Efficient solution of 3D electromagnetic eddy-current problems within the finite volume framework of OpenFOAM

NASA Astrophysics Data System (ADS)

Beckstein, Pascal; Galindo, Vladimir; Vukčević, Vuko

2017-09-01

Eddy-current problems occur in a wide range of industrial and metallurgical applications where conducting material is processed inductively. Motivated by realising coupled multi-physics simulations, we present a new method for the solution of such problems in the finite volume framework of foam-extend, an extended version of the very popular OpenFOAM software. The numerical procedure involves a semi-coupled multi-mesh approach to solve Maxwell's equations for non-magnetic materials by means of the Coulomb gauged magnetic vector potential A and the electric scalar potential ϕ. The concept is further extended on the basis of the impressed and reduced magnetic vector potential and its usage in accordance with Biot-Savart's law to achieve a very efficient overall modelling even for complex three-dimensional geometries. Moreover, we present a special discretisation scheme to account for possible discontinuities in the electrical conductivity. To complement our numerical method, an extensive validation is completing the paper, which provides insight into the behaviour and the potential of our approach.

Implementation of Finite Volume based Navier Stokes Algorithm Within General Purpose Flow Network Code

NASA Technical Reports Server (NTRS)

Schallhorn, Paul; Majumdar, Alok

2012-01-01

This paper describes a finite volume based numerical algorithm that allows multi-dimensional computation of fluid flow within a system level network flow analysis. There are several thermo-fluid engineering problems where higher fidelity solutions are needed that are not within the capacity of system level codes. The proposed algorithm will allow NASA's Generalized Fluid System Simulation Program (GFSSP) to perform multi-dimensional flow calculation within the framework of GFSSP s typical system level flow network consisting of fluid nodes and branches. The paper presents several classical two-dimensional fluid dynamics problems that have been solved by GFSSP's multi-dimensional flow solver. The numerical solutions are compared with the analytical and benchmark solution of Poiseulle, Couette and flow in a driven cavity.

Kirkwood-Buff integrals of finite systems: shape effects

NASA Astrophysics Data System (ADS)

Dawass, Noura; Krüger, Peter; Simon, Jean-Marc; Vlugt, Thijs J. H.

2018-06-01

The Kirkwood-Buff (KB) theory provides an important connection between microscopic density fluctuations in liquids and macroscopic properties. Recently, Krüger et al. derived equations for KB integrals for finite subvolumes embedded in a reservoir. Using molecular simulation of finite systems, KB integrals can be computed either from density fluctuations inside such subvolumes, or from integrals of radial distribution functions (RDFs). Here, based on the second approach, we establish a framework to compute KB integrals for subvolumes with arbitrary convex shapes. This requires a geometric function w(x) which depends on the shape of the subvolume, and the relative position inside the subvolume. We present a numerical method to compute w(x) based on Umbrella Sampling Monte Carlo (MC). We compute KB integrals of a liquid with a model RDF for subvolumes with different shapes. KB integrals approach the thermodynamic limit in the same way: for sufficiently large volumes, KB integrals are a linear function of area over volume, which is independent of the shape of the subvolume.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

BIGHORN Computational Fluid Dynamics Theory, Methodology, and Code Verification & Validation Benchmark Problems

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

Xia, Yidong; Andrs, David; Martineau, Richard Charles

This document presents the theoretical background for a hybrid finite-element / finite-volume fluid flow solver, namely BIGHORN, based on the Multiphysics Object Oriented Simulation Environment (MOOSE) computational framework developed at the Idaho National Laboratory (INL). An overview of the numerical methods used in BIGHORN are discussed and followed by a presentation of the formulation details. The document begins with the governing equations for the compressible fluid flow, with an outline of the requisite constitutive relations. A second-order finite volume method used for solving the compressible fluid flow problems is presented next. A Pressure-Corrected Implicit Continuous-fluid Eulerian (PCICE) formulation for timemore » integration is also presented. The multi-fluid formulation is being developed. Although multi-fluid is not fully-developed, BIGHORN has been designed to handle multi-fluid problems. Due to the flexibility in the underlying MOOSE framework, BIGHORN is quite extensible, and can accommodate both multi-species and multi-phase formulations. This document also presents a suite of verification & validation benchmark test problems for BIGHORN. The intent for this suite of problems is to provide baseline comparison data that demonstrates the performance of the BIGHORN solution methods on problems that vary in complexity from laminar to turbulent flows. Wherever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using BIGHORN.« less

Quadratic Solid⁻Shell Finite Elements for Geometrically Nonlinear Analysis of Functionally Graded Material Plates.

PubMed

Chalal, Hocine; Abed-Meraim, Farid

2018-06-20

In the current contribution, prismatic and hexahedral quadratic solid⁻shell (SHB) finite elements are proposed for the geometrically nonlinear analysis of thin structures made of functionally graded material (FGM). The proposed SHB finite elements are developed within a purely 3D framework, with displacements as the only degrees of freedom. Also, the in-plane reduced-integration technique is combined with the assumed-strain method to alleviate various locking phenomena. Furthermore, an arbitrary number of integration points are placed along a special direction, which represents the thickness. The developed elements are coupled with functionally graded behavior for the modeling of thin FGM plates. To this end, the Young modulus of the FGM plate is assumed to vary gradually in the thickness direction, according to a volume fraction distribution. The resulting formulations are implemented into the quasi-static ABAQUS/Standard finite element software in the framework of large displacements and rotations. Popular nonlinear benchmark problems are considered to assess the performance and accuracy of the proposed SHB elements. Comparisons with reference solutions from the literature demonstrate the good capabilities of the developed SHB elements for the 3D simulation of thin FGM plates.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 1: Theoretical manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1991-01-01

Formulations and algorithms implemented in the MHOST finite element program are discussed. The code uses a novel concept of the mixed iterative solution technique for the efficient 3-D computations of turbine engine hot section components. The general framework of variational formulation and solution algorithms are discussed which were derived from the mixed three field Hu-Washizu principle. This formulation enables the use of nodal interpolation for coordinates, displacements, strains, and stresses. Algorithmic description of the mixed iterative method includes variations for the quasi static, transient dynamic and buckling analyses. The global-local analysis procedure referred to as the subelement refinement is developed in the framework of the mixed iterative solution, of which the detail is presented. The numerically integrated isoparametric elements implemented in the framework is discussed. Methods to filter certain parts of strain and project the element discontinuous quantities to the nodes are developed for a family of linear elements. Integration algorithms are described for linear and nonlinear equations included in MHOST program.

Time-dependent density functional theory with twist-averaged boundary conditions

NASA Astrophysics Data System (ADS)

Schuetrumpf, B.; Nazarewicz, W.; Reinhard, P.-G.

2016-05-01

Background: Time-dependent density functional theory is widely used to describe excitations of many-fermion systems. In its many applications, three-dimensional (3D) coordinate-space representation is used, and infinite-domain calculations are limited to a finite volume represented by a spatial box. For finite quantum systems (atoms, molecules, nuclei, hadrons), the commonly used periodic or reflecting boundary conditions introduce spurious quantization of the continuum states and artificial reflections from boundary; hence, an incorrect treatment of evaporated particles. Purpose: The finite-volume artifacts for finite systems can be practically cured by invoking an absorbing potential in a certain boundary region sufficiently far from the described system. However, such absorption cannot be applied in the calculations of infinite matter (crystal electrons, quantum fluids, neutron star crust), which suffer from unphysical effects stemming from a finite computational box used. Here, twist-averaged boundary conditions (TABC) have been used successfully to diminish the finite-volume effects. In this work, we extend TABC to time-dependent modes. Method: We use the 3D time-dependent density functional framework with the Skyrme energy density functional. The practical calculations are carried out for small- and large-amplitude electric dipole and quadrupole oscillations of 16O. We apply and compare three kinds of boundary conditions: periodic, absorbing, and twist-averaged. Results: Calculations employing absorbing boundary conditions (ABC) and TABC are superior to those based on periodic boundary conditions. For low-energy excitations, TABC and ABC variants yield very similar results. With only four twist phases per spatial direction in TABC, one obtains an excellent reduction of spurious fluctuations. In the nonlinear regime, one has to deal with evaporated particles. In TABC, the floating nucleon gas remains in the box; the amount of nucleons in the gas is found to be roughly the same as the number of absorbed particles in ABC. Conclusion: We demonstrate that by using TABC, one can reduce finite-volume effects drastically without adding any additional parameters associated with absorption at large distances. Moreover, TABC are an obvious choice for time-dependent calculations for infinite systems. Since TABC calculations for different twists can be performed independently, the method is trivially adapted to parallel computing.

