with a low-order finite element spatial discretization, we numerically analyze differences between the standard monodomain model and the hyperbolic monodomain model. In a simple benchmark test, we show that the propagation of the action potential is strongly influenced by the alignment of the fibers with respect to the mesh in both the parabolic and hyperbolic models when using relatively coarse spatial discretizations. Accurate predictions of the conduction velocity require computational mesh spacings on the order of a single cardiac cell. We also compare the two formulations in the case of spiral break up and atrial fibrillation in an anatomically detailed model of the left atrium, and we examine the effect of intracellular and extracellular inductances on the virtual electrode phenomenon.

Performance Characteristics of the Multi-Zone NAS Parallel Benchmarks

NASA Technical Reports Server (NTRS)

Jin, Haoqiang; VanderWijngaart, Rob F.

2003-01-01

We describe a new suite of computational benchmarks that models applications featuring multiple levels of parallelism. Such parallelism is often available in realistic flow computations on systems of grids, but had not previously been captured in bench-marks. The new suite, named NPB Multi-Zone, is extended from the NAS Parallel Benchmarks suite, and involves solving the application benchmarks LU, BT and SP on collections of loosely coupled discretization meshes. The solutions on the meshes are updated independently, but after each time step they exchange boundary value information. This strategy provides relatively easily exploitable coarse-grain parallelism between meshes. Three reference implementations are available: one serial, one hybrid using the Message Passing Interface (MPI) and OpenMP, and another hybrid using a shared memory multi-level programming model (SMP+OpenMP). We examine the effectiveness of hybrid parallelization paradigms in these implementations on three different parallel computers. We also use an empirical formula to investigate the performance characteristics of the multi-zone benchmarks.

A new third order finite volume weighted essentially non-oscillatory scheme on tetrahedral meshes

NASA Astrophysics Data System (ADS)

Zhu, Jun; Qiu, Jianxian

2017-11-01

In this paper a third order finite volume weighted essentially non-oscillatory scheme is designed for solving hyperbolic conservation laws on tetrahedral meshes. Comparing with other finite volume WENO schemes designed on tetrahedral meshes, the crucial advantages of such new WENO scheme are its simplicity and compactness with the application of only six unequal size spatial stencils for reconstructing unequal degree polynomials in the WENO type spatial procedures, and easy choice of the positive linear weights without considering the topology of the meshes. The original innovation of such scheme is to use a quadratic polynomial defined on a big central spatial stencil for obtaining third order numerical approximation at any points inside the target tetrahedral cell in smooth region and switch to at least one of five linear polynomials defined on small biased/central spatial stencils for sustaining sharp shock transitions and keeping essentially non-oscillatory property simultaneously. By performing such new procedures in spatial reconstructions and adopting a third order TVD Runge-Kutta time discretization method for solving the ordinary differential equation (ODE), the new scheme's memory occupancy is decreased and the computing efficiency is increased. So it is suitable for large scale engineering requirements on tetrahedral meshes. Some numerical results are provided to illustrate the good performance of such scheme.

New developments in the method of space-time conservation element and solution element: Applications to the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1993-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods--i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to avoid several key limitations to the above traditional methods. An explicit model scheme for solving a simple 1-D unsteady convection-diffusion equation is constructed and used to illuminate major differences between the current method and those mentioned above. Unexpectedly, its amplification factors for the pure convection and pure diffusion cases are identical to those of the Leapfrog and the DuFort-Frankel schemes, respectively. Also, this explicit scheme and its Navier-Stokes extension have the unusual property that their stabilities are limited only by the CFL condition. Moreover, despite the fact that it does not use any flux-limiter or slope-limiter, the Navier-Stokes solver is capable of generating highly accurate shock tube solutions with shock discontinuities being resolved within one mesh interval. An accurate Euler solver also is constructed through another extension. It has many unusual properties, e.g., numerical diffusion at all mesh points can be controlled by a set of local parameters.

Comments on the Diffusive Behavior of Two Upwind Schemes

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and locally one-dimensional finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2.5 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a speedup of 29 over finite volume.

Diffusion Characteristics of Upwind Schemes on Unstructured Triangulations

NASA Technical Reports Server (NTRS)

Wood, William A.; Kleb, William L.

1998-01-01

The diffusive characteristics of two upwind schemes, multi-dimensional fluctuation splitting and dimensionally-split finite volume, are compared for scalar advection-diffusion problems. Algorithms for the two schemes are developed for node-based data representation on median-dual meshes associated with unstructured triangulations in two spatial dimensions. Four model equations are considered: linear advection, non-linear advection, diffusion, and advection-diffusion. Modular coding is employed to isolate the effects of the two approaches for upwind flux evaluation, allowing for head-to-head accuracy and efficiency comparisons. Both the stability of compressive limiters and the amount of artificial diffusion generated by the schemes is found to be grid-orientation dependent, with the fluctuation splitting scheme producing less artificial diffusion than the dimensionally-split finite volume scheme. Convergence rates are compared for the combined advection-diffusion problem, with a speedup of 2-3 seen for fluctuation splitting versus finite volume when solved on the same mesh. However, accurate solutions to problems with small diffusion coefficients can be achieved on coarser meshes using fluctuation splitting rather than finite volume, so that when comparing convergence rates to reach a given accuracy, fluctuation splitting shows a 20-25 speedup over finite volume.

Studies of finite element analysis of composite material structures

NASA Technical Reports Server (NTRS)

Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.

1975-01-01

Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.

Parareal in time 3D numerical solver for the LWR Benchmark neutron diffusion transient model

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

Baudron, Anne-Marie, E-mail: anne-marie.baudron@cea.fr; CEA-DRN/DMT/SERMA, CEN-Saclay, 91191 Gif sur Yvette Cedex; Lautard, Jean-Jacques, E-mail: jean-jacques.lautard@cea.fr

2014-12-15

In this paper we present a time-parallel algorithm for the 3D neutrons calculation of a transient model in a nuclear reactor core. The neutrons calculation consists in numerically solving the time dependent diffusion approximation equation, which is a simplified transport equation. The numerical resolution is done with finite elements method based on a tetrahedral meshing of the computational domain, representing the reactor core, and time discretization is achieved using a θ-scheme. The transient model presents moving control rods during the time of the reaction. Therefore, cross-sections (piecewise constants) are taken into account by interpolations with respect to the velocity ofmore » the control rods. The parallelism across the time is achieved by an adequate use of the parareal in time algorithm to the handled problem. This parallel method is a predictor corrector scheme that iteratively combines the use of two kinds of numerical propagators, one coarse and one fine. Our method is made efficient by means of a coarse solver defined with large time step and fixed position control rods model, while the fine propagator is assumed to be a high order numerical approximation of the full model. The parallel implementation of our method provides a good scalability of the algorithm. Numerical results show the efficiency of the parareal method on large light water reactor transient model corresponding to the Langenbuch–Maurer–Werner benchmark.« less

IFEMS, an Interactive Finite Element Modeling System Using a CAD/CAM System

NASA Technical Reports Server (NTRS)

Mckellip, S.; Schuman, T.; Lauer, S.

1980-01-01

A method of coupling a CAD/CAM system with a general purpose finite element mesh generator is described. The three computer programs which make up the interactive finite element graphics system are discussed.

GENSURF: A mesh generator for 3D finite element analysis of surface and corner cracks in finite thickness plates subjected to mode-1 loadings

NASA Technical Reports Server (NTRS)

Raju, I. S.

1992-01-01

A computer program that generates three-dimensional (3D) finite element models for cracked 3D solids was written. This computer program, gensurf, uses minimal input data to generate 3D finite element models for isotropic solids with elliptic or part-elliptic cracks. These models can be used with a 3D finite element program called surf3d. This report documents this mesh generator. In this manual the capabilities, limitations, and organization of gensurf are described. The procedures used to develop 3D finite element models and the input for and the output of gensurf are explained. Several examples are included to illustrate the use of this program. Several input data files are included with this manual so that the users can edit these files to conform to their crack configuration and use them with gensurf.

A Technique of Treating Negative Weights in WENO Schemes

NASA Technical Reports Server (NTRS)

Shi, Jing; Hu, Changqing; Shu, Chi-Wang

2000-01-01

High order accurate weighted essentially non-oscillatory (WENO) schemes have recently been developed for finite difference and finite volume methods both in structural and in unstructured meshes. A key idea in WENO scheme is a linear combination of lower order fluxes or reconstructions to obtain a high order approximation. The combination coefficients, also called linear weights, are determined by local geometry of the mesh and order of accuracy and may become negative. WENO procedures cannot be applied directly to obtain a stable scheme if negative linear weights are present. Previous strategy for handling this difficulty is by either regrouping of stencils or reducing the order of accuracy to get rid of the negative linear weights. In this paper we present a simple and effective technique for handling negative linear weights without a need to get rid of them.

A contact algorithm for shell problems via Delaunay-based meshing of the contact domain

NASA Astrophysics Data System (ADS)

Kamran, K.; Rossi, R.; Oñate, E.

2013-07-01

The simulation of the contact within shells, with all of its different facets, represents still an open challenge in Computational Mechanics. Despite the effort spent in the development of techniques for the simulation of general contact problems, an all-seasons algorithm applicable to complex shell contact problems is yet to be developed. This work focuses on the solution of the contact between thin shells by using a technique derived from the particle finite element method together with a rotation-free shell triangle. The key concept is to define a discretization of the contact domain (CD) by constructing a finite element mesh of four-noded tetrahedra that describes the potential contact volume. The problem is completed by using an assumed-strain approach to define an elastic contact strain over the CD.

Capturing Multiscale Phenomena via Adaptive Mesh Refinement (AMR) in 2D and 3D Atmospheric Flows

NASA Astrophysics Data System (ADS)

Ferguson, J. O.; Jablonowski, C.; Johansen, H.; McCorquodale, P.; Ullrich, P. A.; Langhans, W.; Collins, W. D.

2017-12-01

Extreme atmospheric events such as tropical cyclones are inherently complex multiscale phenomena. Such phenomena are a challenge to simulate in conventional atmosphere models, which typically use rather coarse uniform-grid resolutions. To enable study of these systems, Adaptive Mesh Refinement (AMR) can provide sufficient local resolution by dynamically placing high-resolution grid patches selectively over user-defined features of interest, such as a developing cyclone, while limiting the total computational burden of requiring such high-resolution globally. This work explores the use of AMR with a high-order, non-hydrostatic, finite-volume dynamical core, which uses the Chombo AMR library to implement refinement in both space and time on a cubed-sphere grid. The characteristics of the AMR approach are demonstrated via a series of idealized 2D and 3D test cases designed to mimic atmospheric dynamics and multiscale flows. In particular, new shallow-water test cases with forcing mechanisms are introduced to mimic the strengthening of tropical cyclone-like vortices and to include simplified moisture and convection processes. The forced shallow-water experiments quantify the improvements gained from AMR grids, assess how well transient features are preserved across grid boundaries, and determine effective refinement criteria. In addition, results from idealized 3D test cases are shown to characterize the accuracy and stability of the non-hydrostatic 3D AMR dynamical core.

A multiscale fixed stress split iterative scheme for coupled flow and poromechanics in deep subsurface reservoirs

NASA Astrophysics Data System (ADS)

Dana, Saumik; Ganis, Benjamin; Wheeler, Mary F.

2018-01-01

In coupled flow and poromechanics phenomena representing hydrocarbon production or CO2 sequestration in deep subsurface reservoirs, the spatial domain in which fluid flow occurs is usually much smaller than the spatial domain over which significant deformation occurs. The typical approach is to either impose an overburden pressure directly on the reservoir thus treating it as a coupled problem domain or to model flow on a huge domain with zero permeability cells to mimic the no flow boundary condition on the interface of the reservoir and the surrounding rock. The former approach precludes a study of land subsidence or uplift and further does not mimic the true effect of the overburden on stress sensitive reservoirs whereas the latter approach has huge computational costs. In order to address these challenges, we augment the fixed-stress split iterative scheme with upscaling and downscaling operators to enable modeling flow and mechanics on overlapping nonmatching hexahedral grids. Flow is solved on a finer mesh using a multipoint flux mixed finite element method and mechanics is solved on a coarse mesh using a conforming Galerkin method. The multiscale operators are constructed using a procedure that involves singular value decompositions, a surface intersections algorithm and Delaunay triangulations. We numerically demonstrate the convergence of the augmented scheme using the classical Mandel's problem solution.

Method of modifying a volume mesh using sheet insertion

DOEpatents

Borden, Michael J [Albuquerque, NM; Shepherd, Jason F [Albuquerque, NM

2006-08-29

A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet insertion. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify (refine) the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of locating a sheet of hexahedral mesh elements, determining a plurality of hexahedral elements within the sheet to refine, shrinking the plurality of elements, and inserting a new sheet of hexahedral elements adjacently to modify the volume mesh. Additionally, another predetermined algorithm using mesh cutting may be followed to modify a volume mesh.

Finite cover method with mortar elements for elastoplasticity problems

NASA Astrophysics Data System (ADS)

Kurumatani, M.; Terada, K.

2005-06-01

Finite cover method (FCM) is extended to elastoplasticity problems. The FCM, which was originally developed under the name of manifold method, has recently been recognized as one of the generalized versions of finite element methods (FEM). Since the mesh for the FCM can be regular and squared regardless of the geometry of structures to be analyzed, structural analysts are released from a burdensome task of generating meshes conforming to physical boundaries. Numerical experiments are carried out to assess the performance of the FCM with such discretization in elastoplasticity problems. Particularly to achieve this accurately, the so-called mortar elements are introduced to impose displacement boundary conditions on the essential boundaries, and displacement compatibility conditions on material interfaces of two-phase materials or on joint surfaces between mutually incompatible meshes. The validity of the mortar approximation is also demonstrated in the elastic-plastic FCM.

Quadrilateral finite element mesh coarsening

DOEpatents

Staten, Matthew L; Dewey, Mark W; Benzley, Steven E

2012-10-16

Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.

Design of an essentially non-oscillatory reconstruction procedure on finite-element type meshes

NASA Technical Reports Server (NTRS)

Abgrall, R.

1991-01-01

An essentially non-oscillatory reconstruction for functions defined on finite-element type meshes was designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a function from its average in the control volumes surrounding the nodes of the mesh. Concerning the first problem, we have studied the behavior of the highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the best stencil for the interpolation. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, because of the very nature of the mesh, the only method that may work is the so called reconstruction via deconvolution method. Unfortunately, it is well suited only for regular meshes as we show, but we also show how to overcome this difficulty. The global method has the expected order of accuracy but is conservative up to a high order quadrature formula only. Some numerical examples are given which demonstrate the efficiency of the method.

Dynamic model of open shell structures buried in poroelastic soils

NASA Astrophysics Data System (ADS)

Bordón, J. D. R.; Aznárez, J. J.; Maeso, O.

2017-08-01

This paper is concerned with a three-dimensional time harmonic model of open shell structures buried in poroelastic soils. It combines the dual boundary element method (DBEM) for treating the soil and shell finite elements for modelling the structure, leading to a simple and efficient representation of buried open shell structures. A new fully regularised hypersingular boundary integral equation (HBIE) has been developed to this aim, which is then used to build the pair of dual BIEs necessary to formulate the DBEM for Biot poroelasticity. The new regularised HBIE is validated against a problem with analytical solution. The model is used in a wave diffraction problem in order to show its effectiveness. It offers excellent agreement for length to thickness ratios greater than 10, and relatively coarse meshes. The model is also applied to the calculation of impedances of bucket foundations. It is found that all impedances except the torsional one depend considerably on hydraulic conductivity within the typical frequency range of interest of offshore wind turbines.

Hexahedral finite element mesh coarsening using pillowing technique

DOEpatents

Staten, Matthew L [Pittsburgh, PA; Woodbury, Adam C [Provo, UT; Benzley, Steven E [Provo, UT; Shepherd, Jason F [Edgewood, NM

2012-06-05

A techniques for coarsening a hexahedral mesh is described. The technique includes identifying a coarsening region within a hexahedral mesh to be coarsened. A boundary sheet of hexahedral elements is inserted into the hexahedral mesh around the coarsening region. A column of hexahedral elements is identified within the boundary sheet. The column of hexahedral elements is collapsed to create an extraction sheet of hexahedral elements contained within the coarsening region. Then, the extraction sheet of hexahedral elements is extracted to coarsen the hexahedral mesh.

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

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 finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite 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 Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

Application of Parallel Adjoint-Based Error Estimation and Anisotropic Grid Adaptation for Three-Dimensional Aerospace Configurations

NASA Technical Reports Server (NTRS)

Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.

2005-01-01

This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge in order to achieve the requested drag tolerance. Although further adaptation was required to meet the requested tolerance, no further cycles were computed in order to avoid large discrepancies between the surface mesh spacing and the refined field spacing.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

3D CSEM inversion based on goal-oriented adaptive finite element method

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with complex geological scenarios by applying it to the inversion of synthetic marine controlled source EM data generated for a complex 3D offshore model with significant seafloor topography.

Design, Generation and Tooth Contact Analysis (TCA) of Asymmetric Face Gear Drive With Modified Geometry

NASA Technical Reports Server (NTRS)

Litvin, Faydor L.; Fuentes, Alfonso; Hawkins, J. M.; Handschuh, Robert F.

2001-01-01

A new type of face gear drive for application in transmissions, particularly in helicopters, has been developed. The new geometry differs from the existing geometry by application of asymmetric profiles and double-crowned pinion of the face gear mesh. The paper describes the computerized design, simulation of meshing and contact, and stress analysis by finite element method. Special purpose computer codes have been developed to conduct the analysis. The analysis of this new type of face gear is illustrated with a numerical example.

A multi-block adaptive solving technique based on lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Zhang, Yang; Xie, Jiahua; Li, Xiaoyue; Ma, Zhenghai; Zou, Jianfeng; Zheng, Yao

2018-05-01

In this paper, a CFD parallel adaptive algorithm is self-developed by combining the multi-block Lattice Boltzmann Method (LBM) with Adaptive Mesh Refinement (AMR). The mesh refinement criterion of this algorithm is based on the density, velocity and vortices of the flow field. The refined grid boundary is obtained by extending outward half a ghost cell from the coarse grid boundary, which makes the adaptive mesh more compact and the boundary treatment more convenient. Two numerical examples of the backward step flow separation and the unsteady flow around circular cylinder demonstrate the vortex structure of the cold flow field accurately and specifically.

Mixed finite-difference scheme for analysis of simply supported thick plates.

NASA Technical Reports Server (NTRS)

Noor, A. K.

1973-01-01

A mixed finite-difference scheme is presented for the stress and free vibration analysis of simply supported nonhomogeneous and layered orthotropic thick plates. The analytical formulation is based on the linear, three-dimensional theory of orthotropic elasticity and a Fourier approach is used to reduce the governing equations to six first-order ordinary differential equations in the thickness coordinate. The governing equations possess a symmetric coefficient matrix and are free of derivatives of the elastic characteristics of the plate. In the finite difference discretization two interlacing grids are used for the different fundamental unknowns in such a way as to reduce both the local discretization error and the bandwidth of the resulting finite-difference field equations. Numerical studies are presented for the effects of reducing the interior and boundary discretization errors and of mesh refinement on the accuracy and convergence of solutions. It is shown that the proposed scheme, in addition to a number of other advantages, leads to highly accurate results, even when a small number of finite difference intervals is used.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, Michael J.; Berger, Marsha J.; Murman, Scott M.

2003-01-01

The proposed paper presents a variety novel uses of Space-Filling-Curves (SFCs) for Cartesian mesh methods in 0. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, most are applicable on general body-fitted meshes -both structured and unstructured. We demonstrate the use of single O(N log N) SFC-based reordering to produce single-pass (O(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations. Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 512 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 10% of ideal even with only around 50,000 cells in each subdomain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with O(max(M,N)) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for finite-difference-based gradient design methods.