A model for finite-deformation nonlinear thermomechanical response of single crystal copper under shock conditions

NASA Astrophysics Data System (ADS)

Luscher, Darby J.; Bronkhorst, Curt A.; Alleman, Coleman N.; Addessio, Francis L.

2013-09-01

A physically consistent framework for combining pressure-volume-temperature equations of state with crystal plasticity models is developed for the application of modeling the response of single and polycrystals under shock conditions. The particular model is developed for copper, thus the approach focuses on crystals of cubic symmetry although many of the concepts in the approach are applicable to crystals of lower symmetry. We employ a multiplicative decomposition of the deformation gradient into isochoric elastic, thermoelastic dilation, and plastic parts leading to a definition of isochoric elastic Green-Lagrange strain. This finite deformation kinematic decomposition enables a decomposition of Helmholtz free-energy into terms reflecting dilatational thermoelasticity, strain energy due to long-range isochoric elastic deformation of the lattice and a term reflecting energy stored in short range elastic lattice deformation due to evolving defect structures. A model for the single crystal response of copper is implemented consistent with the framework into a three-dimensional Lagrangian finite element code. Simulations exhibit favorable agreement with single and bicrystal experimental data for shock pressures ranging from 3 to 110 GPa.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

Sensitivity analysis on the effective stiffness properties of 3-D orthotropic honeycomb cores

NASA Astrophysics Data System (ADS)

Karakoç, Alp

2018-01-01

The present study investigates the influences of representative volume element RVE mesh and material parameters, here cell wall elastic moduli, on the effective stiffness properties of three dimensional orthotropic honeycomb cores through strain driven computational homogenization in the finite element framework. For this purpose, case studies were carried out, for which hexagonal cellular RVEs were generated, meshed with eight node linear brick finite elements of varying numbers. Periodic boundary conditions were then implemented on the RVE boundaries by using one-to-one nodal match for the corresponding corners, edges and surfaces for the imposed macroscopic strains. As a novelty, orthotropic material properties were assigned for each cell wall by means of the transformation matrices following the cell wall orientations. Thereafter, simulations were conducted and volume averaged macroscopic stresses were obtained. Eventually, effective stiffness properties were obtained, through which RVE sensitivity analysis was carried out. The investigations indicate that there is a strong relation between number of finite elements and most of the effective stiffness parameters. In addition to this, cell wall elastic moduli also play critical role on the effective properties of the investigated materials.

Finite volume model for two-dimensional shallow environmental flow

USGS Publications Warehouse

Simoes, F.J.M.

2011-01-01

This paper presents the development of a two-dimensional, depth integrated, unsteady, free-surface model based on the shallow water equations. The development was motivated by the desire of balancing computational efficiency and accuracy by selective and conjunctive use of different numerical techniques. The base framework of the discrete model uses Godunov methods on unstructured triangular grids, but the solution technique emphasizes the use of a high-resolution Riemann solver where needed, switching to a simpler and computationally more efficient upwind finite volume technique in the smooth regions of the flow. Explicit time marching is accomplished with strong stability preserving Runge-Kutta methods, with additional acceleration techniques for steady-state computations. A simplified mass-preserving algorithm is used to deal with wet/dry fronts. Application of the model is made to several benchmark cases that show the interplay of the diverse solution techniques.

Asynchronous discrete event schemes for PDEs

NASA Astrophysics Data System (ADS)

Stone, D.; Geiger, S.; Lord, G. J.

2017-08-01

A new class of asynchronous discrete-event simulation schemes for advection-diffusion-reaction equations is introduced, based on the principle of allowing quanta of mass to pass through faces of a (regular, structured) Cartesian finite volume grid. The timescales of these events are linked to the flux on the face. The resulting schemes are self-adaptive, and local in both time and space. Experiments are performed on realistic physical systems related to porous media flow applications, including a large 3D advection diffusion equation and advection diffusion reaction systems. The results are compared to highly accurate reference solutions where the temporal evolution is computed with exponential integrator schemes using the same finite volume discretisation. This allows a reliable estimation of the solution error. Our results indicate a first order convergence of the error as a control parameter is decreased, and we outline a framework for analysis.

A combined molecular dynamics/micromechanics/finite element approach for multiscale constitutive modeling of nanocomposites with interface effects

NASA Astrophysics Data System (ADS)

Yang, B. J.; Shin, H.; Lee, H. K.; Kim, H.

2013-12-01

We introduce a multiscale framework based on molecular dynamic (MD) simulation, micromechanics, and finite element method (FEM). A micromechanical model, which considers influences of the interface properties, nanoparticle (NP) size, and microcracks, is developed. Then, we perform MD simulations to characterize the mechanical properties of the nanocomposite system (silica/nylon 6) with varying volume fraction and size of NPs. By comparing the MD with micromechanics results, intrinsic physical properties at interfacial region are derived. Finally, we implement the developed model in the FEM code with the derived interfacial parameters, and predict the mechanical behavior of the nanocomposite at the macroscopic scale.

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.

Generalized Fourier analyses of the advection-diffusion equation - Part I: one-dimensional domains

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Martinez, Mario J.; Voth, Thomas E.

2004-07-01

This paper presents a detailed multi-methods comparison of the spatial errors associated with finite difference, finite element and finite volume semi-discretizations of the scalar advection-diffusion equation. The errors are reported in terms of non-dimensional phase and group speed, discrete diffusivity, artificial diffusivity, and grid-induced anisotropy. It is demonstrated that Fourier analysis provides an automatic process for separating the discrete advective operator into its symmetric and skew-symmetric components and characterizing the spectral behaviour of each operator. For each of the numerical methods considered, asymptotic truncation error and resolution estimates are presented for the limiting cases of pure advection and pure diffusion. It is demonstrated that streamline upwind Petrov-Galerkin and its control-volume finite element analogue, the streamline upwind control-volume method, produce both an artificial diffusivity and a concomitant phase speed adjustment in addition to the usual semi-discrete artifacts observed in the phase speed, group speed and diffusivity. The Galerkin finite element method and its streamline upwind derivatives are shown to exhibit super-convergent behaviour in terms of phase and group speed when a consistent mass matrix is used in the formulation. In contrast, the CVFEM method and its streamline upwind derivatives yield strictly second-order behaviour. In Part II of this paper, we consider two-dimensional semi-discretizations of the advection-diffusion equation and also assess the affects of grid-induced anisotropy observed in the non-dimensional phase speed, and the discrete and artificial diffusivities. Although this work can only be considered a first step in a comprehensive multi-methods analysis and comparison, it serves to identify some of the relative strengths and weaknesses of multiple numerical methods in a common analysis framework. Published in 2004 by John Wiley & Sons, Ltd.