A unified monolithic approach for multi-fluid flows and fluid-structure interaction using the Particle Finite Element Method with fixed mesh

NASA Astrophysics Data System (ADS)

Becker, P.; Idelsohn, S. R.; Oñate, E.

2015-06-01

This paper describes a strategy to solve multi-fluid and fluid-structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (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.

System and method for producing metallic iron nodules

DOEpatents

Bleifuss, Rodney L [Grand Rapids, MN; Englund, David J [Bovey, MN; Iwasaki, Iwao [Grand Rapids, MN; Lindgren, Andrew J [Grand Rapids, MN; Kiesel, Richard F [Hibbing, MN

2011-09-20

A method for producing metallic iron nodules by assembling a shielding entry system to introduce coarse carbonaceous material greater than 6 mesh in to the furnace atmosphere at location(s) where the temperature of the furnace atmosphere adjacent at least partially reduced reducible iron bearing material is between about 2200 and 2650.degree. F. (1200 and 1450.degree. C.), the shielding entry system adapted to inhibit emission of infrared radiation from the furnace atmosphere and seal the furnace atmosphere from exterior atmosphere while introducing coarse carbonaceous material greater than 6 mesh into the furnace to be distributed over the at least partially reduced reducible iron bearing material, and heating the covered at least partially reduced reducible iron bearing material in a fusion atmosphere to assist in fusion and inhibit reoxidation of the reduced material during fusion to assist in fusion and inhibit reoxidation of the reduced material in forming metallic iron nodules.

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.

[Establishment of a 3D finite element model of human skull using MSCT images and mimics software].

PubMed

Huang, Ping; Li, Zheng-dong; Shao, Yu; Zou, Dong-hua; Liu, Ning-guo; Li, Li; Chen, Yuan-yuan; Wan, Lei; Chen, Yi-jiu

2011-02-01

To establish a human 3D finite element skull model, and to explore its value in biomechanics analysis. The cadaveric head was scanned and then 3D skull model was created using Mimics software based on 2D CT axial images. The 3D skull model was optimized by preprocessor along with creation of the surface and volume meshes. The stress changes, after the head was struck by an object or the head hit the ground directly, were analyzed using ANSYS software. The original 3D skull model showed a large number of triangles with a poor quality and high similarity with the real head, while the optimized model showed high quality surface and volume meshes with a small number of triangles comparatively. The model could show the local and global stress changes effectively. The human 3D skull model can be established using MSCT and Mimics software and provides a good finite element model for biomechanics analysis. This model may also provide a base for the study of head stress changes following different forces.

The nonlinear modified equation approach to analyzing finite difference schemes

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1981-01-01

The nonlinear modified equation approach is taken in this paper to analyze the generalized Lax-Wendroff explicit scheme approximation to the unsteady one- and two-dimensional equations of gas dynamics. Three important applications of the method are demonstrated. The nonlinear modified equation analysis is used to (1) generate higher order accurate schemes, (2) obtain more accurate estimates of the discretization error for nonlinear systems of partial differential equations, and (3) generate an adaptive mesh procedure for the unsteady gas dynamic equations. Results are obtained for all three areas. For the adaptive mesh procedure, mesh point requirements for equal resolution of discontinuities were reduced by a factor of five for a 1-D shock tube problem solved by the explicit MacCormack scheme.

Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement

DOE PAGES

Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...

2013-12-10

A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less

A computer program to generate two-dimensional grids about airfoils and other shapes by the use of Poisson's equation

NASA Technical Reports Server (NTRS)

Sorenson, R. L.

1980-01-01

A method for generating two dimensional finite difference grids about airfoils and other shapes by the use of the Poisson differential equation is developed. The inhomogeneous terms are automatically chosen such that two important effects are imposed on the grid at both the inner and outer boundaries. The first effect is control of the spacing between mesh points along mesh lines intersecting the boundaries. The second effect is control of the angles with which mesh lines intersect the boundaries. A FORTRAN computer program has been written to use this method. A description of the program, a discussion of the control parameters, and a set of sample cases are included.

Texturing of continuous LOD meshes with the hierarchical texture atlas

NASA Astrophysics Data System (ADS)

Birkholz, Hermann

2006-02-01

For the rendering of detailed virtual environments, trade-offs have to be made between image quality and rendering time. An immersive experience of virtual reality always demands high frame-rates with the best reachable image qual-ity. Continuous Level of Detail (cLoD) triangle-meshes provide an continuous spectrum of detail for a triangle mesh that can be used to create view-dependent approximations of the environment in real-time. This enables the rendering with a constant number of triangles and thus with constant frame-rates. Normally the construction of such cLoD mesh representations leads to the loss of all texture information of the original mesh. To overcome this problem, a parameter domain can be created, in order to map the surface properties (colour, texture, normal) to it. This parameter domain can be used to map the surface properties back to arbitrary approximations of the original mesh. The parameter domain is often a simplified version of the mesh to be parameterised. This limits the reachable simplification to the domain mesh which has to map the surface of the original mesh with the least possible stretch. In this paper, a hierarchical domain mesh is presented, that scales between very coarse domain meshes and good property-mapping.

Laws, causation and dynamics at different levels.

PubMed

Butterfield, Jeremy

2012-02-06

I have two main aims. The first is general, and more philosophical (§2). The second is specific, and more closely related to physics (§§3 and 4). The first aim is to state my general views about laws and causation at different 'levels'. The main task is to understand how the higher levels sustain notions of law and causation that 'ride free' of reductions to the lower level or levels. I endeavour to relate my views to those of other symposiasts. The second aim is to give a framework for describing dynamics at different levels, emphasizing how the various levels' dynamics can mesh or fail to mesh. This framework is essentially that of elementary dynamical systems theory. The main idea will be, for simplicity, to work with just two levels, dubbed 'micro' and 'macro', which are related by coarse-graining. I use this framework to describe, in part, the first four of Ellis' five types of top-down causation.

Free Wake Analysis of Helicopter Rotor Blades in Hover Using a Finite Volume Technique

DTIC Science & Technology

1988-10-01

inboard, and root) which were replaced by a far wake model after four revolutions. Murman and Stremel 1121 calculated j two-dimensional unsteady wake...distributed to a fixed mesh, on which the velocities were calculated by a finite difference solution of Laplace’s equation. Stremel [131 applied this two...Analysis of a Hovering Rotor," Vertica, Vol. 6, No. 2, 1982. 12. Murman, E.M., and Stremel , P.M., "A Vortex Wake Capturing Method Po- tential Flow

The Space-Time Conservative Schemes for Large-Scale, Time-Accurate Flow Simulations with Tetrahedral Meshes

NASA Technical Reports Server (NTRS)

Venkatachari, Balaji Shankar; Streett, Craig L.; Chang, Chau-Lyan; Friedlander, David J.; Wang, Xiao-Yen; Chang, Sin-Chung

2016-01-01

Despite decades of development of unstructured mesh methods, high-fidelity time-accurate simulations are still predominantly carried out on structured, or unstructured hexahedral meshes by using high-order finite-difference, weighted essentially non-oscillatory (WENO), or hybrid schemes formed by their combinations. In this work, the space-time conservation element solution element (CESE) method is used to simulate several flow problems including supersonic jet/shock interaction and its impact on launch vehicle acoustics, and direct numerical simulations of turbulent flows using tetrahedral meshes. This paper provides a status report for the continuing development of the space-time conservation element solution element (CESE) numerical and software framework under the Revolutionary Computational Aerosciences (RCA) project. Solution accuracy and large-scale parallel performance of the numerical framework is assessed with the goal of providing a viable paradigm for future high-fidelity flow physics simulations.

Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary

PubMed Central

Yang, Shengfeng; Chen, Youping

2015-01-01

In this paper, we present the development of a concurrent atomistic–continuum (CAC) methodology for simulation of the grain boundary (GB) structures and their interaction with other defects in ionic materials. Simulation results show that the CAC simulation allows a smooth passage of cracks through the atomistic–continuum interface without the need for additional constitutive rules or special numerical treatment; both the atomic-scale structures and the energies of the four different [001] tilt GBs in bi-crystal strontium titanate obtained by CAC compare well with those obtained by existing experiments and density function theory calculations. Although 98.4% of the degrees of freedom of the simulated atomistic system have been eliminated in a coarsely meshed finite-element region, the CAC results, including the stress–strain responses, the GB–crack interaction mechanisms and the effect of the interaction on the fracture strength, are comparable with that of all-atom molecular dynamics simulation results. In addition, CAC simulation results show that the GB–crack interaction has a significant effect on the fracture behaviour of bi-crystal strontium titanate; not only the misorientation angle but also the atomic-level details of the GB structure influence the effect of the GB on impeding crack propagation. PMID:25792957

Concurrent atomistic and continuum simulation of bi-crystal strontium titanate with tilt grain boundary.

PubMed

Yang, Shengfeng; Chen, Youping

2015-03-08

In this paper, we present the development of a concurrent atomistic-continuum (CAC) methodology for simulation of the grain boundary (GB) structures and their interaction with other defects in ionic materials. Simulation results show that the CAC simulation allows a smooth passage of cracks through the atomistic-continuum interface without the need for additional constitutive rules or special numerical treatment; both the atomic-scale structures and the energies of the four different [001] tilt GBs in bi-crystal strontium titanate obtained by CAC compare well with those obtained by existing experiments and density function theory calculations. Although 98.4% of the degrees of freedom of the simulated atomistic system have been eliminated in a coarsely meshed finite-element region, the CAC results, including the stress-strain responses, the GB-crack interaction mechanisms and the effect of the interaction on the fracture strength, are comparable with that of all-atom molecular dynamics simulation results. In addition, CAC simulation results show that the GB-crack interaction has a significant effect on the fracture behaviour of bi-crystal strontium titanate; not only the misorientation angle but also the atomic-level details of the GB structure influence the effect of the GB on impeding crack propagation.

Modeling Progressive Failure of Bonded Joints Using a Single Joint Finite Element

NASA Technical Reports Server (NTRS)

Stapleton, Scott E.; Waas, Anthony M.; Bednarcyk, Brett A.

2010-01-01

Enhanced finite elements are elements with an embedded analytical solution which can capture detailed local fields, enabling more efficient, mesh-independent finite element analysis. In the present study, an enhanced finite element 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 finite element. This single finite element thus captures the detailed stress and strain fields within the bonded joint, but it can function within a broader structural finite element 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 finite element results.

Dynamic Analysis of Geared Rotors by Finite Elements

NASA Technical Reports Server (NTRS)

Kahraman, A.; Ozguven, H. Nevzat; Houser, D. R.; Zakrajsek, J. J.

1992-01-01

A finite element model of a geared rotor system on flexible bearings has been developed. The model includes the rotary inertia of on shaft elements, the axial loading on shafts, flexibility and damping of bearings, material damping of shafts and the stiffness and the damping of gear mesh. The coupling between the torsional and transverse vibrations of gears were considered in the model. A constant mesh stiffness was assumed. The analysis procedure can be used for forced vibration analysis geared rotors by calculating the critical speeds and determining the response of any point on the shafts to mass unbalances, geometric eccentricities of gears, and displacement transmission error excitation at the mesh point. The dynamic mesh forces due to these excitations can also be calculated. The model has been applied to several systems for the demonstration of its accuracy and for studying the effect of bearing compliances on system dynamics.

An automatic granular structure generation and finite element analysis of heterogeneous semi-solid materials

NASA Astrophysics Data System (ADS)

Sharifi, Hamid; Larouche, Daniel

2015-09-01

The quality of cast metal products depends on the capacity of the semi-solid metal to sustain the stresses generated during the casting. Predicting the evolution of these stresses with accuracy in the solidification interval should be highly helpful to avoid the formation of defects like hot tearing. This task is however very difficult because of the heterogeneous nature of the material. In this paper, we propose to evaluate the mechanical behaviour of a metal during solidification using a mesh generation technique of the heterogeneous semi-solid material for a finite element analysis at the microscopic level. This task is done on a two-dimensional (2D) domain in which the granular structure of the solid phase is generated surrounded by an intergranular and interdendritc liquid phase. Some basic solid grains are first constructed and projected in the 2D domain with random orientations and scale factors. Depending on their orientation, the basic grains are combined to produce larger grains or separated by a liquid film. Different basic grain shapes can produce different granular structures of the mushy zone. As a result, using this automatic grain generation procedure, we can investigate the effect of grain shapes and sizes on the thermo-mechanical behaviour of the semi-solid material. The granular models are automatically converted to the finite element meshes. The solid grains and the liquid phase are meshed properly using quadrilateral elements. This method has been used to simulate the microstructure of a binary aluminium-copper alloy (Al-5.8 wt% Cu) when the fraction solid is 0.92. Using the finite element method and the Mie-Grüneisen equation of state for the liquid phase, the transient mechanical behaviour of the mushy zone under tensile loading has been investigated. The stress distribution and the bridges, which are formed during the tensile loading, have been detected.

An Approach To Using All Location Tagged Numerical Data Sets As Continuous Fields With User-Assigned Continuity As A Basis For User-Driven Data Assimilation

NASA Astrophysics Data System (ADS)

Vernon, F.; Arrott, M.; Orcutt, J. A.; Mueller, C.; Case, J.; De Wardener, G.; Kerfoot, J.; Schofield, O.

2013-12-01

Any approach sophisticated enough to handle a variety of data sources and scale, yet easy enough to promote wide use and mainstream adoption is required to address the following mappings: - From the authored domain of observation to the requested domain of interest; - From the authored spatiotemporal resolution to the requested resolution; and - From the representation of data placed on wide variety of discrete mesh types to the use of that data as a continuos field with a selectable continuity. The Open Geospatial Consortium's (OGC) Reference Model[1] with its direct association with the ISO 19000 series standards provides a comprehensive foundation to represent all data on any type of mesh structure, aka "Discrete Coverages". The Reference Model also provides the specification for the core operations required to utilize any Discrete Coverage. The FEniCS Project[2] provides a comprehensive model for how to represent the Basis Functions on mesh structures as "Degrees of Freedom" to present discrete data as continuous fields with variable continuity. In this talk, we will present the research and development the OOI Cyberinfrastructure Project is pursuing to integrate these approaches into a comprehensive Application Programming Interface (API) to author, acquire and operate on the broad range of data formulation from time series, trajectories and tables through to time variant finite difference grids and finite element meshes.

ɛ-connectedness, finite approximations, shape theory and coarse graining in hyperspaces

NASA Astrophysics Data System (ADS)

Alonso-Morón, Manuel; Cuchillo-Ibanez, Eduardo; Luzón, Ana

2008-12-01

We use upper semifinite hyperspaces of compacta to describe ε-connectedness and to compute homology from finite approximations. We find a new connection between ε-connectedness and the so-called Shape Theory. We construct a geodesically complete R-tree, by means of ε-components at different resolutions, whose behavior at infinite captures the topological structure of the space of components of a given compact metric space. We also construct inverse sequences of finite spaces using internal finite approximations of compact metric spaces. These sequences can be converted into inverse sequences of polyhedra and simplicial maps by means of what we call the Alexandroff-McCord correspondence. This correspondence allows us to relate upper semifinite hyperspaces of finite approximation with the Vietoris-Rips complexes of such approximations at different resolutions. Two motivating examples are included in the introduction. We propose this procedure as a different mathematical foundation for problems on data analysis. This process is intrinsically related to the methodology of shape theory. This paper reinforces Robins’s idea of using methods from shape theory to compute homology from finite approximations.

Effects of tooth profile modification on dynamic responses of a high speed gear-rotor-bearing system

NASA Astrophysics Data System (ADS)

Hu, Zehua; Tang, Jinyuan; Zhong, Jue; Chen, Siyu; Yan, Haiyan

2016-08-01

A finite element node dynamic model of a high speed gear-rotor-bearing system considering the time-varying mesh stiffness, backlash, gyroscopic effect and transmission error excitation is developed. Different tooth profile modifications are introduced into the gear pair and corresponding time-varying mesh stiffness curves are obtained. Effects of the tooth profile modification on mesh stiffness are analyzed, and the natural frequencies and mode shapes of the gear-rotor-bearing transmission system are given. The dynamic responses with respect to a wide input speed region including dynamic factor, vibration amplitude near the bearing and dynamic transmission error are obtained by introducing the time-varying mesh stiffness in different tooth profile modification cases into the gear-rotor-bearing dynamic system. Effects of the tooth profile modification on the dynamic responses are studied in detail. The numerical simulation results show that both the short profile modification and the long profile modification can affect the mutation of the mesh stiffness when the number of engaging tooth pairs changes. A short profile modification with an appropriate modification amount can improve the dynamic property of the system in certain work condition.

Method of generating a surface mesh

DOEpatents

Shepherd, Jason F [Albuquerque, NM; Benzley, Steven [Provo, UT; Grover, Benjamin T [Tracy, CA

2008-03-04

A method and machine-readable medium provide a technique to generate and modify a quadrilateral finite element surface mesh using dual creation and modification. After generating a dual of a surface (mesh), a predetermined algorithm may be followed to generate and modify a surface mesh of quadrilateral elements. The predetermined algorithm may include the steps of generating two-dimensional cell regions in dual space, determining existing nodes in primal space, generating new nodes in the dual space, and connecting nodes to form the quadrilateral elements (faces) for the generated and modifiable surface mesh.

OpenGl Visualization Tool and Library Version: 1.0

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

2010-06-22

GLVis is an OpenGL tool for visualization of finite element meshes and functions. When started without any options, GLVis starts a server, which waits for a socket connections and visualizes any recieved data. This way the results of simulations on a remote (parallel) machine can be visualized on the lical user desktop. GLVis can also be used to visualize a mesh with or without a finite element function (solution). It can run a batch sequence of commands (GLVis scripts), or display previously saved socket streams.

Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells

DTIC Science & Technology

1988-11-30

where mesh refinement will prove useful. In fact, the deviation of a bilinear element from a smooth shell midsurface can be related to the angle between...comparisons with nonadaptive meshes. Conclusions and further discussions are given in Section 6. -5- 2. FINITE ELEMENT FORMULATION The shape of the midsurface ...8217 22 , and e3 is defined so that e, and e2 are tangent to the midsurface and rotate with the element; 2. for each node, a triad b i is defined so that

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

Transfer impedance measurements of the space shuttle Solid Rocket Motor (SRM) joints, wire meshes and a carbon graphite motor case

NASA Technical Reports Server (NTRS)

Papazian, Peter B.; Perala, Rodney A.; Curry, John D.; Lankford, Alan B.; Keller, J. David

1988-01-01

Using three different current injection methods and a simple voltage probe, transfer impedances for Solid Rocket Motor (SRM) joints, wire meshes, aluminum foil, Thorstrand and a graphite composite motor case were measured. In all cases, the surface current distribution for the particular current injection device was calculated analytically or by finite difference methods. The results of these calculations were used to generate a geometric factor which was the ratio of total injected current to surface current density. The results were validated in several ways. For wire mesh measurements, results showed good agreement with calculated results for a 14 by 18 Al screen. SRM joint impedances were independently verified. The filiment wound case measurement results were validated only to the extent that their curve shape agrees with the expected form of transfer impedance for a homogeneous slab excited by a plane wave source.

Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

NASA Astrophysics Data System (ADS)

Pathak, Harshavardhana S.; Shukla, Ratnesh K.

2016-08-01

A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of discontinuous propagating shocks with simultaneous resolution of smooth yet complex small scale unsteady flow features to an exceptional detail.

Transferable Coarse-Grained Models for Ionic Liquids.