High-order accurate finite-volume formulations for the pressure gradient force in layered ocean models

NASA Astrophysics Data System (ADS)

Engwirda, Darren; Kelley, Maxwell; Marshall, John

2017-08-01

Discretisation of the horizontal pressure gradient force in layered ocean models is a challenging task, with non-trivial interactions between the thermodynamics of the fluid and the geometry of the layers often leading to numerical difficulties. We present two new finite-volume schemes for the pressure gradient operator designed to address these issues. In each case, the horizontal acceleration is computed as an integration of the contact pressure force that acts along the perimeter of an associated momentum control-volume. A pair of new schemes are developed by exploring different control-volume geometries. Non-linearities in the underlying equation-of-state definitions and thermodynamic profiles are treated using a high-order accurate numerical integration framework, designed to preserve hydrostatic balance in a non-linear manner. Numerical experiments show that the new methods achieve high levels of consistency, maintaining hydrostatic and thermobaric equilibrium in the presence of strongly-sloping layer geometries, non-linear equations-of-state and non-uniform vertical stratification profiles. These results suggest that the new pressure gradient formulations may be appropriate for general circulation models that employ hybrid vertical coordinates and/or terrain-following representations.

Size effects in martensitic microstructures: Finite-strain phase field model versus sharp-interface approach

NASA Astrophysics Data System (ADS)

Tůma, K.; Stupkiewicz, S.; Petryk, H.

2016-10-01

A finite-strain phase field model for martensitic phase transformation and twinning in shape memory alloys is developed and confronted with the corresponding sharp-interface approach extended to interfacial energy effects. The model is set in the energy framework so that the kinetic equations and conditions of mechanical equilibrium are fully defined by specifying the free energy and dissipation potentials. The free energy density involves the bulk and interfacial energy contributions, the latter describing the energy of diffuse interfaces in a manner typical for phase-field approaches. To ensure volume preservation during martensite reorientation at finite deformation within a diffuse interface, it is proposed to apply linear mixing of the logarithmic transformation strains. The physically different nature of phase interfaces and twin boundaries in the martensitic phase is reflected by introducing two order-parameters in a hierarchical manner, one as the reference volume fraction of austenite, and thus of the whole martensite, and the second as the volume fraction of one variant of martensite in the martensitic phase only. The microstructure evolution problem is given a variational formulation in terms of incremental fields of displacement and order parameters, with unilateral constraints on volume fractions explicitly enforced by applying the augmented Lagrangian method. As an application, size-dependent microstructures with diffuse interfaces are calculated for the cubic-to-orthorhombic transformation in a CuAlNi shape memory alloy and compared with the sharp-interface microstructures with interfacial energy effects.

High Spatial Resolution Multi-Organ Finite Element Modeling of Ventricular-Arterial Coupling

PubMed Central

Shavik, Sheikh Mohammad; Jiang, Zhenxiang; Baek, Seungik; Lee, Lik Chuan

2018-01-01

While it has long been recognized that bi-directional interaction between the heart and the vasculature plays a critical role in the proper functioning of the cardiovascular system, a comprehensive study of this interaction has largely been hampered by a lack of modeling framework capable of simultaneously accommodating high-resolution models of the heart and vasculature. Here, we address this issue and present a computational modeling framework that couples finite element (FE) models of the left ventricle (LV) and aorta to elucidate ventricular—arterial coupling in the systemic circulation. We show in a baseline simulation that the framework predictions of (1) LV pressure—volume loop, (2) aorta pressure—diameter relationship, (3) pressure—waveforms of the aorta, LV, and left atrium (LA) over the cardiac cycle are consistent with the physiological measurements found in healthy human. To develop insights of ventricular-arterial interactions, the framework was then used to simulate how alterations in the geometrical or, material parameter(s) of the aorta affect the LV and vice versa. We show that changing the geometry and microstructure of the aorta model in the framework led to changes in the functional behaviors of both LV and aorta that are consistent with experimental observations. On the other hand, changing contractility and passive stiffness of the LV model in the framework also produced changes in both the LV and aorta functional behaviors that are consistent with physiology principles. PMID:29551977

Nonlinear electroelastic deformations of dielectric elastomer composites: II - Non-Gaussian elastic dielectrics

NASA Astrophysics Data System (ADS)

Lefèvre, Victor; Lopez-Pamies, Oscar

2017-02-01

This paper presents an analytical framework to construct approximate homogenization solutions for the macroscopic elastic dielectric response - under finite deformations and finite electric fields - of dielectric elastomer composites with two-phase isotropic particulate microstructures. The central idea consists in employing the homogenization solution derived in Part I of this work for ideal elastic dielectric composites within the context of a nonlinear comparison medium method - this is derived as an extension of the comparison medium method of Lopez-Pamies et al. (2013) in nonlinear elastostatics to the coupled realm of nonlinear electroelastostatics - to generate in turn a corresponding solution for composite materials with non-ideal elastic dielectric constituents. Complementary to this analytical framework, a hybrid finite-element formulation to construct homogenization solutions numerically (in three dimensions) is also presented. The proposed analytical framework is utilized to work out a general approximate homogenization solution for non-Gaussian dielectric elastomers filled with nonlinear elastic dielectric particles that may exhibit polarization saturation. The solution applies to arbitrary (non-percolative) isotropic distributions of filler particles. By construction, it is exact in the limit of small deformations and moderate electric fields. For finite deformations and finite electric fields, its accuracy is demonstrated by means of direct comparisons with finite-element solutions. Aimed at gaining physical insight into the extreme enhancement in electrostriction properties displayed by emerging dielectric elastomer composites, various cases wherein the filler particles are of poly- and mono-disperse sizes and exhibit different types of elastic dielectric behavior are discussed in detail. Contrary to an initial conjecture in the literature, it is found (inter alia) that the isotropic addition of a small volume fraction of stiff (semi-)conducting/high-permittivity particles to dielectric elastomers does not lead to the extreme electrostriction enhancements observed in experiments. It is posited that such extreme enhancements are the manifestation of interphasial phenomena.

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.

The Role of Second Phase Hard Particles on Hole Stretchability of two AA6xxx Alloys

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

Hu, Xiaohua; Sun, Xin; Golovashchenko, Sergey F.

The hole stretchability of two Aluminum Alloys (AA6111 and AA6022) are studied by using a two stages integrated finite element framework where the edge geometry and edge damages from the hole piercing processes were considered in the subsequent hole expansion processes. Experimentally it has been found that AA6022 has higher hole expansion ratios than those of AA6111. This observation has been nicely captured by finite element simulations. The main cause of differences have been identified to the volume fractions of the random distributed second phase hard particles which play a critical role in determining the fracture strains of the materials.

Effects of finite volume on the K L – K S mass difference

DOE PAGES

Christ, N.  H.; Feng, X.; Martinelli, G.; ...

2015-06-24

Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the Kmore » L – K S mass difference ΔM K and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less

Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: From first-order to high-orders. Part I: The one-dimensional case

NASA Astrophysics Data System (ADS)

Vilar, François; Shu, Chi-Wang; Maire, Pierre-Henri

2016-05-01

One of the main issues in the field of numerical schemes is to ally robustness with accuracy. Considering gas dynamics, numerical approximations may generate negative density or pressure, which may lead to nonlinear instability and crash of the code. This phenomenon is even more critical using a Lagrangian formalism, the grid moving and being deformed during the calculation. Furthermore, most of the problems studied in this framework contain very intense rarefaction and shock waves. In this paper, the admissibility of numerical solutions obtained by high-order finite-volume-scheme-based methods, such as the discontinuous Galerkin (DG) method, the essentially non-oscillatory (ENO) and the weighted ENO (WENO) finite volume schemes, is addressed in the one-dimensional Lagrangian gas dynamics framework. After briefly recalling how to derive Lagrangian forms of the 1D gas dynamics system of equations, a discussion on positivity-preserving approximate Riemann solvers, ensuring first-order finite volume schemes to be positive, is then given. This study is conducted for both ideal gas and non-ideal gas equations of state (EOS), such as the Jones-Wilkins-Lee (JWL) EOS or the Mie-Grüneisen (MG) EOS, and relies on two different techniques: either a particular definition of the local approximation of the acoustic impedances arising from the approximate Riemann solver, or an additional time step constraint relative to the cell volume variation. Then, making use of the work presented in [89,90,22], this positivity study is extended to high-orders of accuracy, where new time step constraints are obtained, and proper limitation is required. Through this new procedure, scheme robustness is highly improved and hence new problems can be tackled. Numerical results are provided to demonstrate the effectiveness of these methods. This paper is the first part of a series of two. The whole analysis presented here is extended to the two-dimensional case in [85], and proves to fit a wide range of numerical schemes in the literature, such as those presented in [19,64,15,82,84].