PubMed

Wang, Yanting; Feng, Shulu; Voth, Gregory A

2009-04-14

The effective force coarse-graining (EF-CG) method was applied to the imidazolium-based nitrate ionic liquids with various alkyl side-chain lengths. The nonbonded EF-CG forces for the ionic liquid with a short side chain were extended to generate the nonbonded forces for the ionic liquids with longer side chains. The EF-CG force fields for the ionic liquids exhibit very good transferability between different systems at various temperatures and are suitable for investigating the mesoscopic structural properties of this class of ionic liquids. The good additivity and ease of manipulation of the EF-CG force fields can allow for an inverse design methodology of ionic liquids at the coarse-grained level. With the EF-CG force field, the molecular dynamics (MD) simulation at a very large scale has been performed to check the significance of finite size effects on the structural properties. From these MD simulation results, it can be concluded that the finite size effect on the phenomenon of ionic liquid spatial heterogeneity (Wang, Y.; Voth, G. A. J. Am. Chem. Soc. 2005, 127, 12192) is small and that this phenomenon is indeed a nanostructural behavior which leads to the experimentally observed mesoscopic heterogeneous structure of ionic liquids.

MOAB : a mesh-oriented database.

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

Tautges, Timothy James; Ernst, Corey; Stimpson, Clint

A finite element mesh is used to decompose a continuous domain into a discretized representation. The finite element method solves PDEs on this mesh by modeling complex functions as a set of simple basis functions with coefficients at mesh vertices and prescribed continuity between elements. The mesh is one of the fundamental types of data linking the various tools in the FEA process (mesh generation, analysis, visualization, etc.). Thus, the representation of mesh data and operations on those data play a very important role in FEA-based simulations. MOAB is a component for representing and evaluating mesh data. MOAB can storemore » structured and unstructured mesh, consisting of elements in the finite element 'zoo'. The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh. MOAB is optimized for efficiency in space and time, based on access to mesh in chunks rather than through individual entities, while also versatile enough to support individual entity access. The MOAB data model consists of a mesh interface instance, mesh entities (vertices and elements), sets, and tags. Entities are addressed through handles rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms is a powerful yet simple interface for representing metadata or application-specific data. For example, sets and tags can be used together to describe geometric topology, boundary condition, and inter-processor interface groupings in a mesh. MOAB is used in several ways in various applications. MOAB serves as the underlying mesh data representation in the VERDE mesh verification code. MOAB can also be used as a mesh input mechanism, using mesh readers included with MOAB, or as a translator between mesh formats, using readers and writers included with MOAB. The remainder of this report is organized as follows. Section 2, 'Getting Started', provides a few simple examples of using MOAB to perform simple tasks on a mesh. Section 3 discusses the MOAB data model in more detail, including some aspects of the implementation. Section 4 summarizes the MOAB function API. Section 5 describes some of the tools included with MOAB, and the implementation of mesh readers/writers for MOAB. Section 6 contains a brief description of MOAB's relation to the TSTT mesh interface. Section 7 gives a conclusion and future plans for MOAB development. Section 8 gives references cited in this report. A reference description of the full MOAB API is contained in Section 9.« less

a Non-Overlapping Discretization Method for Partial Differential Equations

NASA Astrophysics Data System (ADS)

Rosas-Medina, A.; Herrera, I.

2013-05-01

Mathematical models of many systems of interest, including very important continuous systems of Engineering and Science, lead to a great variety of partial differential equations whose solution methods are based on the computational processing of large-scale algebraic systems. Furthermore, the incredible expansion experienced by the existing computational hardware and software has made amenable to effective treatment problems of an ever increasing diversity and complexity, posed by engineering and scientific applications. The emergence of parallel computing prompted on the part of the computational-modeling community a continued and systematic effort with the purpose of harnessing it for the endeavor of solving boundary-value problems (BVPs) of partial differential equations. Very early after such an effort began, it was recognized that domain decomposition methods (DDM) were the most effective technique for applying parallel computing to the solution of partial differential equations, since such an approach drastically simplifies the coordination of the many processors that carry out the different tasks and also reduces very much the requirements of information-transmission between them. Ideally, DDMs intend producing algorithms that fulfill the DDM-paradigm; i.e., such that "the global solution is obtained by solving local problems defined separately in each subdomain of the coarse-mesh -or domain-decomposition-". Stated in a simplistic manner, the basic idea is that, when the DDM-paradigm is satisfied, full parallelization can be achieved by assigning each subdomain to a different processor. When intensive DDM research began much attention was given to overlapping DDMs, but soon after attention shifted to non-overlapping DDMs. This evolution seems natural when the DDM-paradigm is taken into account: it is easier to uncouple the local problems when the subdomains are separated. However, an important limitation of non-overlapping domain decompositions, as that concept is usually understood today, is that interface nodes are shared by two or more subdomains of the coarse-mesh and, therefore, even non-overlapping DDMs are actually overlapping when seen from the perspective of the nodes used in the discretization. In this talk we present and discuss a discretization method in which the nodes used are non-overlapping, in the sense that each one of them belongs to one and only one subdomain of the coarse-mesh.

Mesh morphing for finite element analysis of implant positioning in cementless total hip replacements.

PubMed

Bah, Mamadou T; Nair, Prasanth B; Browne, Martin

2009-12-01

Finite element (FE) analysis of the effect of implant positioning on the performance of cementless total hip replacements (THRs) requires the generation of multiple meshes to account for positioning variability. This process can be labour intensive and time consuming as CAD operations are needed each time a specific orientation is to be analysed. In the present work, a mesh morphing technique is developed to automate the model generation process. The volume mesh of a baseline femur with the implant in a nominal position is deformed as the prosthesis location is varied. A virtual deformation field, obtained by solving a linear elasticity problem with appropriate boundary conditions, is applied. The effectiveness of the technique is evaluated using two metrics: the percentages of morphed elements exceeding an aspect ratio of 20 and an angle of 165 degrees between the adjacent edges of each tetrahedron. Results show that for 100 different implant positions, the first and second metrics never exceed 3% and 3.5%, respectively. To further validate the proposed technique, FE contact analyses are conducted using three selected morphed models to predict the strain distribution in the bone and the implant micromotion under joint and muscle loading. The entire bone strain distribution is well captured and both percentages of bone volume with strain exceeding 0.7% and bone average strains are accurately computed. The results generated from the morphed mesh models correlate well with those for models generated from scratch, increasing confidence in the methodology. This morphing technique forms an accurate and efficient basis for FE based implant orientation and stability analysis of cementless hip replacements.

Three new models for evaluation of standard involute spur gear mesh stiffness

NASA Astrophysics Data System (ADS)

Liang, Xihui; Zhang, Hongsheng; Zuo, Ming J.; Qin, Yong

2018-02-01

Time-varying mesh stiffness is one of the main internal excitation sources of gear dynamics. Accurate evaluation of gear mesh stiffness is crucial for gear dynamic analysis. This study is devoted to developing new models for spur gear mesh stiffness evaluation. Three models are proposed. The proposed model 1 can give very accurate mesh stiffness result but the gear bore surface must be assumed to be rigid. Enlighted by the proposed model 1, our research discovers that the angular deflection pattern of the gear bore surface of a pair of meshing gears under a constant torque basically follows a cosine curve. Based on this finding, two other models are proposed. The proposed model 2 evaluates gear mesh stiffness by using angular deflections at different circumferential angles of an end surface circle of the gear bore. The proposed model 3 requires using only the angular deflection at an arbitrary circumferential angle of an end surface circle of the gear bore but this model can only be used for a gear with the same tooth profile among all teeth. The proposed models are accurate in gear mesh stiffness evaluation and easy to use. Finite element analysis is used to validate the accuracy of the proposed models.

Iterative methods for elliptic finite element equations on general meshes

NASA Technical Reports Server (NTRS)

Nicolaides, R. A.; Choudhury, Shenaz

1986-01-01

Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.

Modelling the oscillations of the thermocline in a lake by means of a fully consistent and conservative 3D finite-element model with a vertically adaptive mesh

NASA Astrophysics Data System (ADS)

Delandmeter, Philippe; Lambrechts, Jonathan; Vallaeys, Valentin; Naithani, Jaya; Remacle, Jean-François; Legat, Vincent; Deleersnijder, Eric

2017-04-01

Vertical discretisation is crucial in the modelling of lake thermocline oscillations. For finite element methods, a simple way to increase the resolution close to the oscillating thermocline is to use vertical adaptive coordinates. With an Arbitrary Lagrangian-Eulerian (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 finite element 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 finite element 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 one-dimensional numerical ocean models. Ocean Modelling, 6:51-81, 2004. Richard Hofmeister, Hans Burchard and Jean-Marie Beckers. Non-uniform adaptive vertical grids for 3d numerical ocean models. Ocean Modelling, 33:70-86, 2010. Jaya Naithani, Eric Deleersnijder and Pierre-Denis Plisnier. Origin of intraseasonal variability in Lake Tanganyika. Geophysical Research Letters, 29(23), doi:10.1029/2002GL015843, 2002.

Hierarchical coarse-graining transform.

PubMed

Pancaldi, Vera; King, Peter R; Christensen, Kim

2009-03-01

We present a hierarchical transform that can be applied to Laplace-like differential equations such as Darcy's equation for single-phase flow in a porous medium. A finite-difference discretization scheme is used to set the equation in the form of an eigenvalue problem. Within the formalism suggested, the pressure field is decomposed into an average value and fluctuations of different kinds and at different scales. The application of the transform to the equation allows us to calculate the unknown pressure with a varying level of detail. A procedure is suggested to localize important features in the pressure field based only on the fine-scale permeability, and hence we develop a form of adaptive coarse graining. The formalism and method are described and demonstrated using two synthetic toy problems.

The use of supercomputer modelling of high-temperature failure in pipe weldments to optimize weld and heat affected zone materials property selection

NASA Astrophysics Data System (ADS)

Wang, Z. P.; Hayhurst, D. R.

1994-07-01

The creep deformation and damage evolution in a pipe weldment has been modeled by using the finite-element continuum damage mechanics (CDM) method. The finite-element CDM computer program DAMAGE XX has been adapted to run with increased speed on a Cray XMP/416 supercomputer. Run times are sufficiently short (20 min) to permit many parametric studies to be carried out on vessel lifetimes for different weld and heat affected zone (HAZ) materials. Finite-element mesh sensitivity was studied first in order to select a mesh capable of correctly predicting experimentally observed results using at least possible computer time. A study was then made of the effect on the lifetime of a butt welded vessel of each of the commomly measured material parameters for the weld and HAZ materials. Forty different ferritic steel welded vessels were analyzed for a constant internal pressure of 45.5 MPa at a temperature of 565 C; each vessel having the same parent pipe material but different weld and HAZ materials. A lifetime improvement has been demonstrated of 30% over that obtained for the initial materials property data. A methodology for weldment design has been established which uses supercomputer-based CDM analysis techniques; it is quick to use, provides accurate results, and is a viable design tool.

Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, T.; Lou, J.; Katz, D.

1997-01-01

In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.

Algebraic multigrid preconditioning within parallel finite-element solvers for 3-D electromagnetic modelling problems in geophysics

NASA Astrophysics Data System (ADS)

Koldan, Jelena; Puzyrev, Vladimir; de la Puente, Josep; Houzeaux, Guillaume; Cela, José María

2014-06-01

We present an elaborate preconditioning scheme for Krylov subspace methods which has been developed to improve the performance and reduce the execution time of parallel node-based finite-element (FE) solvers for 3-D electromagnetic (EM) numerical modelling in exploration geophysics. This new preconditioner is based on algebraic multigrid (AMG) that uses different basic relaxation methods, such as Jacobi, symmetric successive over-relaxation (SSOR) and Gauss-Seidel, as smoothers and the wave front algorithm to create groups, which are used for a coarse-level generation. We have implemented and tested this new preconditioner within our parallel nodal FE solver for 3-D forward problems in EM induction geophysics. We have performed series of experiments for several models with different conductivity structures and characteristics to test the performance of our AMG preconditioning technique when combined with biconjugate gradient stabilized method. The results have shown that, the more challenging the problem is in terms of conductivity contrasts, ratio between the sizes of grid elements and/or frequency, the more benefit is obtained by using this preconditioner. Compared to other preconditioning schemes, such as diagonal, SSOR and truncated approximate inverse, the AMG preconditioner greatly improves the convergence of the iterative solver for all tested models. Also, when it comes to cases in which other preconditioners succeed to converge to a desired precision, AMG is able to considerably reduce the total execution time of the forward-problem code-up to an order of magnitude. Furthermore, the tests have confirmed that our AMG scheme ensures grid-independent rate of convergence, as well as improvement in convergence regardless of how big local mesh refinements are. In addition, AMG is designed to be a black-box preconditioner, which makes it easy to use and combine with different iterative methods. Finally, it has proved to be very practical and efficient in the parallel context.

3D hierarchical interface-enriched finite element method: Implementation and applications

NASA Astrophysics Data System (ADS)

Soghrati, Soheil; Ahmadian, Hossein

2015-10-01

A hierarchical interface-enriched finite element method (HIFEM) is proposed for the mesh-independent treatment of 3D problems with intricate morphologies. The HIFEM implements a recursive algorithm for creating enrichment functions that capture gradient discontinuities in nonconforming finite elements cut by arbitrary number and configuration of materials interfaces. The method enables the mesh-independent simulation of multiphase problems with materials interfaces that are in close proximity or contact while providing a straightforward general approach for evaluating the enrichments. In this manuscript, we present a detailed discussion on the implementation issues and required computational geometry considerations associated with the HIFEM approximation of thermal and mechanical responses of 3D problems. A convergence study is provided to investigate the accuracy and convergence rate of the HIFEM and compare them with standard FEM benchmark solutions. We will also demonstrate the application of this mesh-independent method for simulating the thermal and mechanical responses of two composite materials systems with complex microstructures.

A Modeling Approach for Burn Scar Assessment Using Natural Features and Elastic Property

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

Tsap, L V; Zhang, Y; Goldgof, D B

2004-04-02

A modeling approach is presented for quantitative burn scar assessment. Emphases are given to: (1) constructing a finite element model from natural image features with an adaptive mesh, and (2) quantifying the Young's modulus of scars using the finite element model and the regularization method. A set of natural point features is extracted from the images of burn patients. A Delaunay triangle mesh is then generated that adapts to the point features. A 3D finite element model is built on top of the mesh with the aid of range images providing the depth information. The Young's modulus of scars ismore » quantified with a simplified regularization functional, assuming that the knowledge of scar's geometry is available. The consistency between the Relative Elasticity Index and the physician's rating based on the Vancouver Scale (a relative scale used to rate burn scars) indicates that the proposed modeling approach has high potentials for image-based quantitative burn scar assessment.« less

Design of Software for Design of Finite Element for Structural Analysis. Ph.D. Thesis - Stuttgart Univ., 22 Nov. 1983

NASA Technical Reports Server (NTRS)

Helfrich, Reinhard

1987-01-01

The concepts of software engineering which allow a user of the finite element method to describe a model, to collect and to check the model data in a data base as well as to form the matrices required for a finite element calculation are examined. Next the components of the model description are conceived including the mesh tree, the topology, the configuration, the kinematic boundary conditions, the data for each element, and the loads. The possibilities for description and review of the data are considered. The concept of the segments for the modularization of the programs follows the components of the model description. The significance of the mesh tree as a globular guiding structure will be understood in view of the principle of the unity of the model, the mesh tree, and the data base. The user-friendly aspects of the software system will be summarized: the principle of language communication, the data generators, error processing, and data security.

RICH: OPEN-SOURCE HYDRODYNAMIC SIMULATION ON A MOVING VORONOI MESH

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

Yalinewich, Almog; Steinberg, Elad; Sari, Re’em

2015-02-01

We present here RICH, a state-of-the-art two-dimensional hydrodynamic code based on Godunov’s method, on an unstructured moving mesh (the acronym stands for Racah Institute Computational Hydrodynamics). This code is largely based on the code AREPO. It differs from AREPO in the interpolation and time-advancement schemeS as well as a novel parallelization scheme based on Voronoi tessellation. Using our code, we study the pros and cons of a moving mesh (in comparison to a static mesh). We also compare its accuracy to other codes. Specifically, we show that our implementation of external sources and time-advancement scheme is more accurate and robustmore » than is AREPO when the mesh is allowed to move. We performed a parameter study of the cell rounding mechanism (Lloyd iterations) and its effects. We find that in most cases a moving mesh gives better results than a static mesh, but it is not universally true. In the case where matter moves in one way and a sound wave is traveling in the other way (such that relative to the grid the wave is not moving) a static mesh gives better results than a moving mesh. We perform an analytic analysis for finite difference schemes that reveals that a Lagrangian simulation is better than a Eulerian simulation in the case of a highly supersonic flow. Moreover, we show that Voronoi-based moving mesh schemes suffer from an error, which is resolution independent, due to inconsistencies between the flux calculation and the change in the area of a cell. Our code is publicly available as open source and designed in an object-oriented, user-friendly way that facilitates incorporation of new algorithms and physical processes.« less

Development of the software tool for generation and visualization of the finite element head model with bone conduction sounds

NASA Astrophysics Data System (ADS)

Nikolić, Dalibor; Milošević, Žarko; Saveljić, Igor; Filipović, Nenad

2015-12-01

Vibration of the skull causes a hearing sensation. We call it Bone Conduction (BC) sound. There are several investigations about transmission properties of bone conducted sound. The aim of this study was to develop a software tool for easy generation of the finite element (FE) model of the human head with different materials based on human head anatomy and to calculate sound conduction through the head. Developed software tool generates a model in a few steps. The first step is to do segmentation of CT medical images (DICOM) and to generate a surface mesh files (STL). Each STL file presents a different layer of human head with different material properties (brain, CSF, different layers of the skull bone, skin, etc.). The next steps are to make tetrahedral mesh from obtained STL files, to define FE model boundary conditions and to solve FE equations. This tool uses PAK solver, which is the open source software implemented in SIFEM FP7 project, for calculations of the head vibration. Purpose of this tool is to show impact of the bone conduction sound of the head on the hearing system and to estimate matching of obtained results with experimental measurements.

Diesel engine emissions and combustion predictions using advanced mixing models applicable to fuel sprays

NASA Astrophysics Data System (ADS)

Abani, Neerav; Reitz, Rolf D.

2010-09-01

An advanced mixing model was applied to study engine emissions and combustion with different injection strategies ranging from multiple injections, early injection and grouped-hole nozzle injection in light and heavy duty diesel engines. The model was implemented in the KIVA-CHEMKIN engine combustion code and simulations were conducted at different mesh resolutions. The model was compared with the standard KIVA spray model that uses the Lagrangian-Drop and Eulerian-Fluid (LDEF) approach, and a Gas Jet spray model that improves predictions of liquid sprays. A Vapor Particle Method (VPM) is introduced that accounts for sub-grid scale mixing of fuel vapor and more accurately and predicts the mixing of fuel-vapor over a range of mesh resolutions. The fuel vapor is transported as particles until a certain distance from nozzle is reached where the local jet half-width is adequately resolved by the local mesh scale. Within this distance the vapor particle is transported while releasing fuel vapor locally, as determined by a weighting factor. The VPM model more accurately predicts fuel-vapor penetrations for early cycle injections and flame lift-off lengths for late cycle injections. Engine combustion computations show that as compared to the standard KIVA and Gas Jet spray models, the VPM spray model improves predictions of in-cylinder pressure, heat released rate and engine emissions of NOx, CO and soot with coarse mesh resolutions. The VPM spray model is thus a good tool for efficiently investigating diesel engine combustion with practical mesh resolutions, thereby saving computer time.

Automated quadrilateral surface discretization method and apparatus usable to generate mesh in a finite element analysis system

DOEpatents

Blacker, Teddy D.