Entropy Stable Wall Boundary Conditions for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2014-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite volume, finite difference, discontinuous Galerkin, and flux reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

Entropy Stable Wall Boundary Conditions for the Three-Dimensional Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-01-01

Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier-Stokes equations. A semi-discrete entropy estimate for the entire domain is achieved when the new boundary conditions are coupled with an entropy stable discrete interior operator. The data at the boundary are weakly imposed using a penalty flux approach and a simultaneous-approximation-term penalty technique. Although discontinuous spectral collocation operators on unstructured grids are used herein for the purpose of demonstrating their robustness and efficacy, the new boundary conditions are compatible with any diagonal norm summation-by-parts spatial operator, including finite element, finite difference, finite volume, discontinuous Galerkin, and flux reconstruction/correction procedure via reconstruction schemes. The proposed boundary treatment is tested for three-dimensional subsonic and supersonic flows. The numerical computations corroborate the non-linear stability (entropy stability) and accuracy of the boundary conditions.

High Performance Computing Technologies for Modeling the Dynamics and Dispersion of Ice Chunks in the Arctic Ocean

DTIC Science & Technology

2016-08-23

SECURITY CLASSIFICATION OF: Hybrid finite element / finite volume based CaMEL shallow water flow solvers have been successfully extended to study wave...effects on ice floes in a simplified 10 sq-km ocean domain. Our solver combines the merits of both the finite element and finite volume methods and...ES) U.S. Army Research Office P.O. Box 12211 Research Triangle Park, NC 27709-2211 sea ice dynamics, shallow water, finite element , finite volume

A Finite-Volume "Shaving" Method for Interfacing NASA/DAO''s Physical Space Statistical Analysis System to the Finite-Volume GCM with a Lagrangian Control-Volume Vertical Coordinate

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; DaSilva, Arlindo; Atlas, Robert (Technical Monitor)

2001-01-01

Toward the development of a finite-volume Data Assimilation System (fvDAS), a consistent finite-volume methodology is developed for interfacing the NASA/DAO's Physical Space Statistical Analysis System (PSAS) to the joint NASA/NCAR finite volume CCM3 (fvCCM3). To take advantage of the Lagrangian control-volume vertical coordinate of the fvCCM3, a novel "shaving" method is applied to the lowest few model layers to reflect the surface pressure changes as implied by the final analysis. Analysis increments (from PSAS) to the upper air variables are then consistently put onto the Lagrangian layers as adjustments to the volume-mean quantities during the analysis cycle. This approach is demonstrated to be superior to the conventional method of using independently computed "tendency terms" for surface pressure and upper air prognostic variables.

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

NASA Astrophysics Data System (ADS)

Ruiz-Baier, Ricardo; Lunati, Ivan

2016-10-01

We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation, deformation of a cantilever bracket, and Boycott effects). The applicability of the method is not limited to flow in porous media, but can also be employed to describe many other physical systems governed by a similar set of equations, including e.g. multi-component materials.

Comparing volume of fluid and level set methods for evaporating liquid-gas flows

NASA Astrophysics Data System (ADS)

Palmore, John; Desjardins, Olivier

2016-11-01

This presentation demonstrates three numerical strategies for simulating liquid-gas flows undergoing evaporation. The practical aim of this work is to choose a framework capable of simulating the combustion of liquid fuels in an internal combustion engine. Each framework is analyzed with respect to its accuracy and computational cost. All simulations are performed using a conservative, finite volume code for simulating reacting, multiphase flows under the low-Mach assumption. The strategies used in this study correspond to different methods for tracking the liquid-gas interface and handling the transport of the discontinuous momentum and vapor mass fractions fields. The first two strategies are based on conservative, geometric volume of fluid schemes using directionally split and un-split advection, respectively. The third strategy is the accurate conservative level set method. For all strategies, special attention is given to ensuring the consistency between the fluxes of mass, momentum, and vapor fractions. The study performs three-dimensional simulations of an isolated droplet of a single component fuel evaporating into air. Evaporation rates and vapor mass fractions are compared to analytical results.

Modeling Complex Biological Flows in Multi-Scale Systems using the APDEC Framework

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

Trebotich, D

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA-laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscousmore » flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.« less

Modeling complex biological flows in multi-scale systems using the APDEC framework

NASA Astrophysics Data System (ADS)

Trebotich, David

2006-09-01

We have developed advanced numerical algorithms to model biological fluids in multiscale flow environments using the software framework developed under the SciDAC APDEC ISIC. The foundation of our computational effort is an approach for modeling DNA laden fluids as ''bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity, leveraging algorithms and solvers in the APDEC Framework. Our Cartesian grid embedded boundary approach to incompressible viscous flow in irregular geometries has also been interfaced to a fast and accurate level-sets method within the APDEC Framework for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.

Stabilized Finite Elements in FUN3D

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Newman, James C.; Karman, Steve L.

2017-01-01

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Symmetry Energy and Its Components in Finite Nuclei

NASA Astrophysics Data System (ADS)

Antonov, A. N.; Gaidarov, M. K.; Kadrev, D. N.; Sarriguren, P.; Moya de Guerra, E.

2018-05-01

We derive the volume and surface components of the nuclear symmetry energy (NSE) and their ratio within the coherent density fluctuation model. The estimations use the results of the model for the NSE in finite nuclei based on the Brueckner and Skyrme energy-density functionals for nuclear matter. The obtained values of the volume and surface contributions to the NSE and their ratio for the Ni, Sn, and Pb isotopic chains are compared with estimations of other approaches which have used available experimental data on binding energies, neutron-skin thicknesses, and excitation energies to isobaric analog states (IAS). Apart from the density dependence investigated in our previous works, we study also the temperature dependence of the symmetry energy in finite nuclei in the framework of the local density approximation combining it with the self-consistent Skyrme-HFB method using the cylindrical transformed deformed harmonic-oscillator basis. The results for the thermal evolution of the NSE in the interval T = 0–4 MeV show that its values decrease with temperature. The investigations of the T-dependence of the neutron and proton root-mean-square radii and the corresponding neutron skin thickness point out that the effect of temperature leads mainly to a substantial increase of the neutron radii and skins, especially in nuclei which are more rich of neutrons.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

Finite volume effects on the electric polarizability of neutral hadrons in lattice QCD

NASA Astrophysics Data System (ADS)

Lujan, M.; Alexandru, A.; Freeman, W.; Lee, F. X.

2016-10-01

We study the finite volume effects on the electric polarizability for the neutron, neutral pion, and neutral kaon using eight dynamically generated two-flavor nHYP-clover ensembles at two different pion masses: 306(1) and 227(2) MeV. An infinite volume extrapolation is performed for each hadron at both pion masses. For the neutral kaon, finite volume effects are relatively mild. The dependence on the quark mass is also mild, and a reliable chiral extrapolation can be performed along with the infinite volume extrapolation. Our result is αK0 phys=0.356 (74 )(46 )×10-4 fm3 . In contrast, for neutron, the electric polarizability depends strongly on the volume. After removing the finite volume corrections, our neutron polarizability results are in good agreement with chiral perturbation theory. For the connected part of the neutral pion polarizability, the negative trend persists, and it is not due to finite volume effects but likely sea quark charging effects.

Some implementational issues of convection schemes for finite volume formulations

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1993-01-01

Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementation as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.

Some implementational issues of convection schemes for finite-volume formulations

NASA Technical Reports Server (NTRS)

Thakur, Siddharth; Shyy, Wei

1993-01-01

Two higher-order upwind schemes - second-order upwind and QUICK - are examined in terms of their interpretation, implementations, as well as performance for a recirculating flow in a lid-driven cavity, in the context of a control-volume formulation using the SIMPLE algorithm. The present formulation of these schemes is based on a unified framework wherein the first-order upwind scheme is chosen as the basis, with the remaining terms being assigned to the source term. The performance of these schemes is contrasted with the first-order upwind and second-order central difference schemes. Also addressed in this study is the issue of boundary treatment associated with these higher-order upwind schemes. Two different boundary treatments - one that uses a two-point scheme consistently within a given control volume at the boundary, and the other that maintains consistency of flux across the interior face between the adjacent control volumes - are formulated and evaluated.

United States Air Force Graduate Student Summer Support Program (1987). Program Technical Report. Volume 1.

DTIC Science & Technology

1987-12-01

developed for a large percentage of the participants in the Summer Faculty Research Program in 1979-1983 period through an AFOSR Minigrant Program . On 1...Analysis of a Bimodal Nuclear Rocket Core by Dav,, C. Carpenter ABSTRACT The framework for a general purpose finite element analysis code was developed ...to study the 2-D temperature distribution in a hot-channel S hexagonal fuel element in the core of a bimodal nuclear’ rocket. Prelim- inary thermal

Mingus Discontinuous Multiphysics

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

Pat Notz, Dan Turner

Mingus provides hybrid coupled local/non-local mechanics analysis capabilities that extend several traditional methods to applications with inherent discontinuities. Its primary features include adaptations of solid mechanics, fluid dynamics and digital image correlation that naturally accommodate dijointed data or irregular solution fields by assimilating a variety of discretizations (such as control volume finite elements, peridynamics and meshless control point clouds). The goal of this software is to provide an analysis framework form multiphysics engineering problems with an integrated image correlation capability that can be used for experimental validation and model

Finite-volume scheme for anisotropic diffusion

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

Es, Bram van, E-mail: bramiozo@gmail.com; FOM Institute DIFFER, Dutch Institute for Fundamental Energy Research, The Netherlands"1; Koren, Barry

In this paper, we apply a special finite-volume scheme, limited to smooth temperature distributions and Cartesian grids, to test the importance of connectivity of the finite volumes. The area of application is nuclear fusion plasma with field line aligned temperature gradients and extreme anisotropy. We apply the scheme to the anisotropic heat-conduction equation, and compare its results with those of existing finite-volume schemes for anisotropic diffusion. Also, we introduce a general model adaptation of the steady diffusion equation for extremely anisotropic diffusion problems with closed field lines.

Shock-driven fluid-structure interaction for civil design

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

Wood, Stephen L; Deiterding, Ralf

The multiphysics fluid-structure interaction simulation of shock-loaded structures requires the dynamic coupling of a shock-capturing flow solver to a solid mechanics solver for large deformations. The Virtual Test Facility combines a Cartesian embedded boundary approach with dynamic mesh adaptation in a generic software framework of flow solvers using hydrodynamic finite volume upwind schemes that are coupled to various explicit finite element solid dynamics solvers (Deiterding et al., 2006). This paper gives a brief overview of the computational approach and presents first simulations that utilize the general purpose solid dynamics code DYNA3D for complex 3D structures of interest in civil engineering.more » Results from simulations of a reinforced column, highway bridge, multistory building, and nuclear reactor building are presented.« less

Morphing continuum theory for turbulence: Theory, computation, and visualization.

PubMed

Chen, James

2017-10-01

A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second-order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based direct numerical simulation (DNS) provides a better prediction than Navier-Stokes (NS)-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based Q criterion, the MCT-based Q criterion is objective without the limitation of Galilean invariance.

Dissipative properties of hot and dense hadronic matter in an excluded-volume hadron resonance gas model

NASA Astrophysics Data System (ADS)

Kadam, Guru Prakash; Mishra, Hiranmaya

2015-09-01

We estimate dissipative properties, viz., shear and bulk viscosities of hadronic matter using relativistic Boltzmann equation in relaxation time approximation within the framework of excluded-volume hadron resonance gas (EHRG) model. We find that at zero baryon chemical potential the shear viscosity to entropy ratio (η /s ) decreases with temperature while at finite baryon chemical potential this ratio shows the same behavior as a function of temperature but reaches close to the Kovtun-Son-Starinets (KSS) bound. Further along the chemical freezeout curve, ratio η /s is almost constant apart from small initial monotonic rise. This observation may have some relevance to the experimental finding that the differential elliptic flow of charged hadrons does not change considerably at lower center-of-mass energy. We further find that bulk viscosity to entropy density (ζ /s ) decreases with temperature while this ratio has higher value at finite baryon chemical potential at higher temperature. Along the freezeout curve ζ /s decreases monotonically at lower center-of-mass energy and then saturates.

A NURBS-enhanced finite volume solver for steady Euler equations

NASA Astrophysics Data System (ADS)

Meng, Xucheng; Hu, Guanghui

2018-04-01

In Hu and Yi (2016) [20], a non-oscillatory k-exact reconstruction method was proposed towards the high-order finite volume methods for steady Euler equations, which successfully demonstrated the high-order behavior in the simulations. However, the degeneracy of the numerical accuracy of the approximate solutions to problems with curved boundary can be observed obviously. In this paper, the issue is resolved by introducing the Non-Uniform Rational B-splines (NURBS) method, i.e., with given discrete description of the computational domain, an approximate NURBS curve is reconstructed to provide quality quadrature information along the curved boundary. The advantages of using NURBS include i). both the numerical accuracy of the approximate solutions and convergence rate of the numerical methods are improved simultaneously, and ii). the NURBS curve generation is independent of other modules of the numerical framework, which makes its application very flexible. It is also shown in the paper that by introducing more elements along the normal direction for the reconstruction patch of the boundary element, significant improvement in the convergence to steady state can be achieved. The numerical examples confirm the above features very well.

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

Development of a Hydrodynamic Model of Puget Sound and Northwest Straits

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

Yang, Zhaoqing; Khangaonkar, Tarang P.

2007-12-10

The hydrodynamic model used in this study is the Finite Volume Coastal Ocean Model (FVCOM) developed by the University of Massachusetts at Dartmouth. The unstructured grid and finite volume framework, as well as the capability of wetting/drying simulation and baroclinic simulation, makes FVCOM a good fit to the modeling needs for nearshore restoration in Puget Sound. The model domain covers the entire Puget Sound, Strait of Juan de Fuca, San Juan Passages, and Georgia Strait at the United States-Canada Border. The model is driven by tide, freshwater discharge, and surface wind. Preliminary model validation was conducted for tides at variousmore » locations in the straits and Puget Sound using National Oceanic and Atmospheric Administration (NOAA) tide data. The hydrodynamic model was successfully linked to the NOAA oil spill model General NOAA Operational Modeling Environment model (GNOME) to predict particle trajectories at various locations in Puget Sound. Model results demonstrated that the Puget Sound GNOME model is a useful tool to obtain first-hand information for emergency response such as oil spill and fish migration pathways.« less

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.