1994-01-01

An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.

Local mesh adaptation technique for front tracking problems

NASA Astrophysics Data System (ADS)

Lock, N.; Jaeger, M.; Medale, M.; Occelli, R.

1998-09-01

A numerical model is developed for the simulation of moving interfaces in viscous incompressible flows. The model is based on the finite element method with a pseudo-concentration technique to track the front. Since a Eulerian approach is chosen, the interface is advected by the flow through a fixed mesh. Therefore, material discontinuity across the interface cannot be described accurately. To remedy this problem, the model has been supplemented with a local mesh adaptation technique. This latter consists in updating the mesh at each time step to the interface position, such that element boundaries lie along the front. It has been implemented for unstructured triangular finite element meshes. The outcome of this technique is that it allows an accurate treatment of material discontinuity across the interface and, if necessary, a modelling of interface phenomena such as surface tension by using specific boundary elements. For illustration, two examples are computed and presented in this paper: the broken dam problem and the Rayleigh-Taylor instability. Good agreement has been obtained in the comparison of the numerical results with theory or available experimental data.

Applications of Space-Filling-Curves to Cartesian Methods for CFD

NASA Technical Reports Server (NTRS)

Aftosmis, M. J.; Murman, S. M.; Berger, M. J.

2003-01-01

This paper presents a variety of novel uses of space-filling-curves (SFCs) for Cartesian mesh methods in CFD. While these techniques will be demonstrated using non-body-fitted Cartesian meshes, many are applicable on general body-fitted meshes-both structured and unstructured. We demonstrate the use of single theta(N log N) SFC-based reordering to produce single-pass (theta(N)) algorithms for mesh partitioning, multigrid coarsening, and inter-mesh interpolation. The intermesh interpolation operator has many practical applications including warm starts on modified geometry, or as an inter-grid transfer operator on remeshed regions in moving-body simulations Exploiting the compact construction of these operators, we further show that these algorithms are highly amenable to parallelization. Examples using the SFC-based mesh partitioner show nearly linear speedup to 640 CPUs even when using multigrid as a smoother. Partition statistics are presented showing that the SFC partitions are, on-average, within 15% of ideal even with only around 50,000 cells in each sub-domain. The inter-mesh interpolation operator also has linear asymptotic complexity and can be used to map a solution with N unknowns to another mesh with M unknowns with theta(M + N) operations. This capability is demonstrated both on moving-body simulations and in mapping solutions to perturbed meshes for control surface deflection or finite-difference-based gradient design methods.

Varying Degrees of Nonlinear Mechanical Behavior Arising From Geometric Differences of Urogynecological Meshes

PubMed Central

Feola, Andrew; Pal, Siladitya; Moalli, Pamela; Maiti, Spandan; Abramowitch, Steven

2014-01-01

Synthetic polypropylene meshes were designed to restore pelvic organ support for women suffering from pelvic organ prolapse; however, the FDA released two notifications regarding the potential complications associated with mesh implantation. Our aim was to characterize the structural properties of Restorelle and UltraPro subjected to uniaxial tension along perpendicular directions, and then model the tensile behavior of these meshes utilizing a co-rotational finite element model, with an imbedded linear or fiber-recruitment local stress-strain relationship. Both meshes exhibited highly nonlinear stress-strain behavior; Restorelle had no significant differences between the two perpendicular directions, while UltraPro had a 93% difference in the low (initial) stiffness (p=0.009) between loading directions. Our model predicted that early alignment of the mesh segments in the loading direction and subsequent stretching could explain the observed nonlinear tensile behavior. However, a nonlinear stress-strain response in the stretching regime, that may be inherent to the mesh segment, was required to better capture experimental results. Utilizing a nonlinear fiber recruitment model with two parameters A and B, we observed improved agreement between the simulations and the experimental results. An inverse analysis found A=120 MPa and B=1.75 for Restorelle (RMSE=0.36). This approach yielded A=30 MPa and B=3.5 for UltraPro along one direction (RMSE=0.652), while the perpendicular orientation resulted in A=130 MPa and B=4.75 (RMSE=4.36). From the uniaxial protocol, Restorelle was found to have little variance in structural properties along these two perpendicular directions; however, UltraPro was found to behave anisotropically. PMID:25011619

An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA

NASA Technical Reports Server (NTRS)

Djomehri, M. Jahed; Erickson, Larry L.

1994-01-01

A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.

ISSM: Ice Sheet System Model

NASA Technical Reports Server (NTRS)

Larour, Eric; Schiermeier, John E.; Seroussi, Helene; Morlinghem, Mathieu

2013-01-01

In order to have the capability to use satellite data from its own missions to inform future sea-level rise projections, JPL needed a full-fledged ice-sheet/iceshelf flow model, capable of modeling the mass balance of Antarctica and Greenland into the near future. ISSM was developed with such a goal in mind, as a massively parallelized, multi-purpose finite-element framework dedicated to ice-sheet modeling. ISSM features unstructured meshes (Tria in 2D, and Penta in 3D) along with corresponding finite elements for both types of meshes. Each finite element can carry out diagnostic, prognostic, transient, thermal 3D, surface, and bed slope simulations. Anisotropic meshing enables adaptation of meshes to a certain metric, and the 2D Shelfy-Stream, 3D Blatter/Pattyn, and 3D Full-Stokes formulations capture the bulk of the ice-flow physics. These elements can be coupled together, based on the Arlequin method, so that on a large scale model such as Antarctica, each type of finite element is used in the most efficient manner. For each finite element referenced above, ISSM implements an adjoint. This adjoint can be used to carry out model inversions of unknown model parameters, typically ice rheology and basal drag at the ice/bedrock interface, using a metric such as the observed InSAR surface velocity. This data assimilation capability is crucial to allow spinning up of ice flow models using available satellite data. ISSM relies on the PETSc library for its vectors, matrices, and solvers. This allows ISSM to run efficiently on any parallel platform, whether shared or distrib- ISSM: Ice Sheet System Model NASA's Jet Propulsion Laboratory, Pasadena, California uted. It can run on the largest clusters, and is fully scalable. This allows ISSM to tackle models the size of continents. ISSM is embedded into MATLAB and Python, both open scientific platforms. This improves its outreach within the science community. It is entirely written in C/C++, which gives it flexibility in its design, and the power/speed that C/C++ allows. ISSM is svn (subversion) hosted, on a JPL repository, to facilitate its development and maintenance. ISSM can also model propagation of rifts using contact mechanics and mesh splitting, and can interface to the Dakota software. To carry out sensitivity analysis, mesh partitioning algorithms are available, based on the Scotch, Chaco, and Metis partitioners that ensure equal area mesh partitions can be done, which are then usable for sampling and local reliability methods.

Finite element meshing of ANSYS (trademark) solid models

NASA Technical Reports Server (NTRS)

Kelley, F. S.

1987-01-01

A large scale, general purpose finite element 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 finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.

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 Lagrangian formulations that are based on a fixed computational grid and which instead evolve the mapping of the reference configuration to the current one. Our new Lagrangian-type DG scheme adopts the novel a posteriori sub-cell finite volume limiter method recently developed in [62] for fixed unstructured grids. In this approach, the validity of the candidate solution produced in each cell by an unlimited ADER-DG scheme is verified against a set of physical and numerical detection criteria, such as the positivity of pressure and density, the absence of floating point errors (NaN) and the satisfaction of a relaxed discrete maximum principle (DMP) in the sense of polynomials. Those cells which do not satisfy all of the above criteria are flagged as troubled cells and are recomputed at the aid of a more robust second order TVD finite volume scheme. To preserve the subcell resolution capability of the original DG scheme, the FV limiter is run on a sub-grid that is 2 N + 1 times finer compared to the mesh of the original unlimited DG scheme. The new subcell averages are then gathered back into a high order DG polynomial by a usual conservative finite volume reconstruction operator. The numerical convergence rates of the new ALE ADER-DG schemes are studied up to fourth order in space and time and several test problems are simulated in order to check the accuracy and the robustness of the proposed numerical method in the context of the Euler and Navier-Stokes equations for compressible gas dynamics, considering both inviscid and viscous fluids. Finally, an application inspired by Inertial Confinement Fusion (ICF) type flows is considered by solving the Euler equations and the PDE of viscous and resistive magnetohydrodynamics (VRMHD).

Structure organization and magnetic properties of microscale ferrogels: The effect of particle magnetic anisotropy

NASA Astrophysics Data System (ADS)

Ryzhkov, Aleksandr V.; Melenev, Petr V.; Balasoiu, Maria; Raikher, Yuriy L.

2016-08-01

The equilibrium structure and magnetic properties of a ferrogel object of small size (microferrogel(MFG)) are investigated by coarse-grained molecular dynamics. As a generic model of a microferrogel (MFG), a sample with a lattice-like mesh is taken. The solid phase of the MFG consists of magnetic (e.g., ferrite) nanoparticles which are mechanically linked to the mesh making some part of its nodes. Unlike previous models, the finite uniaxial magnetic anisotropy of the particles, as it is the case for real ferrogels, is taken into account. For comparison, two types of MFGs are considered: MFG-1, which dwells in virtually non-aggregated state independently of the presence of an external magnetic field, and MFG-2, which displays aggregation yet under zero field. The structure states of the samples are analyzed with the aid of angle-resolved radial distribution functions and cluster counts. The results reveal the crucial role of the matrix elasticity on the structure organization as well as on magnetization of both MFGs. The particle anisotropy, which plays insignificant role in MFG-1 (moderate interparticle magnetodipole interaction), becomes an important factor in MFG-2 (strong interaction). There, the restrictions imposed on the particle angular freedom by the elastic matrix result in notable diminution of the particle chain lengths as well as the magnetization of the sample. The approach proposed enables one to investigate a large variety of MFGs, including those of capsule type and to purposefully choose the combination of their magnetoelastic parameters.

Finite element analysis of TAVI: Impact of native aortic root computational modeling strategies on simulation outcomes.

PubMed

Finotello, Alice; Morganti, Simone; Auricchio, Ferdinando

2017-09-01

In the last few years, several studies, each with different aim and modeling detail, have been proposed to investigate transcatheter aortic valve implantation (TAVI) with finite elements. The present work focuses on the patient-specific finite element modeling of the aortic valve complex. In particular, we aim at investigating how different modeling strategies in terms of material models/properties and discretization procedures can impact analysis results. Four different choices both for the mesh size (from  20 k elements to  200 k elements) and for the material model (from rigid to hyperelastic anisotropic) are considered. Different approaches for modeling calcifications are also taken into account. Post-operative CT data of the real implant are used as reference solution with the aim of outlining a trade-off between computational model complexity and reliability of the results. Copyright © 2017 IPEM. Published by Elsevier Ltd. All rights reserved.

A method for modeling finite-core vortices in wake-flow calculations

NASA Technical Reports Server (NTRS)

Stremel, P. M.

1984-01-01

A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian 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 finite-core model. Two distributions of vorticity, or core models, are investigated: a finite 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.

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

Moving and adaptive grid methods for compressible flows

NASA Technical Reports Server (NTRS)

Trepanier, Jean-Yves; Camarero, Ricardo

1995-01-01

This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology.

A novel finite volume discretization method for advection-diffusion systems on stretched meshes

NASA Astrophysics Data System (ADS)

Merrick, D. G.; Malan, A. G.; van Rooyen, J. A.

2018-06-01

This work is concerned with spatial advection and diffusion discretization technology within the field of Computational Fluid Dynamics (CFD). In this context, a novel method is proposed, which is dubbed the Enhanced Taylor Advection-Diffusion (ETAD) scheme. The model equation employed for design of the scheme is the scalar advection-diffusion equation, the industrial application being incompressible laminar and turbulent flow. Developed to be implementable into finite volume codes, ETAD places specific emphasis on improving accuracy on stretched structured and unstructured meshes while considering both advection and diffusion aspects in a holistic manner. A vertex-centered structured and unstructured finite volume scheme is used, and only data available on either side of the volume face is employed. This includes the addition of a so-called mesh stretching metric. Additionally, non-linear blending with the existing NVSF scheme was performed in the interest of robustness and stability, particularly on equispaced meshes. The developed scheme is assessed in terms of accuracy - this is done analytically and numerically, via comparison to upwind methods which include the popular QUICK and CUI techniques. Numerical tests involved the 1D scalar advection-diffusion equation, a 2D lid driven cavity and turbulent flow case. Significant improvements in accuracy were achieved, with L2 error reductions of up to 75%.

Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

NASA Technical Reports Server (NTRS)

Hua, Chongyu; Volakis, John L.

1990-01-01

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

Simulation of Needle-Type Corona Electrodes by the Finite Element Method

NASA Astrophysics Data System (ADS)

Yang, Shiyou; José Márcio, Machado; Nancy Mieko, Abe; Angelo, Passaro

2007-12-01

This paper describes a software tool, called LEVSOFT, suitable for the electric field simulations of corona electrodes by the Finite Element Method (FEM). Special attention was paid to the user friendly construction of geometries with corners and sharp points, and to the fast generation of highly refined triangular meshes and field maps. The execution of self-adaptive meshes was also implemented. These customized features make the code attractive for the simulation of needle-type corona electrodes. Some case examples involving needle type electrodes are presented.

CFD methodology and validation for turbomachinery flows

NASA Astrophysics Data System (ADS)

Hirsch, Ch.

1994-05-01

The essential problem today, in the application of 3D Navier-Stokes simulations to the design and analysis of turbomachinery components, is the validation of the numerical approximation and of the physical models, in particular the turbulence modelling. Although most of the complex 3D flow phenomena occurring in turbomachinery bladings can be captured with relatively coarse meshes, many detailed flow features are dependent on mesh size, on the turbulence and transition models. A brief review of the present state of the art of CFD methodology is given with emphasis on quality and accuracy of numerical approximations related to viscous flow computations. Considerations related to the mesh influence on solution accuracy are stressed. The basic problems of turbulence and transition modelling are discussed next, with a short summary of the main turbulence models and their applications to representative turbomachinery flows. Validations of present turbulence models indicate that none of the available turbulence models is able to predict all the detailed flow behavior in complex flow interactions. In order to identify the phenomena that can be captured on coarser meshes a detailed understanding of the complex 3D flow in compressor and turbines is necessary. Examples of global validations for different flow configurations, representative of compressor and turbine aerodynamics are presented, including secondary and tip clearance flows.

Interior Fluid Dynamics of Liquid-Filled Projectiles

DTIC Science & Technology

1989-12-01

the Sandia code. The previous codes are primarily based on finite-difference approximations with relatively coarse grid and were designed without...exploits Chorin’s method of artificial compressibility. The steady solution at 11 X 24 X 21 grid points in r, 0, z-direction is obtained by integrating...differences in radial and axial direction and pseudoepectral differencing in the azimuthal direction. Nonuniform grids are introduced for increased

Simulation of Natural Convection Heat Transfer in an Inclined Square Cavity With Perfectly Conducting Side Walls Using Finite Difference Approach

NASA Astrophysics Data System (ADS)

Azwadi, C. S. Nor; Fairus, M. Y. Mohd

2010-06-01

This study is about numerical simulation of natural heat transfer inside an inclined square cavity with perfectly conducting boundary conditions for the side walls. The Navier Stokes equations were solved using finite difference approach with uniform mesh procedure. Three different inclination angels were applied and the results are presented in terms of streamlines and isotherms plots. Based on the fluid flow pattern and the isothermal lines behaviour, the convection heat transfer has shown domination over the conduction as the tilt angle increases. The simulation of natural convection inside an air filled-tilted cavity is the first time to be done to the best of our knowledge.

Arbitrary Order Mixed Mimetic Finite Differences Method with Nodal Degrees of Freedom

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

Iaroshenko, Oleksandr; Gyrya, Vitaliy; Manzini, Gianmarco

2016-09-01

In this work we consider a modification to an arbitrary order mixed mimetic finite difference method (MFD) for a diffusion equation on general polygonal meshes [1]. The modification is based on moving some degrees of freedom (DoF) for a flux variable from edges to vertices. We showed that for a non-degenerate element this transformation is locally equivalent, i.e. there is a one-to-one map between the new and the old DoF. Globally, on the other hand, this transformation leads to a reduction of the total number of degrees of freedom (by up to 40%) and additional continuity of the discrete flux.

Mesh generation for two-dimensional regions using the Tektronix DVST (direct view storage tube) graphics terminal

NASA Technical Reports Server (NTRS)

Gabrielson, V. K.

1975-01-01

The computer program DVMESH and the use of the Tektronix DVST graphics terminal were described for applications of preparing mesh data for use in various two-dimensional axisymmetric finite element stress analysis and heat transfer codes.

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

PubMed Central

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN). In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging. PMID:23227108

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

PubMed

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC) method, the validation results show the merits and potential of the XFEM for optical imaging.

A 3D finite element ALE method using an approximate Riemann solution

DOE PAGES

Chiravalle, V. P.; Morgan, N. R.

2016-08-09

Arbitrary Lagrangian–Eulerian finite 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 finite element arbitrary Lagrangian–Eulerian 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

A 3D finite element ALE method using an approximate Riemann solution

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

Chiravalle, V. P.; Morgan, N. R.

Arbitrary Lagrangian–Eulerian finite 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 finite element arbitrary Lagrangian–Eulerian 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

N%-Superconvergence of Finite Element Approximations in the Interior of General Meshes of Triangles

DTIC Science & Technology

1993-12-01

RODiGuEz, On the asymptotic exactness of error estimators for linear triangular finite elements, Numer. Math., 59 (1991), pp. 107-127. 27. R. DURAN ...WAHLDIN, Interior maxmum norma estimates for finite element methods, Part H, unpublished manuscript. 38. I. BABUfKA, T. STROUBOULIS, A. MATHU. AND C.S

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

NASA Technical Reports Server (NTRS)

Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

2013-01-01

This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

An Automated Method for Landmark Identification and Finite-Element Modeling of the Lumbar Spine.

PubMed

Campbell, Julius Quinn; Petrella, Anthony J

2015-11-01

The purpose of this study was to develop a method for the automated creation of finite-element models of the lumbar spine. Custom scripts were written to extract bone landmarks of lumbar vertebrae and assemble L1-L5 finite-element models. End-plate borders, ligament attachment points, and facet surfaces were identified. Landmarks were identified to maintain mesh correspondence between meshes for later use in statistical shape modeling. 90 lumbar vertebrae were processed creating 18 subject-specific finite-element models. Finite-element model surfaces and ligament attachment points were reproduced within 1e-5 mm of the bone surface, including the critical contact surfaces of the facets. Element quality exceeded specifications in 97% of elements for the 18 models created. The current method is capable of producing subject-specific finite-element models of the lumbar spine with good accuracy, quality, and robustness. The automated methods developed represent advancement in the state of the art of subject-specific lumbar spine modeling to a scale not possible with prior manual and semiautomated methods.

Shrink-wrapped isosurface from cross sectional images

PubMed Central

Choi, Y. K.; Hahn, J. K.

2010-01-01

Summary This paper addresses a new surface reconstruction scheme for approximating the isosurface from a set of tomographic cross sectional images. Differently from the novel Marching Cubes (MC) algorithm, our method does not extract the iso-density surface (isosurface) directly from the voxel data but calculates the iso-density point (isopoint) first. After building a coarse initial mesh approximating the ideal isosurface by the cell-boundary representation, it metamorphoses the mesh into the final isosurface by a relaxation scheme, called shrink-wrapping process. Compared with the MC algorithm, our method is robust and does not make any cracks on surface. Furthermore, since it is possible to utilize lots of additional isopoints during the surface reconstruction process by extending the adjacency definition, theoretically the resulting surface can be better in quality than the MC algorithm. According to experiments, it is proved to be very robust and efficient for isosurface reconstruction from cross sectional images. PMID:20703361

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

Greve, L., E-mail: lars.greve@volkswagen.de; Medricky, M., E-mail: miloslav.medricky@volkswagen.de; Andres, M., E-mail: miloslav.medricky@volkswagen.de

A comprehensive strain hardening and fracture characterization of different grades of boron steel blanks has been performed, providing the foundation for the implementation into the modular material model (MMM) framework developed by Volkswagen Group Research for an explicit crash code. Due to the introduction of hardness-based interpolation rules for the characterized main grades, the hardening and fracture behavior is solely described by the underlying Vickers hardness. In other words, knowledge of the hardness distribution within a hot-formed component is enough to set up the newly developed computational model. The hardness distribution can be easily introduced via an experimentally measured hardnessmore » curve or via hardness mapping from a corresponding hot-forming simulation. For industrial application using rather coarse and computationally inexpensive shell element meshes, the user material model has been extended by a necking/post-necking model with reduced mesh-dependency as an additional failure mode. The present paper mainly addresses the necking/post-necking model.« less

Optimization of droplets for UV-NIL using coarse-grain simulation of resist flow

NASA Astrophysics Data System (ADS)

Sirotkin, Vadim; Svintsov, Alexander; Zaitsev, Sergey

2009-03-01

A mathematical model and numerical method are described, which make it possible to simulate ultraviolet ("step and flash") nanoimprint lithography (UV-NIL) process adequately even using standard Personal Computers. The model is derived from 3D Navier-Stokes equations with the understanding that the resist motion is largely directed along the substrate surface and characterized by ultra-low values of the Reynolds number. By the numerical approximation of the model, a special finite difference method is applied (a coarse-grain method). A coarse-grain modeling tool for detailed analysis of resist spreading in UV-NIL at the structure-scale level is tested. The obtained results demonstrate the high ability of the tool to calculate optimal dispensing for given stamp design and process parameters. This dispensing provides uniform filled areas and a homogeneous residual layer thickness in UV-NIL.

A coarse-grid-projection acceleration method for finite-element incompressible flow computations

NASA Astrophysics Data System (ADS)

Kashefi, Ali; Staples, Anne; FiN Lab Team

2015-11-01

Coarse grid projection (CGP) methodology provides a framework for accelerating computations by performing some part of the computation on a coarsened grid. We apply the CGP to pressure projection methods for finite element-based incompressible flow simulations. Based on it, the predicted velocity field data is restricted to a coarsened grid, the pressure is determined by solving the Poisson equation on the coarse grid, and the resulting data are prolonged to the preset fine grid. The contributions of the CGP method to the pressure correction technique are twofold: first, it substantially lessens the computational cost devoted to the Poisson equation, which is the most time-consuming part of the simulation process. Second, it preserves the accuracy of the velocity field. The velocity and pressure spaces are approximated by Galerkin spectral element using piecewise linear basis functions. A restriction operator is designed so that fine data are directly injected into the coarse grid. The Laplacian and divergence matrices are driven by taking inner products of coarse grid shape functions. Linear interpolation is implemented to construct a prolongation operator. A study of the data accuracy and the CPU time for the CGP-based versus non-CGP computations is presented. Laboratory for Fluid Dynamics in Nature.

Modal density of rectangular structures in a wide frequency range

NASA Astrophysics Data System (ADS)

Parrinello, A.; Ghiringhelli, G. L.

2018-04-01

A novel approach to investigate the modal density of a rectangular structure in a wide frequency range is presented. First, the modal density is derived, in the whole frequency range of interest, on the basis of sound transmission through the infinite counterpart of the structure; then, it is corrected by means of the low-frequency modal behavior of the structure, taking into account actual size and boundary conditions. A statistical analysis reveals the connection between the modal density of the structure and the transmission of sound through its thickness. A transfer matrix approach is used to compute the required acoustic parameters, making it possible to deal with structures having arbitrary stratifications of different layers. A finite element method is applied on coarse grids to derive the first few eigenfrequencies required to correct the modal density. Both the transfer matrix approach and the coarse grids involved in the finite element analysis grant high efficiency. Comparison with alternative formulations demonstrates the effectiveness of the proposed methodology.

New Software Developments for Quality Mesh Generation and Optimization from Biomedical Imaging Data

PubMed Central

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2013-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. PMID:24252469

Impact of solids on composite materials

NASA Technical Reports Server (NTRS)

Bronson, Arturo; Maldonado, Jerry; Chern, Tzong; Martinez, Francisco; Mccord-Medrano, Johnnie; Roschke, Paul N.

1987-01-01

The failure modes of composite materials as a result of low velocity impact were investigated by simulating the impact with a finite element analysis. An important facet of the project is the modeling of the impact of a solid onto cylindrical shells composed of composite materials. The model under development will simulate the delamination sustained when a composite material encounters impact from another rigid body. The computer equipment was installed, the computer network tested, and a finite element method model was developed to compare results with known experimental data. The model simulated the impact of a steel rod onto a rotating shaft. Pre-processing programs (GMESH and TANVEL) were developed to generate node and element data for the input into the three dimensional, dynamic finite element analysis code (DYNA3D). The finite element mesh was configured with a fine mesh near the impact zone and a coarser mesh for the impacting rod and the regions surrounding the impacting zone. For the computer simulation, five impacting loads were used to determine the time history of the stresses, the scribed surface areas, and the amount of ridging. The processing time of the computer codes amounted from 1 to 4 days. The calculated surface area were within 6-12 percent, relative error when compated to the actual scratch area.

Investigation of Coupled model of Pore network and Continuum in shale gas

NASA Astrophysics Data System (ADS)

Cao, G.; Lin, M.

2016-12-01

Flow in shale spanning over many scales, makes the majority of conventional treatment methods disabled. For effectively simulating, a coupled model of pore-scale and continuum-scale was proposed in this paper. Based on the SEM image, we decompose organic-rich-shale into two subdomains: kerogen and inorganic matrix. In kerogen, the nanoscale pore-network is the main storage space and migration pathway so that the molecular phenomena (slip and diffusive transport) is significant. Whereas, inorganic matrix, with relatively large pores and micro fractures, the flow is approximate to Darcy. We use pore-scale network models (PNM) to represent kerogen and continuum-scale models (FVM or FEM) to represent matrix. Finite element mortars are employed to couple pore- and continuum-scale models by enforcing continuity of pressures and fluxes at shared boundary interfaces. In our method, the process in the coupled model is described by pressure square equation, and uses Dirichlet boundary conditions. We discuss several problems: the optimal element number of mortar faces, two categories boundary faces of pore network, the difference between 2D and 3D models, and the difference between continuum models FVM and FEM in mortars. We conclude that: (1) too coarse mesh in mortars will decrease the accuracy, while too fine mesh will lead to an ill-condition even singular system, the optimal element number is depended on boundary pores and nodes number. (2) pore network models are adjacent to two different mortar faces (PNM to PNM, PNM to continuum model), incidental repeated mortar nodes must be deleted. (3) 3D models can be replaced by 2D models under certain condition. (4) FVM is more convenient than FEM, for its simplicity in assigning interface nodes pressure and calculating interface fluxes. This work is supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB10020302), the 973 Program (2014CB239004), the Key Instrument Developing Project of the CAS (ZDYZ2012-1-08-02), the National Natural Science Foundation of China (41574129).

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species

PubMed Central

Dossa, Gbadamassi G. O.; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D.

2016-01-01

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11–1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition. PMID:27698461

A Computational Icing Effects Study for a Three-Dimensional Wing: Comparison with Experimental Data and Investigation of Spanwise Variation

NASA Technical Reports Server (NTRS)

Thompson, D.; Mogili, P.; Chalasani, S.; Addy, H.; Choo, Y.

2004-01-01

Steady-state solutions of the Reynolds-averaged Navier-Stokes (RANS) equations were computed using the Colbalt flow solver for a constant-section, rectangular wing based on an extruded two-dimensional glaze ice shape. The one equation Spalart-Allmaras turbulence model was used. The results were compared with data obtained from a recent wind tunnel test. Computed results indicate that the steady RANS solutions do not accurately capture the recirculating region downstream of the ice accretion, even after a mesh refinement. The resulting predicted reattachment is farther downstream than indicated by the experimental data. Additionally, the solutions computed on a relatively coarse baseline mesh had detailed flow characteristics that were different from those computed on the refined mesh or the experimental data. Steady RANS solutions were also computed to investigate the effects of spanwise variation in the ice shape. The spanwise variation was obtained via a bleeding function that merged the ice shape with the clean wing using a sinusoidal spanwise variation. For these configurations, the results predicted for the extruded shape provided conservative estimates for the performance degradation of the wing. Additionally, the spanwise variation in the ice shape and the resulting differences in the flow fields did not significantly change the location of the primary reattachment.

Factors controlling bark decomposition and its role in wood decomposition in five tropical tree species.

PubMed

Dossa, Gbadamassi G O; Paudel, Ekananda; Cao, Kunfang; Schaefer, Douglas; Harrison, Rhett D

2016-10-04

Organic matter decomposition represents a vital ecosystem process by which nutrients are made available for plant uptake and is a major flux in the global carbon cycle. Previous studies have investigated decomposition of different plant parts, but few considered bark decomposition or its role in decomposition of wood. However, bark can comprise a large fraction of tree biomass. We used a common litter-bed approach to investigate factors affecting bark decomposition and its role in wood decomposition for five tree species in a secondary seasonal tropical rain forest in SW China. For bark, we implemented a litter bag experiment over 12 mo, using different mesh sizes to investigate effects of litter meso- and macro-fauna. For wood, we compared the decomposition of branches with and without bark over 24 mo. Bark in coarse mesh bags decomposed 1.11-1.76 times faster than bark in fine mesh bags. For wood decomposition, responses to bark removal were species dependent. Three species with slow wood decomposition rates showed significant negative effects of bark-removal, but there was no significant effect in the other two species. Future research should also separately examine bark and wood decomposition, and consider bark-removal experiments to better understand roles of bark in wood decomposition.

A two-level stochastic collocation method for semilinear elliptic equations with random coefficients

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

Chen, Luoping; Zheng, Bin; Lin, Guang

In this work, we propose a novel two-level discretization for solving semilinear elliptic equations with random coefficients. Motivated by the two-grid method for deterministic partial differential equations (PDEs) introduced by Xu, our two-level stochastic collocation method utilizes a two-grid finite element discretization in the physical space and a two-level collocation method in the random domain. In particular, we solve semilinear equations on a coarse meshmore » $$\\mathcal{T}_H$$ with a low level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_{P}$$) and solve linearized equations on a fine mesh $$\\mathcal{T}_h$$ using high level stochastic collocation (corresponding to the polynomial space $$\\mathcal{P}_p$$). We prove that the approximated solution obtained from this method achieves the same order of accuracy as that from solving the original semilinear problem directly by stochastic collocation method with $$\\mathcal{T}_h$$ and $$\\mathcal{P}_p$$. The two-level method is computationally more efficient, especially for nonlinear problems with high random dimensions. Numerical experiments are also provided to verify the theoretical results.« less

Cell-Averaged discretization for incompressible Navier-Stokes with embedded boundaries and locally refined Cartesian meshes: a high-order finite volume approach

NASA Astrophysics Data System (ADS)

Bhalla, Amneet Pal Singh; Johansen, Hans; Graves, Dan; Martin, Dan; Colella, Phillip; Applied Numerical Algorithms Group Team

2017-11-01

We present a consistent cell-averaged discretization for incompressible Navier-Stokes equations on complex domains using embedded boundaries. The embedded boundary is allowed to freely cut the locally-refined background Cartesian grid. Implicit-function representation is used for the embedded boundary, which allows us to convert the required geometric moments in the Taylor series expansion (upto arbitrary order) of polynomials into an algebraic problem in lower dimensions. The computed geometric moments are then used to construct stencils for various operators like the Laplacian, divergence, gradient, etc., by solving a least-squares system locally. We also construct the inter-level data-transfer operators like prolongation and restriction for multi grid solvers using the same least-squares system approach. This allows us to retain high-order of accuracy near coarse-fine interface and near embedded boundaries. Canonical problems like Taylor-Green vortex flow and flow past bluff bodies will be presented to demonstrate the proposed method. U.S. Department of Energy, Office of Science, ASCR (Award Number DE-AC02-05CH11231).

NASCAP simulation of PIX 2 experiments

NASA Technical Reports Server (NTRS)

Roche, J. C.; Mandell, M. J.

1985-01-01

The latest version of the NASCAP/LEO digital computer code used to simulate the PIX 2 experiment is discussed. NASCAP is a finite-element code and previous versions were restricted to a single fixed mesh size. As a consequence the resolution was dictated by the largest physical dimension to be modeled. The latest version of NASCAP/LEO can subdivide selected regions. This permitted the modeling of the overall Delta launch vehicle in the primary computational grid at a coarse resolution, with subdivided regions at finer resolution being used to pick up the details of the experiment module configuration. Langmuir probe data from the flight were used to estimate the space plasma density and temperature and the Delta ground potential relative to the space plasma. This information is needed for input to NASCAP. Because of the uncertainty or variability in the values of these parameters, it was necessary to explore a range around the nominal value in order to determine the variation in current collection. The flight data from PIX 2 were also compared with the results of the NASCAP simulation.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

A three dimensional immersed smoothed finite element method (3D IS-FEM) for fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Zhang, Zhi-Qian; Liu, G. R.; Khoo, Boo Cheong

2013-02-01

A three-dimensional immersed smoothed finite element method (3D IS-FEM) using four-node tetrahedral element 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 finite element 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 Lagrangian 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.

A downloadable meshed human canine tooth model with PDL and bone for finite element simulations.

PubMed

Boryor, Andrew; Hohmann, Ansgar; Geiger, Martin; Wolfram, Uwe; Sander, Christian; Sander, Franz Günter

2009-09-01

The aim of this study is to relieve scientists from the complex and time-consuming task of model generation by providing a model of a canine tooth and its periradicular tissues for Finite Element Method (FEM) simulations. This was achieved with diverse commercial software, based on a micro-computed tomography of the specimen. The Finite Element (FE) Model consists of enamel, dentin, nerve (innervation), periodontal ligament (PDL), and the surrounding cortical bone with trabecular structure. The area and volume meshes are of a very high quality in order to represent the model in a detailed form. Material properties are to be set individually by every user. The tooth model is provided for Abaqus, Ansys, HyperMesh, Nastran and as STL files, in an ASCII format for free download. This can help reduce the cost and effort of generating a tooth model for some research institutions, and may encourage other research groups to provide their high quality models for other researchers. By providing FE models, research results, especially FEM simulations, could be easily verified by others.

Finite element modeling of mass transport in high-Péclet cardiovascular flows

NASA Astrophysics Data System (ADS)

Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn

2016-11-01

Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.

Adaptive Finite Element Methods for Continuum Damage Modeling

NASA Technical Reports Server (NTRS)

Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.

1995-01-01

The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.

Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods

NASA Astrophysics Data System (ADS)

Kozdon, J. E.; Wilcox, L.

2013-12-01

Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.

Meshless Method for Simulation of Compressible Flow

NASA Astrophysics Data System (ADS)

Nabizadeh Shahrebabak, Ebrahim

In the present age, rapid development in computing technology and high speed supercomputers has made numerical analysis and computational simulation more practical than ever before for large and complex cases. Numerical simulations have also become an essential means for analyzing the engineering problems and the cases that experimental analysis is not practical. There are so many sophisticated and accurate numerical schemes, which do these simulations. The finite difference method (FDM) has been used to solve differential equation systems for decades. Additional numerical methods based on finite volume and finite element techniques are widely used in solving problems with complex geometry. All of these methods are mesh-based techniques. Mesh generation is an essential preprocessing part to discretize the computation domain for these conventional methods. However, when dealing with mesh-based complex geometries these conventional mesh-based techniques can become troublesome, difficult to implement, and prone to inaccuracies. In this study, a more robust, yet simple numerical approach is used to simulate problems in an easier manner for even complex problem. The meshless, or meshfree, method is one such development that is becoming the focus of much research in the recent years. The biggest advantage of meshfree methods is to circumvent mesh generation. Many algorithms have now been developed to help make this method more popular and understandable for everyone. These algorithms have been employed over a wide range of problems in computational analysis with various levels of success. Since there is no connectivity between the nodes in this method, the challenge was considerable. The most fundamental issue is lack of conservation, which can be a source of unpredictable errors in the solution process. This problem is particularly evident in the presence of steep gradient regions and discontinuities, such as shocks that frequently occur in high speed compressible flow problems. To solve this discontinuity problem, this research study deals with the implementation of a conservative meshless method and its applications in computational fluid dynamics (CFD). One of the most common types of collocating meshless method the RBF-DQ, is used to approximate the spatial derivatives. The issue with meshless methods when dealing with highly convective cases is that they cannot distinguish the influence of fluid flow from upstream or downstream and some methodology is needed to make the scheme stable. Therefore, an upwinding scheme similar to one used in the finite volume method is added to capture steep gradient or shocks. This scheme creates a flexible algorithm within which a wide range of numerical flux schemes, such as those commonly used in the finite volume method, can be employed. In addition, a blended RBF is used to decrease the dissipation ensuing from the use of a low shape parameter. All of these steps are formulated for the Euler equation and a series of test problems used to confirm convergence of the algorithm. The present scheme was first employed on several incompressible benchmarks to validate the framework. The application of this algorithm is illustrated by solving a set of incompressible Navier-Stokes problems. Results from the compressible problem are compared with the exact solution for the flow over a ramp and compared with solutions of finite volume discretization and the discontinuous Galerkin method, both requiring a mesh. The applicability of the algorithm and its robustness are shown to be applied to complex problems.

Analysis and computation of a least-squares method for consistent mesh tying

DOE PAGES

Day, David; Bochev, Pavel

2007-07-10

We report in the finite element method, a standard approach to mesh tying is to apply Lagrange multipliers. If the interface is curved, however, discretization generally leads to adjoining surfaces that do not coincide spatially. Straightforward Lagrange multiplier methods lead to discrete formulations failing a first-order patch test [T.A. Laursen, M.W. Heinstein, Consistent mesh-tying methods for topologically distinct discretized surfaces in non-linear solid mechanics, Internat. J. Numer. Methods Eng. 57 (2003) 1197–1242]. This paper presents a theoretical and computational study of a least-squares method for mesh tying [P. Bochev, D.M. Day, A least-squares method for consistent mesh tying, Internat. J.more » Numer. Anal. Modeling 4 (2007) 342–352], applied to the partial differential equation -∇ 2φ+αφ=f. We prove optimal convergence rates for domains represented as overlapping subdomains and show that the least-squares method passes a patch test of the order of the finite element space by construction. To apply the method to subdomain configurations with gaps and overlaps we use interface perturbations to eliminate the gaps. Finally, theoretical error estimates are illustrated by numerical experiments.« less

Divergence-free MHD on unstructured meshes using high order finite volume schemes based on multidimensional Riemann solvers

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Dumbser, Michael

2015-10-01

Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on unstructured meshes. Several stringent two- and three-dimensional problems are shown to work well with the methods presented here.