Taylor bubbles at high viscosity ratios: experiments and numerical simulations

NASA Astrophysics Data System (ADS)

Hewakandamby, Buddhika; Hasan, Abbas; Azzopardi, Barry; Xie, Zhihua; Pain, Chris; Matar, Omar

2015-11-01

The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube, often occurring in gas-liquid slug flows in many industrial applications, particularly oil and gas production. The objective of this study is to investigate the fluid dynamics of three-dimensional Taylor bubble rising in highly viscous silicone oil in a vertical pipe. An adaptive unstructured mesh modelling framework is adopted here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rising and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a `volume of fluid'-type method for the interface-capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Experimental results for the Taylor bubble shape and rise velocity are presented, together with numerical results for the dynamics of the bubbles. A comparison of the simulation predictions with experimental data available in the literature is also presented to demonstrate the capabilities of our numerical method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.

Development of solute transport models in YMPYRÄ framework to simulate solute migration in military shooting and training areas

NASA Astrophysics Data System (ADS)

Warsta, L.; Karvonen, T.

2017-12-01

There are currently 25 shooting and training areas in Finland managed by The Finnish Defence Forces (FDF), where military activities can cause contamination of open waters and groundwater reservoirs. In the YMPYRÄ project, a computer software framework is being developed that combines existing open environmental data and proprietary information collected by FDF with computational models to investigate current and prevent future environmental problems. A data centric philosophy is followed in the development of the system, i.e. the models are updated and extended to handle available data from different areas. The results generated by the models are summarized as easily understandable flow and risk maps that can be opened in GIS programs and used in environmental assessments by experts. Substances investigated with the system include explosives and metals such as lead, and both surface and groundwater dominated areas can be simulated. The YMPYRÄ framework is composed of a three dimensional soil and groundwater flow model, several solute transport models and an uncertainty assessment system. Solute transport models in the framework include particle based, stream tube and finite volume based approaches. The models can be used to simulate solute dissolution from source area, transport in the unsaturated layers to groundwater and finally migration in groundwater to water extraction wells and springs. The models can be used to simulate advection, dispersion, equilibrium adsorption on soil particles, solubility and dissolution from solute phase and dendritic solute decay chains. Correct numerical solutions were confirmed by comparing results to analytical 1D and 2D solutions and by comparing the numerical solutions to each other. The particle based and stream tube type solute transport models were useful as they could complement the traditional finite volume based approach which in certain circumstances produced numerical dispersion due to piecewise solution of the governing equations in computational grids and included computationally intensive and in some cases unstable iterative solutions. The YMPYRÄ framework is being developed by WaterHope, Gain Oy, and SITO Oy consulting companies and funded by FDF.

Three-body unitarity in the finite volume

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

Mai, M.; Döring, M.

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Three-body unitarity in the finite volume

DOE PAGES

Mai, M.; Döring, M.

2017-12-18

We present the physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativisticmore » $$3\\to 3$$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. Lastly, the corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.« less

Establishing the 3-D finite element solid model of femurs in partial by volume rendering.

PubMed

Zhang, Yinwang; Zhong, Wuxue; Zhu, Haibo; Chen, Yun; Xu, Lingjun; Zhu, Jianmin

2013-01-01

It remains rare to report three-dimensional (3-D) finite element solid model of femurs in partial by volume rendering method, though several methods of femoral 3-D finite element modeling are already available. We aim to analyze the advantages of the modeling method by establishing the 3-D finite element solid model of femurs in partial by volume rendering. A 3-D finite element model of the normal human femurs, made up of three anatomic structures: cortical bone, cancellous bone and pulp cavity, was constructed followed by pretreatment of the CT original image. Moreover, the finite-element analysis was carried on different material properties, three types of materials given for cortical bone, six assigned for cancellous bone, and single for pulp cavity. The established 3-D finite element of femurs contains three anatomical structures: cortical bone, cancellous bone, and pulp cavity. The compressive stress primarily concentrated in the medial surfaces of femur, especially in the calcar femorale. Compared with whole modeling by volume rendering method, the 3-D finite element solid model created in partial is more real and fit for finite element analysis. Copyright © 2013 Surgical Associates Ltd. Published by Elsevier Ltd. All rights reserved.

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids

NASA Technical Reports Server (NTRS)

Svard, Magnus; Gong, Jing; Nordstrom, Jan

2006-01-01

Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilized. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

Chiral crossover transition in a finite volume

NASA Astrophysics Data System (ADS)

Shi, Chao; Jia, Wenbao; Sun, An; Zhang, Liping; Zong, Hongshi

2018-02-01

Finite volume effects on the chiral crossover transition of strong interactions at finite temperature are studied by solving the quark gap equation within a cubic volume of finite size L. With the anti-periodic boundary condition, our calculation shows the chiral quark condensate, which characterizes the strength of dynamical chiral symmetry breaking, decreases as L decreases below 2.5 fm. We further study the finite volume effects on the pseudo-transition temperature {T}{{c}} of the crossover, showing a significant decrease in {T}{{c}} as L decreases below 3 fm. Supported by National Natural Science Foundation of China (11475085, 11535005, 11690030, 51405027), the Fundamental Research Funds for the Central Universities (020414380074), China Postdoctoral Science Foundation (2016M591808) and Open Research Foundation of State Key Lab. of Digital Manufacturing Equipment & Technology in Huazhong University of Science & Technology (DMETKF2015015)

Volume dependence of baryon number cumulants and their ratios

DOE PAGES

Almási, Gábor A.; Pisarski, Robert D.; Skokov, Vladimir V.

2017-03-17

Here, we explore the influence of finite-volume effects on cumulants of baryon/quark number fluctuations in a nonperturbative chiral model. In order to account for soft modes, we use the functional renormalization group in a finite volume, using a smooth regulator function in momentum space. We compare the results for a smooth regulator with those for a sharp (or Litim) regulator, and show that in a finite volume, the latter produces spurious artifacts. In a finite volume there are only apparent critical points, about which we compute the ratio of the fourth- to the second-order cumulant of quark number fluctuations. Finally,more » when the volume is sufficiently small the system has two apparent critical points; as the system size decreases, the location of the apparent critical point can move to higher temperature and lower chemical potential.« less

The Development of a Finite Volume Method for Modeling Sound in Coastal Ocean Environment

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

Long, Wen; Yang, Zhaoqing; Copping, Andrea E.

: As the rapid growth of marine renewable energy and off-shore wind energy, there have been concerns that the noises generated from construction and operation of the devices may interfere marine animals’ communication. In this research, a underwater sound model is developed to simulate sound prorogation generated by marine-hydrokinetic energy (MHK) devices or offshore wind (OSW) energy platforms. Finite volume and finite difference methods are developed to solve the 3D Helmholtz equation of sound propagation in the coastal environment. For finite volume method, the grid system consists of triangular grids in horizontal plane and sigma-layers in vertical dimension. A 3Dmore » sparse matrix solver with complex coefficients is formed for solving the resulting acoustic pressure field. The Complex Shifted Laplacian Preconditioner (CSLP) method is applied to efficiently solve the matrix system iteratively with MPI parallelization using a high performance cluster. The sound model is then coupled with the Finite Volume Community Ocean Model (FVCOM) for simulating sound propagation generated by human activities in a range-dependent setting, such as offshore wind energy platform constructions and tidal stream turbines. As a proof of concept, initial validation of the finite difference solver is presented for two coastal wedge problems. Validation of finite volume method will be reported separately.« less

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

NASA Astrophysics Data System (ADS)

Re, B.; Dobrzynski, C.; Guardone, A.