Hybrid simulation combining two space-time discretization of the discrete-velocity Boltzmann equation

NASA Astrophysics Data System (ADS)

Horstmann, Jan Tobias; Le Garrec, Thomas; Mincu, Daniel-Ciprian; Lévêque, Emmanuel

2017-11-01

Despite the efficiency and low dissipation of the stream-collide scheme of the discrete-velocity Boltzmann equation, which is nowadays implemented in many lattice Boltzmann solvers, a major drawback exists over alternative discretization schemes, i.e. finite-volume or finite-difference, that is the limitation to Cartesian uniform grids. In this paper, an algorithm is presented that combines the positive features of each scheme in a hybrid lattice Boltzmann method. In particular, the node-based streaming of the distribution functions is coupled with a second-order finite-volume discretization of the advection term of the Boltzmann equation under the Bhatnagar-Gross-Krook approximation. The algorithm is established on a multi-domain configuration, with the individual schemes being solved on separate sub-domains and connected by an overlapping interface of at least 2 grid cells. A critical parameter in the coupling is the CFL number equal to unity, which is imposed by the stream-collide algorithm. Nevertheless, a semi-implicit treatment of the collision term in the finite-volume formulation allows us to obtain a stable solution for this condition. The algorithm is validated in the scope of three different test cases on a 2D periodic mesh. It is shown that the accuracy of the combined discretization schemes agrees with the order of each separate scheme involved. The overall numerical error of the hybrid algorithm in the macroscopic quantities is contained between the error of the two individual algorithms. Finally, we demonstrate how such a coupling can be used to adapt to anisotropic flows with some gradual mesh refinement in the FV domain.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements 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 Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element 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.

Adaptively-refined overlapping grids for the numerical solution of systems of hyperbolic conservation laws

NASA Technical Reports Server (NTRS)

Brislawn, Kristi D.; Brown, David L.; Chesshire, Geoffrey S.; Saltzman, Jeffrey S.

1995-01-01

Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.

Computer-Aided Design and Optimization of High-Performance Vacuum Electronic Devices

DTIC Science & Technology

2006-08-15

approximations to the metric, and space mapping wherein low-accuracy (coarse mesh) solutions can potentially be used more effectively in an...interface and algorithm development. • Work on space - mapping or related methods for utilizing models of varying levels of approximation within an

An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

NASA Technical Reports Server (NTRS)

Ehlers, F. E.; Sebastian, J. D.; Weatherill, W. H.

1979-01-01

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.

The Application of COMSOL Multiphysics Package on the Modelling of Complex 3-D Lithospheric Electrical Resistivity Structures - A Case Study from the Proterozoic Orogenic belt within the North China Craton

NASA Astrophysics Data System (ADS)

Guo, L.; Yin, Y.; Deng, M.; Guo, L.; Yan, J.

2017-12-01

At present, most magnetotelluric (MT) forward modelling and inversion codes are based on finite difference method. But its structured mesh gridding cannot be well adapted for the conditions with arbitrary topography or complex tectonic structures. By contrast, the finite element method is more accurate in calculating complex and irregular 3-D region and has lower requirement of function smoothness. However, the complexity of mesh gridding and limitation of computer capacity has been affecting its application. COMSOL Multiphysics is a cross-platform finite element analysis, solver and multiphysics full-coupling simulation software. It achieves highly accurate numerical simulations with high computational performance and outstanding multi-field bi-directional coupling analysis capability. In addition, its AC/DC and RF module can be used to easily calculate the electromagnetic responses of complex geological structures. Using the adaptive unstructured grid, the calculation is much faster. In order to improve the discretization technique of computing area, we use the combination of Matlab and COMSOL Multiphysics to establish a general procedure for calculating the MT responses for arbitrary resistivity models. The calculated responses include the surface electric and magnetic field components, impedance components, magnetic transfer functions and phase tensors. Then, the reliability of this procedure is certificated by 1-D, 2-D and 3-D and anisotropic forward modeling tests. Finally, we establish the 3-D lithospheric resistivity model for the Proterozoic Wutai-Hengshan Mts. within the North China Craton by fitting the real MT data collected there. The reliability of the model is also verified by induced vectors and phase tensors. Our model shows more details and better resolution, compared with the previously published 3-D model based on the finite difference method. In conclusion, COMSOL Multiphysics package is suitable for modeling the 3-D lithospheric resistivity structures under complex tectonic deformation backgrounds, which could be a good complement to the existing finite-difference inversion algorithms.

Edge gradients evaluation for 2D hybrid finite volume method model

USDA-ARS?s Scientific Manuscript database

In this study, a two-dimensional depth-integrated hydrodynamic model was developed using FVM on a hybrid unstructured collocated mesh system. To alleviate the negative effects of mesh irregularity and non-uniformity, a conservative evaluation method for edge gradients based on the second-order Tayl...

The Simulation of Precipitation Evolutions and Mechanical Properties in Friction Stir Welding with Post-Weld Heat Treatments

NASA Astrophysics Data System (ADS)

Zhang, Z.; Wan, Z. Y.; Lindgren, L.-E.; Tan, Z. J.; Zhou, X.

2017-12-01

A finite element model of friction stir welding capable of re-meshing is used to simulate the temperature variations. Re-meshing of the finite element model is used to maintain a fine mesh resolving the gradients of the solution. The Kampmann-Wagner numerical model for precipitation is then used to study the relation between friction stir welds with post-weld heat treatment (PWHT) and the changes in mechanical properties. Results indicate that the PWHT holding time and PWHT holding temperature need to be optimally designed to obtain FSW with better mechanical properties. Higher precipitate number with lower precipitate sizes gives higher strength in the stirring zone after PWHT. The coarsening of precipitates in HAZ are the main reason to hinder the improvement of mechanical property when PWHT is used.

Refinement of Out of Circularity and Thickness Measurements of a Cylinder for Finite Element Analysis

DTIC Science & Technology

2016-09-01

UNCLASSIFIED UNCLASSIFIED Refinement of Out of Circularity and Thickness Measurements of a Cylinder for Finite Element Analysis...significant effect on the collapse strength and must be accurately represented in finite element analysis to obtain accurate results. Often it is necessary...to interpolate measurements from a relatively coarse grid to a refined finite element model and methods that have wide general acceptance are

Accurate evaluation of exchange fields in finite element micromagnetic solvers

NASA Astrophysics Data System (ADS)

Chang, R.; Escobar, M. A.; Li, S.; Lubarda, M. V.; Lomakin, V.

2012-04-01

Quadratic basis functions (QBFs) are implemented for solving the Landau-Lifshitz-Gilbert equation via the finite element method. This involves the introduction of a set of special testing functions compatible with the QBFs for evaluating the Laplacian operator. The results by using QBFs are significantly more accurate than those via linear basis functions. QBF approach leads to significantly more accurate results than conventionally used approaches based on linear basis functions. Importantly QBFs allow reducing the error of computing the exchange field by increasing the mesh density for structured and unstructured meshes. Numerical examples demonstrate the feasibility of the method.

An Element-Based Concurrent Partitioner for Unstructured Finite Element Meshes

NASA Technical Reports Server (NTRS)

Ding, Hong Q.; Ferraro, Robert D.

1996-01-01

A concurrent partitioner for partitioning unstructured finite element meshes on distributed memory architectures is developed. The partitioner uses an element-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 element centroids using a recursive inertial bisection algorithm. Elements 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.

SutraPlot, a graphical post-processor for SUTRA, a model for ground-water flow with solute or energy transport

USGS Publications Warehouse

Souza, W.R.

1999-01-01

This report documents a graphical display post-processor (SutraPlot) for the U.S. Geological Survey Saturated-Unsaturated flow and solute or energy TRAnsport simulation model SUTRA, Version 2D3D.1. This version of SutraPlot is an upgrade to SutraPlot for the 2D-only SUTRA model (Souza, 1987). It has been modified to add 3D functionality, a graphical user interface (GUI), and enhanced graphic output options. Graphical options for 2D SUTRA (2-dimension) simulations include: drawing the 2D finite-element mesh, mesh boundary, and velocity vectors; plots of contours for pressure, saturation, concentration, and temperature within the model region; 2D finite-element based gridding and interpolation; and 2D gridded data export files. Graphical options for 3D SUTRA (3-dimension) simulations include: drawing the 3D finite-element mesh; plots of contours for pressure, saturation, concentration, and temperature in 2D sections of the 3D model region; 3D finite-element based gridding and interpolation; drawing selected regions of velocity vectors (projected on principal coordinate planes); and 3D gridded data export files. Installation instructions and a description of all graphic options are presented. A sample SUTRA problem is described and three step-by-step SutraPlot applications are provided. In addition, the methodology and numerical algorithms for the 2D and 3D finite-element based gridding and interpolation, developed for SutraPlot, are described. 1

HFEM3D

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

Weiss, Chester J

Software solves the three-dimensional Poisson equation div(k(grad(u)) = f, by the finite element method for the case when material properties, k, are distributed over hierarchy of edges, facets and tetrahedra in the finite element mesh. Method is described in Weiss, CJ, Finite element analysis for model parameters distributed on a hierarchy of geometric simplices, Geophysics, v82, E155-167, doi:10.1190/GEO2017-0058.1 (2017). A standard finite element method for solving Poisson’s equation is augmented by including in the 3D stiffness matrix additional 2D and 1D stiffness matrices representing the contributions from material properties associated with mesh faces and edges, respectively. The resulting linear systemmore » is solved iteratively using the conjugate gradient method with Jacobi preconditioning. To minimize computer storage for program execution, the linear solver computes matrix-vector contractions element-by-element over the mesh, without explicit storage of the global stiffness matrix. Program output vtk compliant for visualization and rendering by 3rd party software. Program uses dynamic memory allocation and as such there are no hard limits on problem size outside of those imposed by the operating system and configuration on which the software is run. Dimension, N, of the finite element solution vector is constrained by the the addressable space in 32-vs-64 bit operating systems. Total storage requirements for the problem. Total working space required for the program is approximately 13*N double precision words.« less

Finite-element 3D simulation tools for high-current relativistic electron beams

NASA Astrophysics Data System (ADS)

Humphries, Stanley; Ekdahl, Carl

2002-08-01

The DARHT second-axis injector is a challenge for computer simulations. Electrons are subject to strong beam-generated forces. The fields are fully three-dimensional and accurate calculations at surfaces are critical. We describe methods applied in OmniTrak, a 3D finite-element code suite that can address DARHT and the full range of charged-particle devices. The system handles mesh generation, electrostatics, magnetostatics and self-consistent particle orbits. The MetaMesh program generates meshes of conformal hexahedrons to fit any user geometry. The code has the unique ability to create structured conformal meshes with cubic logic. Organized meshes offer advantages in speed and memory utilization in the orbit and field solutions. OmniTrak is a versatile charged-particle code that handles 3D electric and magnetic field solutions on independent meshes. The program can update both 3D field solutions from the calculated beam space-charge and current-density. We shall describe numerical methods for orbit tracking on a hexahedron mesh. Topics include: 1) identification of elements along the particle trajectory, 2) fast searches and adaptive field calculations, 3) interpolation methods to terminate orbits on material surfaces, 4) automatic particle generation on multiple emission surfaces to model space-charge-limited emission and field emission, 5) flexible Child law algorithms, 6) implementation of the dual potential model for 3D magnetostatics, and 7) assignment of charge and current from model particle orbits for self-consistent fields.

Evaluation on Compressive Characteristics of Medical Stents Applied by Mesh Structures

NASA Astrophysics Data System (ADS)

Hirayama, Kazuki; He, Jianmei

2017-11-01

There are concerns about strength reduction and fatigue fracture due to stress concentration in currently used medical stents. To address these problems, meshed stents applied by mesh structures were interested for achieving long life and high strength perfromance of medical stents. The purpose of this study is to design basic mesh shapes to obatin three dimensional (3D) meshed stent models for mechanical property evaluation. The influence of introduced design variables on compressive characteristics of meshed stent models are evaluated through finite element analysis using ANSYS Workbench code. From the analytical results, the compressive stiffness are changed periodically with compressive directions, average results need to be introduced as the mean value of compressive stiffness of meshed stents. Secondly, compressive flexibility of meshed stents can be improved by increasing the angle proportional to the arm length of the mesh basic shape. By increasing the number of basic mesh shapes arranged in stent’s circumferential direction, compressive rigidity of meshed stent tends to be increased. Finaly reducing the mesh line width is found effective to improve compressive flexibility of meshed stents.

Simulation of patch and slot antennas using FEM with prismatic elements and investigations of artificial absorber mesh termination schemes

NASA Technical Reports Server (NTRS)

Gong, J.; Ozdemir, T.; Volakis, J; Nurnberger, M.

1995-01-01

Year 1 progress can be characterized with four major achievements which are crucial toward the development of robust, easy to use antenna analysis code on doubly conformal platforms. (1) A new FEM code was developed using prismatic meshes. This code is based on a new edge based distorted prism and is particularly attractive for growing meshes associated with printed slot and patch antennas on doubly conformal platforms. It is anticipated that this technology will lead to interactive, simple to use codes for a large class of antenna geometries. Moreover, the codes can be expanded to include modeling of the circuit characteristics. An attached report describes the theory and validation of the new prismatic code using reference calculations and measured data collected at the NASA Langley facilities. The agreement between the measured and calculated data is impressive even for the coated patch configuration. (2) A scheme was developed for improved feed modeling in the context of FEM. A new approach based on the voltage continuity condition was devised and successfully tested in modeling coax cables and aperture fed antennas. An important aspect of this new feed modeling approach is the ability to completely separate the feed and antenna mesh regions. In this manner, different elements can be used in each of the regions leading to substantially improved accuracy and meshing simplicity. (3) A most important development this year has been the introduction of the perfectly matched interface (PMI) layer for truncating finite element meshes. So far the robust boundary integral method has been used for truncating the finite element meshes. However, this approach is not suitable for antennas on nonplanar platforms. The PMI layer is a lossy anisotropic absorber with zero reflection at its interface. (4) We were able to interface our antenna code FEMA_CYL (for antennas on cylindrical platforms) with a standard high frequency code. This interface was achieved by first generating equivalent magnetic currents across the antenna aperture using the FEM code. These currents were employed as the sources in the high frequency code.

Third-order accurate conservative method on unstructured meshes for gasdynamic simulations

NASA Astrophysics Data System (ADS)

Shirobokov, D. A.

2017-04-01

A third-order accurate finite-volume method on unstructured meshes is proposed for solving viscous gasdynamic problems. The method is described as applied to the advection equation. The accuracy of the method is verified by computing the evolution of a vortex on meshes of various degrees of detail with variously shaped cells. Additionally, unsteady flows around a cylinder and a symmetric airfoil are computed. The numerical results are presented in the form of plots and tables.

Simulation of the turbulent Rayleigh-Benard problem using a spectral/finite difference technique

NASA Technical Reports Server (NTRS)

Eidson, T. M.; Hussaini, M. Y.; Zang, T. A.

1986-01-01

The three-dimensional, incompressible Navier-Stokes and energy equations with the Bousinesq assumption have been directly simulated at a Rayleigh number of 3.8 x 10 to the 5th power and a Prandtl number of 0.76. In the vertical direction, wall boundaries were used and in the horizontal, periodic boundary conditions were used. A spectral/finite difference numerical method was used to simulate the flow. The flow at these conditions is turbulent and a sufficiently fine mesh was used to capture all relevant flow scales. The results of the simulation are compared to experimental data to justify the conclusion that the small scale motion is adequately resolved.

A MacCormack-TVD finite difference method to simulate the mass flow in mountainous terrain with variable computational domain

NASA Astrophysics Data System (ADS)

Ouyang, Chaojun; He, Siming; Xu, Qiang; Luo, Yu; Zhang, Wencheng

2013-03-01

A two-dimensional mountainous mass flow dynamic procedure solver (Massflow-2D) using the MacCormack-TVD finite difference scheme is proposed. The solver is implemented in Matlab on structured meshes with variable computational domain. To verify the model, a variety of numerical test scenarios, namely, the classical one-dimensional and two-dimensional dam break, the landslide in Hong Kong in 1993 and the Nora debris flow in the Italian Alps in 2000, are executed, and the model outputs are compared with published results. It is established that the model predictions agree well with both the analytical solution as well as the field observations.

Nitsche Extended Finite Element Methods for Earthquake Simulation

NASA Astrophysics Data System (ADS)

Coon, Ethan T.

Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities. The most difficult aspect of modeling physics on complicated domains is the mesh. Most numerical methods involve meshing the geometry; nodes are placed on the discontinuities, and edges are chosen to coincide with faults. The resulting mesh is highly unstructured, making the derivation of finite difference discretizations difficult. Therefore, most models use the finite element method. Standard finite element methods place requirements on the mesh for the sake of stability, accuracy, and efficiency. The formation of a mesh which both conforms to fault geometry and satisfies these requirements is an open problem, especially for three dimensional, physically realistic fault. geometries. In addition, if the fault system evolves over the course of a dynamic simulation (i.e. in the case of growing cracks or breaking new faults), the geometry must he re-meshed at each time step. This can be expensive computationally. The fault-conforming approach is undesirable when complicated meshes are required, and impossible to implement when the geometry is evolving. Therefore, meshless and hybrid finite element methods that handle discontinuities without placing them on element boundaries are a desirable and natural way to discretize these problems. Several such methods are being actively developed for use in engineering mechanics involving crack propagation and material failure. While some theory and application of these methods exist, implementations for the simulation of networks of many cracks have not yet been considered. For my thesis, I implement and extend one such method, the eXtended Finite Element Method (XFEM), for use in static and dynamic models of fault networks. Once this machinery is developed, it is applied to open questions regarding the behavior of networks of faults, including questions of distributed deformation in fault systems and ensembles of magnitude, location, and frequency in repeat ruptures. The theory of XFEM is augmented to allow for solution of problems with alternating regimes of static solves for elastic stress conditions and short, dynamic earthquakes on networks of faults. This is accomplished using Nitsche's approach for implementing boundary conditions. Finally, an optimization problem is developed to determine tractions along the fault, enabling the calculation of frictional constraints and the rupture front. This method is verified via a series of static, quasistatic, and dynamic problems. Armed with this technique, we look at several problems regarding geometry within the earthquake cycle in which geometry is crucial. We first look at quasistatic simulations on a community fault model of Southern California, and model slip distribution across that system. We find the distribution of deformation across faults compares reasonably well with slip rates across the region, as constrained by geologic data. We find geometry can provide constraints for friction, and consider the minimization of shear strain across the zone as a function of friction and plate loading direction, and infer bounds on fault strength in the region. Then we consider the repeated rupture problem, modeling the full earthquake cycle over the course of many events on several fault geometries. In this work, we look at distributions of events, studying the effect of geometry on statistical metrics of event ensembles. Finally, this thesis is a proof of concept for the XFEM on earthquake cycle models on fault systems. We identify strengths and weaknesses of the method, and identify places for future improvement. We discuss the feasibility of the method's use in three dimensions, and find the method to be a strong candidate for future crustal deformation simulations.

Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme

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

Graham, Aaron M; Collins, Benjamin S; Downar, Thomas

Oak Ridge National Laboratory and the University of Michigan are jointly developing the MPACTcode to be the primary neutron transport code for the Virtual Environment for Reactor Applications (VERA). To solve the transport equation, MPACT uses the 2D/1D method, which decomposes the problem into a stack of 2D planes that are then coupled with a 1D axial calculation. MPACT uses the Method of Characteristics for the 2D transport calculations and P3 for the 1D axial calculations, then accelerates the solution using the 3D Coarse mesh Finite Dierence (CMFD) method. Increasing the number of 2D MOC planes will increase the accuracymore » of the alculation, but will increase the computational burden of the calculations and can cause slow convergence or instability. To prevent these problems while maintaining accuracy, the sub-plane scheme has been implemented in MPACT. This method sub-divides the MOC planes into sub-planes, refining the 1D P3 and 3D CMFD calculations without increasing the number of 2D MOC planes. To test the sub-plane scheme, three of the VERA Progression Problems were selected: Problem 3, a single assembly problem; Problem 4, a 3x3 assembly problem with control rods and pyrex burnable poisons; and Problem 5, a quarter core problem. These three problems demonstrated that the sub-plane scheme can accurately produce intra-plane axial flux profiles that preserve the accuracy of the fine mesh solution. The eigenvalue dierences are negligibly small, and dierences in 3D power distributions are less than 0.1% for realistic axial meshes. Furthermore, the convergence behavior with the sub-plane scheme compares favorably with the conventional 2D/1D method, and the computational expense is decreased for all calculations due to the reduction in expensive MOC calculations.« less

A Nonlinear Dynamic Model and Free Vibration Analysis of Deployable Mesh Reflectors

NASA Technical Reports Server (NTRS)

Shi, H.; Yang, B.; Thomson, M.; Fang, H.