2017-07-01

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian-Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

Order of accuracy of QUICK and related convection-diffusion schemes

NASA Technical Reports Server (NTRS)

Leonard, B. P.

1993-01-01

This report attempts to correct some misunderstandings that have appeared in the literature concerning the order of accuracy of the QUICK scheme for steady-state convective modeling. Other related convection-diffusion schemes are also considered. The original one-dimensional QUICK scheme written in terms of nodal-point values of the convected variable (with a 1/8-factor multiplying the 'curvature' term) is indeed a third-order representation of the finite volume formulation of the convection operator average across the control volume, written naturally in flux-difference form. An alternative single-point upwind difference scheme (SPUDS) using node values (with a 1/6-factor) is a third-order representation of the finite difference single-point formulation; this can be written in a pseudo-flux difference form. These are both third-order convection schemes; however, the QUICK finite volume convection operator is 33 percent more accurate than the single-point implementation of SPUDS. Another finite volume scheme, writing convective fluxes in terms of cell-average values, requires a 1/6-factor for third-order accuracy. For completeness, one can also write a single-point formulation of the convective derivative in terms of cell averages, and then express this in pseudo-flux difference form; for third-order accuracy, this requires a curvature factor of 5/24. Diffusion operators are also considered in both single-point and finite volume formulations. Finite volume formulations are found to be significantly more accurate. For example, classical second-order central differencing for the second derivative is exactly twice as accurate in a finite volume formulation as it is in single-point.

2D and 3D Multiscale/Multicomponent Modeling of Impact Response of Heterogeneous Energetic Composites

DTIC Science & Technology

2016-06-01

7 Development of Cohesive Finite Element Method (CFEM) Capability ................................7 3D...Cohesive Finite Element Method (CFEM) framework A new scientific framework and technical capability is developed for the computational analyses of...this section should shift from reporting activities to reporting accomplishments. Development of Cohesive Finite Element Method (CFEM) Capability

Modelling cell motility and chemotaxis with evolving surface finite elements

PubMed Central

Elliott, Charles M.; Stinner, Björn; Venkataraman, Chandrasekhar

2012-01-01

We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction–diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html. PMID:22675164

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

Solution of the Average-Passage Equations for the Incompressible Flow through Multiple-Blade-Row Turbomachinery

DTIC Science & Technology

1994-02-01

numerical treatment. An explicit numerical procedure based on Runqe-Kutta time stepping for cell-centered, hexahedral finite volumes is...An explicit numerical procedure based on Runge-Kutta time stepping for cell-centered, hexahedral finite volumes is outlined for the approximate...Discretization 16 3.1 Cell-Centered Finite -Volume Discretization in Space 16 3.2 Artificial Dissipation 17 3.3 Time Integration 21 3.4 Convergence

Vector two-point functions in finite volume using partially quenched chiral perturbation theory at two loops

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Relefors, Johan

2017-12-01

We calculate vector-vector correlation functions at two loops using partially quenched chiral perturbation theory including finite volume effects and twisted boundary conditions. We present expressions for the flavor neutral cases and the flavor charged case with equal masses. Using these expressions we give an estimate for the ratio of disconnected to connected contributions for the strange part of the electromagnetic current. We give numerical examples for the effects of partial quenching, finite volume and twisting and suggest the use of different twists to check the size of finite volume effects. The main use of this work is expected to be for lattice QCD calculations of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment.

Climate Simulations with an Isentropic Finite Volume Dynamical Core

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

Chen, Chih-Chieh; Rasch, Philip J.

2012-04-15

This paper discusses the impact of changing the vertical coordinate from a hybrid pressure to a hybrid-isentropic coordinate within the finite volume dynamical core of the Community Atmosphere Model (CAM). Results from a 20-year climate simulation using the new model coordinate configuration are compared to control simulations produced by the Eulerian spectral and FV dynamical cores of CAM which both use a pressure-based ({sigma}-p) coordinate. The same physical parameterization package is employed in all three dynamical cores. The isentropic modeling framework significantly alters the simulated climatology and has several desirable features. The revised model produces a better representation of heatmore » transport processes in the atmosphere leading to much improved atmospheric temperatures. We show that the isentropic model is very effective in reducing the long standing cold temperature bias in the upper troposphere and lower stratosphere, a deficiency shared among most climate models. The warmer upper troposphere and stratosphere seen in the isentropic model reduces the global coverage of high clouds which is in better agreement with observations. The isentropic model also shows improvements in the simulated wintertime mean sea-level pressure field in the northern hemisphere.« less

Impressed sources and fields in the volume-integral-equation formulation of electromagnetic scattering by a finite object: A tutorial

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Yurkin, Maxim A.

2018-07-01

Although free space cannot generate electromagnetic waves, the majority of existing accounts of frequency-domain electromagnetic scattering by particles and particle groups are based on the postulate of existence of an impressed incident field, usually in the form of a plane wave. In this tutorial we discuss how to account for the actual existence of impressed source currents rather than impressed incident fields. Specifically, we outline a self-consistent theoretical formalism describing electromagnetic scattering by an arbitrary finite object in the presence of arbitrarily distributed impressed currents, some of which can be far removed from the object and some can reside in its vicinity, including inside the object. To make the resulting formalism applicable to a wide range of scattering-object morphologies, we use the framework of the volume integral equation formulation of electromagnetic scattering, couple it with the notion of the transition operator, and exploit the fundamental symmetry property of this operator. Among novel results, this tutorial includes a streamlined proof of fundamental symmetry (reciprocity) relations, a simplified derivation of the Foldy equations, and an explicit analytical expression for the transition operator of a multi-component scattering object.

An adhesive contact mechanics formulation based on atomistically induced surface traction

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

Fan, Houfu; Ren, Bo; Li, Shaofan, E-mail: shaofan@berkeley.edu

2015-12-01

In this work, we have developed a novel multiscale computational contact formulation based on the generalized Derjuguin approximation for continua that are characterized by atomistically enriched constitutive relations in order to study macroscopic interaction between arbitrarily shaped deformable continua. The proposed adhesive contact formulation makes use of the microscopic interaction forces between individual particles in the interacting bodies. In particular, the double-layer volume integral describing the contact interaction (energy, force vector, matrix) is converted into a double-layer surface integral through a mathematically consistent approach that employs the divergence theorem and a special partitioning technique. The proposed contact model is formulatedmore » in the nonlinear continuum mechanics framework and implemented using the standard finite element method. With no large penalty constant, the stiffness matrix of the system will in general be well-conditioned, which is of great significance for quasi-static analysis. Three numerical examples are presented to illustrate the capability of the proposed method. Results indicate that with the same mesh configuration, the finite element computation based on the surface integral approach is faster and more accurate than the volume integral based approach. In addition, the proposed approach is energy preserving even in a very long dynamic simulation.« less

Entropy stable discontinuous interfaces coupling for the three-dimensional compressible Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Parsani, Matteo; Carpenter, Mark H.; Nielsen, Eric J.

2015-06-01

Non-linear entropy stability and a summation-by-parts (SBP) framework are used to derive entropy stable interior interface coupling for the semi-discretized three-dimensional (3D) compressible Navier-Stokes equations. A complete semi-discrete entropy estimate for the interior domain is achieved combining a discontinuous entropy conservative operator of any order [1,2] with an entropy stable coupling condition for the inviscid terms, and a local discontinuous Galerkin (LDG) approach with an interior penalty (IP) procedure for the viscous terms. The viscous penalty contributions scale with the inverse of the Reynolds number (Re) so that for Re → ∞ their contributions vanish and only the entropy stable inviscid interface penalty term is recovered. This paper extends the interface couplings presented [1,2] and provides a simple and automatic way to compute the magnitude of the viscous IP term. The approach presented herein is compatible with any diagonal norm summation-by-parts (SBP) spatial operator, including finite element, finite volume, finite difference schemes and the class of high-order accurate methods which include the large family of discontinuous Galerkin discretizations and flux reconstruction schemes.