2011-01-01

This paper presents a dynamic model of deployable mesh reflectors, in which geometric and material nonlinearities of such a space structure are fully described. Then, by linearization around an equilibrium configuration of the reflector structure, a linearized model is obtained. With this linearized model, the natural frequencies and mode shapes of a reflector can be computed. The nonlinear dynamic model of deployable mesh reflectors is verified by using commercial finite element software in numerical simulation. As shall be seen, the proposed nonlinear model is useful for shape (surface) control of deployable mesh reflectors under thermal loads.

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

Herrnstein, Aaron R.

An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration,more » and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO 2 concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No dramatic or persistent signs of error growth in the passive tracer outgassing or the ocean circulation are observed to result from AMR.« less

Spectral Upscaling for Graph Laplacian Problems with Application to Reservoir Simulation

DOE PAGES

Barker, Andrew T.; Lee, Chak S.; Vassilevski, Panayot S.

2017-10-26

Here, we consider coarsening procedures for graph Laplacian problems written in a mixed saddle-point form. In that form, in addition to the original (vertex) degrees of freedom (dofs), we also have edge degrees of freedom. We extend previously developed aggregation-based coarsening procedures applied to both sets of dofs to now allow more than one coarse vertex dof per aggregate. Those dofs are selected as certain eigenvectors of local graph Laplacians associated with each aggregate. Additionally, we coarsen the edge dofs by using traces of the discrete gradients of the already constructed coarse vertex dofs. These traces are defined on themore » interface edges that connect any two adjacent aggregates. The overall procedure is a modification of the spectral upscaling procedure developed in for the mixed finite element discretization of diffusion type PDEs which has the important property of maintaining inf-sup stability on coarse levels and having provable approximation properties. We consider applications to partitioning a general graph and to a finite volume discretization interpreted as a graph Laplacian, developing consistent and accurate coarse-scale models of a fine-scale problem.« less

New software developments for quality mesh generation and optimization from biomedical imaging data.

PubMed

Yu, Zeyun; Wang, Jun; Gao, Zhanheng; Xu, Ming; Hoshijima, Masahiko

2014-01-01

In this paper we present a new software toolkit for generating and optimizing surface and volumetric meshes from three-dimensional (3D) biomedical imaging data, targeted at image-based finite element analysis of some biomedical activities in a single material domain. Our toolkit includes a series of geometric processing algorithms including surface re-meshing and quality-guaranteed tetrahedral mesh generation and optimization. All methods described have been encapsulated into a user-friendly graphical interface for easy manipulation and informative visualization of biomedical images and mesh models. Numerous examples are presented to demonstrate the effectiveness and efficiency of the described methods and toolkit. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Do Invertebrate Activity and Current Velocity Affect Fungal Assemblage Structure in Leaves?

NASA Astrophysics Data System (ADS)

Ferreira, Verónica; Graça, Manuel A. S.

2006-02-01

In this study we assessed the effect of current velocity and shredder presence, manipulated in artificial channels, on the structure of the fungal assemblage colonizing alder (Alnus glutinosa (L.) Gaertner) leaves incubated in coarse and fine mesh bags. Fungal sporulation rates, cumulative conidial production and number of species of aquatic hyphomycetes were higher in leaves exposed to high rather than to low current velocity. The opposite was observed regarding Simpson's index (D) on the fungal assemblage. Some species of aquatic hyphomycetes were consistently stimulated in high current channels. No effect of shredders or of mesh type was observed.

Recent Development of Multigrid Algorithms for Mixed and Noncomforming Methods for Second Order Elliptical Problems

NASA Technical Reports Server (NTRS)

Chen, Zhangxin; Ewing, Richard E.

1996-01-01

Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered. The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed. The equivalence between the nonconforming and mixed finite element methods with and without projection of the coefficient of the differential problems into finite element spaces is described.

Evaluation of Strip Footing Bearing Capacity Built on the Anthropogenic Embankment by Random Finite Element Method

NASA Astrophysics Data System (ADS)

Pieczynska-Kozlowska, Joanna

2014-05-01

One of a geotechnical problem in the area of Wroclaw is an anthropogenic embankment layer delaying to the depth of 4-5m, arising as a result of historical incidents. In such a case an assumption of bearing capacity of strip footing might be difficult. The standard solution is to use a deep foundation or foundation soil replacement. However both methods generate significant costs. In the present paper the authors focused their attention on the influence of anthropogenic embankment variability on bearing capacity. Soil parameters were defined on the basis of CPT test and modeled as 2D anisotropic random fields and the assumption of bearing capacity were made according deterministic finite element methods. Many repeated of the different realizations of random fields lead to stable expected value of bearing capacity. The algorithm used to estimate the bearing capacity of strip footing was the random finite element method (e.g. [1]). In traditional approach of bearing capacity the formula proposed by [2] is taken into account. qf = c'Nc + qNq + 0.5γBN- γ (1) where: qf is the ultimate bearing stress, cis the cohesion, qis the overburden load due to foundation embedment, γ is the soil unit weight, Bis the footing width, and Nc, Nq and Nγ are the bearing capacity factors. The method of evaluation the bearing capacity of strip footing based on finite element method incorporate five parameters: Young's modulus (E), Poisson's ratio (ν), dilation angle (ψ), cohesion (c), and friction angle (φ). In the present study E, ν and ψ are held constant while c and φ are randomized. Although the Young's modulus does not affect the bearing capacity it governs the initial elastic response of the soil. Plastic stress redistribution is accomplished using a viscoplastic algorithm merge with an elastic perfectly plastic (Mohr - Coulomb) failure criterion. In this paper a typical finite element mesh was assumed with 8-node elements consist in 50 columns and 20 rows. Footings width B occupies 10 elements, 0.1 x 0.1 meter size. The footings are placed at the center of the mesh. Figure 1 shows the mesh used in probabilistic bearing capacity analysis. PIC Figure 1- Mesh used in analyses REFERENCES Fenton, G.A., Griffiths, D.V., (2008) Risk Assessment in Geotechnical Engineering, John Wiley & Sons, New York, Terzaghi, K. (1943). Theoretical Soil Mechanics, New York: John Wiley & Sons.

Adaptation of an unstructured-mesh, finite-element ocean model to the simulation of ocean circulation beneath ice shelves

NASA Astrophysics Data System (ADS)

Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian

2013-07-01

Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.

Development of Finite-Volume Methods for Three-Dimensional Transonic Flows.

DTIC Science & Technology

1980-08-01

rapidly. Away from the airfoil, the streamlines spread. This type of mesh can easily be blended into a Cartesian mesh for the far field. A disadvantage...E. W., and Stern, M. A. (1980) "Simulated Transonic Flows for Aircraft with Nacelles, Pylons and Winglets ," AIAA Paper 80-0130, January. Caughey, D. A

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

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

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

dfnWorks: A discrete fracture network framework for modeling subsurface flow and transport

DOE PAGES

Hyman, Jeffrey D.; Karra, Satish; Makedonska, Nataliia; ...

2015-11-01

DFNWORKS is a parallelized computational suite to generate three-dimensional discrete fracture networks (DFN) and simulate flow and transport. Developed at Los Alamos National Laboratory over the past five years, it has been used to study flow and transport in fractured media at scales ranging from millimeters to kilometers. The networks are created and meshed using DFNGEN, which combines FRAM (the feature rejection algorithm for meshing) methodology to stochastically generate three-dimensional DFNs with the LaGriT meshing toolbox to create a high-quality computational mesh representation. The representation produces a conforming Delaunay triangulation suitable for high performance computing finite volume solvers in anmore » intrinsically parallel fashion. Flow through the network is simulated in dfnFlow, which utilizes the massively parallel subsurface flow and reactive transport finite volume code PFLOTRAN. A Lagrangian approach to simulating transport through the DFN is adopted within DFNTRANS to determine pathlines and solute transport through the DFN. Example applications of this suite in the areas of nuclear waste repository science, hydraulic fracturing and CO 2 sequestration are also included.« less

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

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

Di Pietro, Daniele A.; Droniou, Jérôme; Manzini, Gianmarco

Here, in this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart–Thomas–Nédélec subspace. We prove that the novelmore » DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Lastly, links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition.« less

Discontinuous Skeletal Gradient Discretisation methods on polytopal meshes

DOE PAGES

Di Pietro, Daniele A.; Droniou, Jérôme; Manzini, Gianmarco

2017-11-21

Here, in this work we develop arbitrary-order Discontinuous Skeletal Gradient Discretisations (DSGD) on general polytopal meshes. Discontinuous Skeletal refers to the fact that the globally coupled unknowns are broken polynomials on the mesh skeleton. The key ingredient is a high-order gradient reconstruction composed of two terms: (i) a consistent contribution obtained mimicking an integration by parts formula inside each element and (ii) a stabilising term for which sufficient design conditions are provided. An example of stabilisation that satisfies the design conditions is proposed based on a local lifting of high-order residuals on a Raviart–Thomas–Nédélec subspace. We prove that the novelmore » DSGDs satisfy coercivity, consistency, limit-conformity, and compactness requirements that ensure convergence for a variety of elliptic and parabolic problems. Lastly, links with Hybrid High-Order, non-conforming Mimetic Finite Difference and non-conforming Virtual Element methods are also studied. Numerical examples complete the exposition.« less

Comparison of Gap Elements and Contact Algorithm for 3D Contact Analysis of Spiral Bevel Gears

NASA Technical Reports Server (NTRS)

Bibel, G. D.; Tiku, K.; Kumar, A.; Handschuh, R.

1994-01-01

Three dimensional stress analysis of spiral bevel gears in mesh using the finite element method is presented. A finite element model is generated by solving equations that identify tooth surface coordinates. Contact is simulated by the automatic generation of nonpenetration constraints. This method is compared to a finite element contact analysis conducted with gap elements.

CFD Analysis of the SBXC Glider Airframe

DTIC Science & Technology

2016-06-01

mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the previous research data...greater than 15 m/s. 14. SUBJECT TERMS finite element method, computational fluid dynamics, Y Plus, mesh element quality, aerodynamic data, fluid...based mathematically on finite element methods. To validate and verify the methodology developed, a mathematical comparison was made with the

Numerical Analysis of Solids at Failure

DTIC Science & Technology

2011-08-20

failure analyses include the formulation of invariant finite elements for thin Kirchhoff rods, and preliminary initial studies of growth in...analysis of the failure of other structural/mechanical systems, including the finite element modeling of thin Kirchhoff rods and the constitutive...algorithm based on the connectivity graph of the underlying finite element mesh. In this setting, the discontinuities are defined by fronts propagating

Generating unstructured nuclear reactor core meshes in parallel

DOE PAGES

Jain, Rajeev; Tautges, Timothy J.

2014-10-24

Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor coremore » examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.« less

The optimization of high resolution topographic data for 1D hydrodynamic models

NASA Astrophysics Data System (ADS)

Ales, Ronovsky; Michal, Podhoranyi

2016-06-01

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domain and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.

The optimization of high resolution topographic data for 1D hydrodynamic models

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

Ales, Ronovsky, E-mail: ales.ronovsky@vsb.cz; Michal, Podhoranyi

2016-06-08

The main focus of our research presented in this paper is to optimize and use high resolution topographical data (HRTD) for hydrological modelling. Optimization of HRTD is done by generating adaptive mesh by measuring distance of coarse mesh and the surface of the dataset and adapting the mesh from the perspective of keeping the geometry as close to initial resolution as possible. Technique described in this paper enables computation of very accurate 1-D hydrodynamic models. In the paper, we use HEC-RAS software as a solver. For comparison, we have chosen the amount of generated cells/grid elements (in whole discretization domainmore » and selected cross sections) with respect to preservation of the accuracy of the computational domain. Generation of the mesh for hydrodynamic modelling is strongly reliant on domain size and domain resolution. Topographical dataset used in this paper was created using LiDAR method and it captures 5.9km long section of a catchment of the river Olše. We studied crucial changes in topography for generated mesh. Assessment was done by commonly used statistical and visualization methods.« less

On the dynamics of some grid adaption schemes

NASA Technical Reports Server (NTRS)

Sweby, Peter K.; Yee, Helen C.

1994-01-01

The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.

A FORTRAN program for calculating three dimensional, inviscid and rotational flows with shock waves in axial compressor blade rows: User's manual

NASA Technical Reports Server (NTRS)

Thompkins, W. T., Jr.

1982-01-01

A FORTRAN-IV computer program was developed for the calculation of the inviscid transonic/supersonic flow field in a fully three dimensional blade passage of an axial compressor rotor or stator. Rotors may have dampers (part span shrouds). MacCormack's explicit time marching method is used to solve the unsteady Euler equations on a finite difference mesh. This technique captures shocks and smears them over several grid points. Input quantities are blade row geometry, operating conditions and thermodynamic quanities. Output quantities are three velocity components, density and internal energy at each mesh point. Other flow quanities are calculated from these variables. A short graphics package is included with the code, and may be used to display the finite difference grid, blade geometry and static pressure contour plots on blade to blade calculation surfaces or blade suction and pressure surfaces. The flow in a low aspect ratio transonic compressor was analyzed and compared with high response total pressure probe measurements and gas fluorescence static density measurements made in the MIT blowdown wind tunnel. These comparisons show that the computed flow fields accurately model the measured shock wave locations and overall aerodynamic performance.

Assessment of sub-grid scale dispersion closure with regularized deconvolution method in a particle-laden turbulent jet

NASA Astrophysics Data System (ADS)

Wang, Qing; Zhao, Xinyu; Ihme, Matthias

2017-11-01

Particle-laden turbulent flows are important in numerous industrial applications, such as spray combustion engines, solar energy collectors etc. It is of interests to study this type of flows numerically, especially using large-eddy simulations (LES). However, capturing the turbulence-particle interaction in LES remains challenging due to the insufficient representation of the effect of sub-grid scale (SGS) dispersion. In the present work, a closure technique for the SGS dispersion using regularized deconvolution method (RDM) is assessed. RDM was proposed as the closure for the SGS dispersion in a counterflow spray that is studied numerically using finite difference method on a structured mesh. A presumed form of LES filter is used in the simulations. In the present study, this technique has been extended to finite volume method with an unstructured mesh, where no presumption on the filter form is required. The method is applied to a series of particle-laden turbulent jets. Parametric analyses of the model performance are conducted for flows with different Stokes numbers and Reynolds numbers. The results from LES will be compared against experiments and direct numerical simulations (DNS).

QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.

PubMed

Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit

2014-01-01

We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.

Fictitious domain method for fully resolved reacting gas-solid flow simulation

NASA Astrophysics Data System (ADS)

Zhang, Longhui; Liu, Kai; You, Changfu

2015-10-01

Fully resolved simulation (FRS) for gas-solid multiphase flow considers solid objects as finite sized regions in flow fields and their behaviours are predicted by solving equations in both fluid and solid regions directly. Fixed mesh numerical methods, such as fictitious domain method, are preferred in solving FRS problems and have been widely researched. However, for reacting gas-solid flows no suitable fictitious domain numerical method has been developed. This work presents a new fictitious domain finite element method for FRS of reacting particulate flows. Low Mach number reacting flow governing equations are solved sequentially on a regular background mesh. Particles are immersed in the mesh and driven by their surface forces and torques integrated on immersed interfaces. Additional treatments on energy and surface reactions are developed. Several numerical test cases validated the method and a burning carbon particles array falling simulation proved the capability for solving moving reacting particle cluster problems.

The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

NASA Astrophysics Data System (ADS)

Liu, Jiangguo; Tavener, Simon; Wang, Zhuoran

2018-04-01

This paper investigates the lowest-order weak Galerkin finite element method for solving the Darcy equation on quadrilateral and hybrid meshes consisting of quadrilaterals and triangles. In this approach, the pressure is approximated by constants in element interiors and on edges. The discrete weak gradients of these constant basis functions are specified in local Raviart-Thomas spaces, specifically RT0 for triangles and unmapped RT[0] for quadrilaterals. These discrete weak gradients are used to approximate the classical gradient when solving the Darcy equation. The method produces continuous normal fluxes and is locally mass-conservative, regardless of mesh quality, and has optimal order convergence in pressure, velocity, and normal flux, when the quadrilaterals are asymptotically parallelograms. Implementation is straightforward and results in symmetric positive-definite discrete linear systems. We present numerical experiments and comparisons with other existing methods.

Fully automatic hp-adaptivity for acoustic and electromagnetic scattering in three dimensions

NASA Astrophysics Data System (ADS)

Kurtz, Jason Patrick

We present an algorithm for fully automatic hp-adaptivity for finite element approximations of elliptic and Maxwell boundary value problems in three dimensions. The algorithm automatically generates a sequence of coarse grids, and a corresponding sequence of fine grids, such that the energy norm of the error decreases exponentially with respect to the number of degrees of freedom in either sequence. At each step, we employ a discrete optimization algorithm to determine the refinements for the current coarse grid such that the projection-based interpolation error for the current fine grid solution decreases with an optimal rate with respect to the number of degrees of freedom added by the refinement. The refinements are restricted only by the requirement that the resulting mesh is at most 1-irregular, but they may be anisotropic in both element size h and order of approximation p. While we cannot prove that our method converges at all, we present numerical evidence of exponential convergence for a diverse suite of model problems from acoustic and electromagnetic scattering. In particular we show that our method is well suited to the automatic resolution of exterior problems truncated by the introduction of a perfectly matched layer. To enable and accelerate the solution of these problems on commodity hardware, we include a detailed account of three critical aspects of our implementation, namely an efficient implementation of sum factorization, several efficient interfaces to the direct multi-frontal solver MUMPS, and some fast direct solvers for the computation of a sequence of nested projections.

Investigation of advanced counterrotation blade configuration concepts for high speed turboprop systems. Task 4: Advanced fan section aerodynamic analysis

NASA Technical Reports Server (NTRS)

Crook, Andrew J.; Delaney, Robert A.

1992-01-01

The purpose of this study is the development of a three-dimensional Euler/Navier-Stokes flow analysis for fan section/engine geometries containing multiple blade rows and multiple spanwise flow splitters. An existing procedure developed by Dr. J. J. Adamczyk and associates and the NASA Lewis Research Center was modified to accept multiple spanwise splitter geometries and simulate engine core conditions. The procedure was also modified to allow coarse parallelization of the solution algorithm. This document is a final report outlining the development and techniques used in the procedure. The numerical solution is based upon a finite volume technique with a four stage Runge-Kutta time marching procedure. Numerical dissipation is used to gain solution stability but is reduced in viscous dominated flow regions. Local time stepping and implicit residual smoothing are used to increase the rate of convergence. Multiple blade row solutions are based upon the average-passage system of equations. The numerical solutions are performed on an H-type grid system, with meshes being generated by the system (TIGG3D) developed earlier under this contract. The grid generation scheme meets the average-passage requirement of maintaining a common axisymmetric mesh for each blade row grid. The analysis was run on several geometry configurations ranging from one to five blade rows and from one to four radial flow splitters. Pure internal flow solutions were obtained as well as solutions with flow about the cowl/nacelle and various engine core flow conditions. The efficiency of the solution procedure was shown to be the same as the original analysis.

A three-dimensional finite element model of human atrial anatomy: New methods for cubic Hermite meshes with extraordinary vertices

PubMed Central

Gonzales, Matthew J.; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M.; Zhang, Yongjie; Segars, W. Paul; McCulloch, Andrew D.

2013-01-01

High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the “local-to-global” derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 millimeters, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. PMID:23602918

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

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

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

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.

Geometry reconstruction method for patient-specific finite element models for the assessment of tibia fracture risk in osteogenesis imperfecta.

PubMed

Caouette, Christiane; Ikin, Nicole; Villemure, Isabelle; Arnoux, Pierre-Jean; Rauch, Frank; Aubin, Carl-Éric

2017-04-01

Lower limb deformation in children with osteogenesis imperfecta (OI) impairs ambulation and may lead to fracture. Corrective surgery is based on empirical assessment criteria. The objective was to develop a reconstruction method of the tibia for OI patients that could be used as input of a comprehensive finite element model to assess fracture risks. Data were obtained from three children with OI and tibia deformities. Four pQCT scans were registered to biplanar radiographs, and a template mesh was deformed to fit the bone outline. Cortical bone thickness was computed. Sensitivity of the model to missing slices of pQCT was assessed by calculating maximal von Mises stress for a vertical hopping load case. Sensitivity of the model to ±5 % of cortical thickness measurements was assessed by calculating loads at fracture. Difference between the mesh contour and bone outline on the radiographs was below 1 mm. Removal of one pQCT slice increased maximal von Mises stress by up to 10 %. Simulated ±5 % variation of cortical bone thickness leads to variations of up to 4.1 % on predicted fracture loads. Using clinically available tibia imaging from children with OI, the developed reconstruction method allowed the building of patient-specific finite element models.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

LBMD : a layer-based mesh data structure tailored for generic API infrastructures.

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

Ebeida, Mohamed S.; Knupp, Patrick Michael

2010-11-01

A new mesh data structure is introduced for the purpose of mesh processing in Application Programming Interface (API) infrastructures. This data structure utilizes a reduced mesh representation to increase its ability to handle significantly larger meshes compared to full mesh representation. In spite of the reduced representation, each mesh entity (vertex, edge, face, and region) is represented using a unique handle, with no extra storage cost, which is a crucial requirement in most API libraries. The concept of mesh layers makes the data structure more flexible for mesh generation and mesh modification operations. This flexibility can have a favorable impactmore » in solver based queries of finite volume and multigrid methods. The capabilities of LBMD make it even more attractive for parallel implementations using Message Passing Interface (MPI) or Graphics Processing Units (GPUs). The data structure is associated with a new classification method to relate mesh entities to their corresponding geometrical entities. The classification technique stores the related information at the node level without introducing any ambiguities. Several examples are presented to illustrate the strength of this new data structure.« less

Unstructured Finite Elements and Dynamic Meshing for Explicit Phase Tracking in Multiphase Problems

NASA Astrophysics Data System (ADS)

Chandra, Anirban; Yang, Fan; Zhang, Yu; Shams, Ehsan; Sahni, Onkar; Oberai, Assad; Shephard, Mark

2017-11-01

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 finite element 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 Lagrangian-Eulerian (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.

Design of an essentially non-oscillatory reconstruction procedure in finite-element type meshes

NASA Technical Reports Server (NTRS)

Abgrall, Remi

1992-01-01

An essentially non oscillatory reconstruction for functions defined on finite element type meshes is designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitary meshes and the reconstruction of a function from its averages in the control volumes surrounding the nodes of the mesh. Concerning the first problem, the behavior of the highest coefficients of two polynomial interpolations of a function that may admit discontinuities of locally regular curves is studied: the Lagrange interpolation and an approximation such that the mean of the polynomial on any control volume is equal to that of the function to be approximated. This enables the best stencil for the approximation to be chosen. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, two methods were studied: one based on an adaptation of the so called reconstruction via deconvolution method to irregular meshes and one that lies on the approximation on the mean as defined above. The first method is conservative up to a quadrature formula and the second one is exactly conservative. The two methods have the expected order of accuracy, but the second one is much less expensive than the first one. Some numerical examples are given which demonstrate the efficiency of the reconstruction.

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Finite element strategies to satisfy clinical and engineering requirements in the field of percutaneous valves.

PubMed

Capelli, Claudio; Biglino, Giovanni; Petrini, Lorenza; Migliavacca, Francesco; Cosentino, Daria; Bonhoeffer, Philipp; Taylor, Andrew M; Schievano, Silvia

2012-12-01

Finite element (FE) modelling can be a very resourceful tool in the field of cardiovascular devices. To ensure result reliability, FE models must be validated experimentally against physical data. Their clinical application (e.g., patients' suitability, morphological evaluation) also requires fast simulation process and access to results, while engineering applications need highly accurate results. This study shows how FE models with different mesh discretisations can suit clinical and engineering requirements for studying a novel device designed for percutaneous valve implantation. Following sensitivity analysis and experimental characterisation of the materials, the stent-graft was first studied in a simplified geometry (i.e., compliant cylinder) and validated against in vitro data, and then in a patient-specific implantation site (i.e., distensible right ventricular outflow tract). Different meshing strategies using solid, beam and shell elements were tested. Results showed excellent agreement between computational and experimental data in the simplified implantation site. Beam elements were found to be convenient for clinical applications, providing reliable results in less than one hour in a patient-specific anatomical model. Solid elements remain the FE choice for engineering applications, albeit more computationally expensive (>100 times). This work also showed how information on device mechanical behaviour differs when acquired in a simplified model as opposed to a patient-specific model.

Development of a hip joint model for finite volume simulations.

PubMed

Cardiff, P; Karač, A; FitzPatrick, D; Ivanković, A

2014-01-01

This paper establishes a procedure for numerical analysis of a hip joint using the finite volume method. Patient-specific hip joint geometry is segmented directly from computed tomography and magnetic resonance imaging datasets and the resulting bone surfaces are processed into a form suitable for volume meshing. A high resolution continuum tetrahedral mesh has been generated, where a sandwich model approach is adopted; the bones are represented as a stiffer cortical shells surrounding more flexible cancellous cores. Cartilage is included as a uniform thickness extruded layer and the effect of layer thickness is investigated. To realistically position the bones, gait analysis has been performed giving the 3D positions of the bones for the full gait cycle. Three phases of the gait cycle are examined using a finite volume based custom structural contact solver implemented in open-source software OpenFOAM.

Numerical evaluation of discontinuous and nonconforming finite element methods in nonlinear solid mechanics

NASA Astrophysics Data System (ADS)

Bayat, Hamid Reza; Krämer, Julian; Wunderlich, Linus; Wulfinghoff, Stephan; Reese, Stefanie; Wohlmuth, Barbara; Wieners, Christian

2018-03-01

This work presents a systematic study of discontinuous and nonconforming finite element methods for linear elasticity, finite elasticity, and small strain plasticity. In particular, we consider new hybrid methods with additional degrees of freedom on the skeleton of the mesh and allowing for a local elimination of the element-wise degrees of freedom. We show that this process leads to a well-posed approximation scheme. The quality of the new methods with respect to locking and anisotropy is compared with standard and in addition locking-free conforming methods as well as established (non-) symmetric discontinuous Galerkin methods with interior penalty. For several benchmark configurations, we show that all methods converge asymptotically for fine meshes and that in many cases the hybrid methods are more accurate for a fixed size of the discrete system.

An adaptive multiblock high-order finite-volume method for solving the shallow-water equations on the sphere

DOE PAGES

McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...

2015-09-04

We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.

Biological decomposition efficiency in different woodland soils.

PubMed

Herlitzius, H

1983-03-01

The decomposition (meaning disappearance) of different leaf types and artificial leaves made from cellulose hydrate foil was studied in three forests - an alluvial forest (Ulmetum), a beech forest on limestone soil (Melico-Fagetum), and a spruce forest in soil overlying limestone bedrock.Fine, medium, and coarse mesh litter bags of special design were used to investigate the roles of abiotic factors, microorganisms, and meso- and macrofauna in effecting decomposition in the three habitats. Additionally, the experimental design was carefully arranged so as to provide information about the effects on decomposition processes of the duration of exposure and the date or moment of exposure. 1. Exposure of litter samples oor 12 months showed: a) Litter enclosed in fine mesh bags decomposed to some 40-44% of the initial amount placed in each of the three forests. Most of this decomposition can be attributed to abiotic factors and microoganisms. b) Litter placed in medium mesh litter bags reduced by ca. 60% in alluvial forest, ca. 50% in beech forest and ca. 44% in spruce forest. c) Litter enclosed in coarse mesh litter bags was reduced by 71% of the initial weights exposed in alluvial and beech forests; in the spruce forest decomposition was no greater than observed with fine and medium mesh litter bags. Clearly, in spruce forest the macrofauna has little or no part to play in effecting decomposition. 2. Sequential month by month exposure of hazel leaves and cellulose hydrate foil in coarse mesh litter bags in all three forests showed that one month of exposure led to only slight material losses, they did occur smallest between March and May, and largest between June and October/November. 3. Coarse mesh litter bags containing either hazel or artificial leaves of cellulose hydrate foil were exposed to natural decomposition processes in December 1977 and subsampled monthly over a period of one year, this series constituted the From-sequence of experiments. Each of the From-sequence samples removed was immediately replaced by a fresh litter bag which was left in place until December 1978, this series constituted the To-sequence of experiments. The results arising from the designated From- and To-sequences showed: a) During the course of one year hazel leaves decomposed completely in alluvial forest, almost completely in beech forest but to only 50% of the initial value in spruce forest. b) Duration of exposure and not the date of exposure is the major controlling influence on decomposition in alluvial forest, a characteristic reflected in the mirror-image courses of the From- and To-sequences curves with respect to the abscissa or time axis. Conversely the date of exposure and not the duration of exposure is the major controlling influence on decomposition in the spruce forest, a characteristic reflected in the mirror-image courses of the From-and To-sequences with respect to the ordinate or axis of percentage decomposition. c) Leaf powder amendment increased the decomposition rate of the hazel and cellulose hydrate leaves in the spruce forest but had no significant effect on their decomposition rate in alluvial and beech forests. It is concluded from this, and other evidence, that litter amendment by leaf fragments of phytophage frass in sites of low biological decomposition activity (eg. spruce) enhances decomposition processes. d) The time course of hazel leaf decomposition in both alluvial and beech forest is sigmoidal. Three s-phases are distinguished and correspond to the activity of microflora/microfauna, mesofauna/macrofauna, and then microflora/microfauna again. In general, the sigmoidal pattern of the curve can be considered valid for all decomposition processes occurring in terrestrial situations. It is contended that no decomposition (=disappearance) curve actually follows an e-type exponential function. A logarithmic linear regression can be constructed from the sigmoid curve data and although this facilitates inter-system comparisons it does not clearly express the dynamics of decomposition. 4. The course of the curve constructed from information about the standard deviations of means derived from the From- and To-sequence data does reflect the dynamics of litter decomposition. The three s-phases can be recognised and by comparing the actual From-sequence deviation curve with a mirror inversion representation of the To-sequence curve it is possible to determine whether decomposition is primarily controlled by the duration of exposure or the date of exposure. As is the case for hazel leaf decomposition in beech forest intermediate conditions can be readily recognised.

Mesoscopic-microscopic spatial stochastic simulation with automatic system partitioning.

PubMed

Hellander, Stefan; Hellander, Andreas; Petzold, Linda

2017-12-21

The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian dynamics or Green's function reaction dynamics, the RDME can be orders of magnitude faster if the lattice spacing can be chosen coarse enough. However, strongly diffusion-controlled reactions mandate a very fine mesh resolution for acceptable accuracy. It is common that reactions in the same model differ in their degree of diffusion control and therefore require different degrees of mesh resolution. This renders mesoscopic simulation inefficient for systems with multiscale properties. Mesoscopic-microscopic hybrid methods address this problem by resolving the most challenging reactions with a microscale, off-lattice simulation. However, all methods to date require manual partitioning of a system, effectively limiting their usefulness as "black-box" simulation codes. In this paper, we propose a hybrid simulation algorithm with automatic system partitioning based on indirect a priori error estimates. We demonstrate the accuracy and efficiency of the method on models of diffusion-controlled networks in 3D.

On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

NASA Astrophysics Data System (ADS)

Wu, Kailiang; Tang, Huazhong

2018-06-01

The paper studies the physical-constraints-preserving (PCP) schemes for multi-dimensional special relativistic magnetohydrodynamics with a general equation of state (EOS) on more general meshes. It is an extension of the work (Wu and Tang in Math. Models Methods Appl. Sci. 27:1871-1928, 2017) which focuses on the ideal EOS and uniform Cartesian meshes. The general EOS without a special expression poses some additional difficulties in discussing the mathematical properties of admissible state set with the physical constraints on the fluid velocity, density and pressure. Rigorous analyses are provided for the PCP property of finite volume or discontinuous Galerkin schemes with the Lax-Friedrichs (LxF)-type flux on a general mesh with non-self-intersecting polytopes. Those are built on a more general form of generalized LxF splitting property and a different convex decomposition technique. It is shown in theory that the PCP property is closely connected with a discrete divergence-free condition, which is proposed on the general mesh and milder than that in Wu and Tang (2017).

Numerical modelling of new rockfall interception nets

NASA Astrophysics Data System (ADS)

von Boetticher, Albrecht; Volkwein, Axel; Wendeler, Corinna

2010-05-01

The design and certification of effective rockfall protection barriers is mainly achieved through 1:1 prototype testing. In order to reduce development costs of a prototype it is recommended that pre-studies using numerical simulations are performed. A large component to modelling rockfall protection systems is the numerical simulation of the nets. To date there exist several approaches to model the different mesh types such as ring nets or diagonal meshes (Nicot 1999, Cazzani et al. 2002, Volkwein 2004). However, the consideration of chain link meshes has not yet been realised. Chain link meshes are normally found as standard fence structures. However, they also exist in setups using high-strength steel and wire bundles. These variants show an enormous capacity to retain loads e.g. rockfalls, and at the same time are very efficient due to their low demand of steel material. The increasing application of chain link mesh in barrier systems requires an accurate model is available to complete prototype studies. A new approach now aims to perform a Finite Element simulation of such chain link meshes. The main challenge herein is to achieve the net deformation behaviour that is observed in field tests also in the simulation. A simulation using simple truss elements would not work since it neglects the out-of-plane-height of the mesh construction providing important reserves for local and global high deformations. Thus addressing this, a specially developed Discrete Element is able to reconstruct the mechanical behaviour of the single chain wire (bundles). As input parameters it utilises typical properties such as longitudinal and transversal mesh widths, and break loads resulting from in-plane-tension tests and steel strength. The single chain elements then can be combined to a complete mesh (e.g. 130 x 65 mm, 3 - 4 mm wire with a strength of 1770 N-mm2). Combining these elements with a supporting structure consisting of posts, ropes and energy absorbers, enables the simulation of protection barriers used for natural hazards such as rockfalls or even landslides. The contribution explains the mechanical behaviour of the chain mesh, the calibration procedures and their application in flexible rockfall protection systems. The investigated meshes are built using three or four millimeter wire with a minimum yield strength of 1770 N-mm2: The maximal load in longitudinal mesh direction ranges about 130 - 380 kN-m and transversal 50 - 170 kN-m. The mesh size varies from 83 × 143 mm to 292 × 500 mm. References Cazzani, A., Mongiovi, L. and Frenez, T. (2002) Dynamic Finite Element Analysis of Interceptive Devices for Falling Rocks, International Journal of Rock Mechanics & Mining Sciences. 39,303-321. Volkwein, A. (2004) Numerische Simulation von flexiblen Steinschlagschutzsystemen. Diss. ETH Nr. 15641. Nicot, F. (1999) Etude du comportement méchanique des ouvrages souples de protection contre les éboulements rocheux. Diss. Ecole Centrale de Lyon.

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Anisotropic three-dimensional inversion of CSEM data using finite-element techniques on unstructured grids

NASA Astrophysics Data System (ADS)

Wang, Feiyan; Morten, Jan Petter; Spitzer, Klaus

2018-05-01

In this paper, we present a recently developed anisotropic 3-D inversion framework for interpreting controlled-source electromagnetic (CSEM) data in the frequency domain. The framework integrates a high-order finite-element forward operator and a Gauss-Newton inversion algorithm. Conductivity constraints are applied using a parameter transformation. We discretize the continuous forward and inverse problems on unstructured grids for a flexible treatment of arbitrarily complex geometries. Moreover, an unstructured mesh is more desirable in comparison to a single rectilinear mesh for multisource problems because local grid refinement will not significantly influence the mesh density outside the region of interest. The non-uniform spatial discretization facilitates parametrization of the inversion domain at a suitable scale. For a rapid simulation of multisource EM data, we opt to use a parallel direct solver. We further accelerate the inversion process by decomposing the entire data set into subsets with respect to frequencies (and transmitters if memory requirement is affordable). The computational tasks associated with each data subset are distributed to different processes and run in parallel. We validate the scheme using a synthetic marine CSEM model with rough bathymetry, and finally, apply it to an industrial-size 3-D data set from the Troll field oil province in the North Sea acquired in 2008 to examine its robustness and practical applicability.

Minimizing EIT image artefacts from mesh variability in finite element models.

PubMed

Adler, Andy; Lionheart, William R B

2011-07-01

Electrical impedance tomography (EIT) solves an inverse problem to estimate the conductivity distribution within a body from electrical simulation and measurements at the body surface, where the inverse problem is based on a solution of Laplace's equation in the body. Most commonly, a finite element model (FEM) is used, largely because of its ability to describe irregular body shapes. In this paper, we show that simulated variations in the positions of internal nodes within a FEM can result in serious image artefacts in the reconstructed images. Such variations occur when designing FEM meshes to conform to conductivity targets, but the effects may also be seen in other applications of absolute and difference EIT. We explore the hypothesis that these artefacts result from changes in the projection of the anisotropic conductivity tensor onto the FEM system matrix, which introduces anisotropic components into the simulated voltages, which cannot be reconstructed onto an isotropic image, and appear as artefacts. The magnitude of the anisotropic effect is analysed for a small regular FEM, and shown to be proportional to the relative node movement as a fraction of element size. In order to address this problem, we show that it is possible to incorporate a FEM node movement component into the formulation of the inverse problem. These results suggest that it is important to consider artefacts due to FEM mesh geometry in EIT image reconstruction.

Conservative multizonal interface algorithm for the 3-D Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Molvik, G. A.

1991-01-01

A conservative zonal interface algorithm using features of both structured and unstructured mesh CFD technology is presented. The flow solver within each of the zones is based on structured mesh CFD technology. The interface algorithm was implemented into two three-dimensional Navier-Stokes finite volume codes and was found to yield good results.

Examples of finite element mesh generation using SDRC IDEAS

NASA Technical Reports Server (NTRS)

Zapp, John; Volakis, John L.

1990-01-01

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, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.

Finite element models of the thigh-buttock complex for assessing static sitting discomfort and pressure sore risk: a literature review.

PubMed

Savonnet, Léo; Wang, Xuguang; Duprey, Sonia

2018-03-01

Being seated for long periods, while part of many leisure or occupational activities, can lead to discomfort, pain and sometimes health issues. The impact of prolonged sitting on the body has been widely studied in the literature, with a large number of human-body finite element models developed to simulate sitting and assess seat-induced discomfort or to investigate the biomechanical factors involved. Here, we review the finite element models developed to investigate sitting discomfort or risk of pressure sores. Our study examines finite element models from twenty-seven papers, seventeen dedicated to assessing seating discomfort and ten dedicated to investigating pressure ulcers caused by prolonged sitting. The models' mesh composition and material properties are found to differ widely. These models share a lack of validation and generally make little allowance for anthropometric diversity.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063