Nanothermodynamics in the strong coupling regime

NASA Astrophysics Data System (ADS)

Jarzynski, Christopher

In macroscopic thermodynamics, energy gained by a system is lost by its surroundings (or vice-versa), in accordance with the first law of thermodynamics. However, if the system-environment interaction energy cannot be neglected - as in the case of a microscopic system such as a single molecule in solution - then it is not immediately clear where to draw the line between the energy of the system and that of the environment. To which subsystem does the interaction energy belong? I will describe a microscopic formulation of both the first and second laws of thermodynamics that applies to this situation. In this framework, seven key thermodynamic quantities - internal energy, entropy, volume, enthalpy, Gibbs free energy, heat and work - are given precise microscopic definitions, and the first and second laws are preserved without requiring corrections due to finite system-environment coupling. Furthermore, these definitions reduce to the usual ones in the limit of macroscopic systems of interest. This condition establishes that a unifying framework can be developed, encompassing stochastic thermodynamics at one end and macroscopic thermodynamics at the other. A central element of this framework is a thermodynamic definition of the volume of the system of interest, which converges to the usual geometric definition when the system is large. This research was supported by the U.S. National Science Foundation through Grant No. DMR-1506969.

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

Two-Nucleon Systems in a Finite Volume

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

Briceno, Raul

2014-11-01

I present the formalism and methodology for determining the nucleon-nucleon scattering parameters from the finite volume spectra obtained from lattice quantum chromodynamics calculations. Using the recently derived energy quantization conditions and the experimentally determined scattering parameters, the bound state spectra for finite volume systems with overlap with the 3S1-3D3 channel are predicted for a range of volumes. It is shown that the extractions of the infinite-volume deuteron binding energy and the low-energy scattering parameters, including the S-D mixing angle, are possible from Lattice QCD calculations of two-nucleon systems with boosts of |P| <= 2pi sqrt{3}/L in volumes with spatial extentsmore » L satisfying fm <~ L <~ 14 fm.« less

Strain localization in usnaturated soils with large deformation

NASA Astrophysics Data System (ADS)

Song, X.; Borja, R. I.

2014-12-01

Strain localization is a ubiquitous feature of granular materials undergoing nonhomogeneous deformation. In unsaturated porous media, how the localized deformation band is formed depends crucially on the degree of saturation, since fluid in the pores of a solid imposes a volume constraint on the deformation of the solid. When fluid flow is involved, the inception of the localized deformation band also depends on the heterogeneity of a material, which is quantified in terms of the spatial variation of density, the degree of saturation, and matric suction. We present a mathematical framework for coupled solid-deformation/fluid-diffusion in unsaturated porous media that takes into account material and geometric nonlinearities [1, 2]. The framework relies on the continuum principle of thermodynamics to identify an effective, or constitutive, stress for the solid matrix, and a water retention law that highlights the interdependence of degree of saturation, suction, and porosity of the material. We discuss the role of heterogeneity, quantified either deterministically or stochastically, on the development of a persistent shear band. We derive bifurcation conditions [3] governing the initiation of such a shear band. This research is inspired by current testing techniques that allow nondestructive and non-invasive measurement of density and the degree of saturation through high-resolution imaging [4]. The numerical simulations under plane strain condition demonstrate that the bifurcation not only manifests itself on the loading response curve and but also in the space of the degree of saturation, specific volume and suction stress. References[1] Song X, Borja RI, Mathematical framework for unsaturated flow in the finite deformation range. Int. J. Numer. Meth. Engng 2014; 97: 658-686. [2] Song X, Borja RI, Finite deformation and fluid flow in unsaturated soils with random heterogeneity. Vadose Zone Journal 2014; doi:10.2136/vzj2013.07.0131. [3] Song X, Borja RI, Instability and bifurcation in partially saturated porous media. 2014. to be submitted. [4] Song X, Strain localization in unsaturated porous media. 2014. Ph.D. Dissertation, Stanford University, California.

Finite volume for three-flavour Partially Quenched Chiral Perturbation Theory through NNLO in the meson sector

NASA Astrophysics Data System (ADS)

Bijnens, Johan; Rössler, Thomas

2015-11-01

We present a calculation of the finite volume corrections to meson masses and decay constants in three flavour Partially Quenched Chiral Perturbation Theory (PQChPT) through two-loop order in the chiral expansion for the flavour-charged (or off-diagonal) pseudoscalar mesons. The analytical results are obtained for three sea quark flavours with one, two or three different masses. We reproduce the known infinite volume results and the finite volume results in the unquenched case. The calculation has been performed using the supersymmetric formulation of PQChPT as well as with a quark flow technique.

Efficient conservative ADER schemes based on WENO reconstruction and space-time predictor in primitive variables

NASA Astrophysics Data System (ADS)

Zanotti, Olindo; Dumbser, Michael

2016-01-01

We present a new version of conservative ADER-WENO finite volume schemes, in which both the high order spatial reconstruction as well as the time evolution of the reconstruction polynomials in the local space-time predictor stage are performed in primitive variables, rather than in conserved ones. To obtain a conservative method, the underlying finite volume scheme is still written in terms of the cell averages of the conserved quantities. Therefore, our new approach performs the spatial WENO reconstruction twice: the first WENO reconstruction is carried out on the known cell averages of the conservative variables. The WENO polynomials are then used at the cell centers to compute point values of the conserved variables, which are subsequently converted into point values of the primitive variables. This is the only place where the conversion from conservative to primitive variables is needed in the new scheme. Then, a second WENO reconstruction is performed on the point values of the primitive variables to obtain piecewise high order reconstruction polynomials of the primitive variables. The reconstruction polynomials are subsequently evolved in time with a novel space-time finite element predictor that is directly applied to the governing PDE written in primitive form. The resulting space-time polynomials of the primitive variables can then be directly used as input for the numerical fluxes at the cell boundaries in the underlying conservative finite volume scheme. Hence, the number of necessary conversions from the conserved to the primitive variables is reduced to just one single conversion at each cell center. We have verified the validity of the new approach over a wide range of hyperbolic systems, including the classical Euler equations of gas dynamics, the special relativistic hydrodynamics (RHD) and ideal magnetohydrodynamics (RMHD) equations, as well as the Baer-Nunziato model for compressible two-phase flows. In all cases we have noticed that the new ADER schemes provide less oscillatory solutions when compared to ADER finite volume schemes based on the reconstruction in conserved variables, especially for the RMHD and the Baer-Nunziato equations. For the RHD and RMHD equations, the overall accuracy is improved and the CPU time is reduced by about 25 %. Because of its increased accuracy and due to the reduced computational cost, we recommend to use this version of ADER as the standard one in the relativistic framework. At the end of the paper, the new approach has also been extended to ADER-DG schemes on space-time adaptive grids (AMR).

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

Source fields reconstruction with 3D mapping by means of the virtual acoustic volume concept

NASA Astrophysics Data System (ADS)

Forget, S.; Totaro, N.; Guyader, J. L.; Schaeffer, M.

2016-10-01

This paper presents the theoretical framework of the virtual acoustic volume concept and two related inverse Patch Transfer Functions (iPTF) identification methods (called u-iPTF and m-iPTF depending on the chosen boundary conditions for the virtual volume). They are based on the application of Green's identity on an arbitrary closed virtual volume defined around the source. The reconstruction of sound source fields combines discrete acoustic measurements performed at accessible positions around the source with the modal behavior of the chosen virtual acoustic volume. The mode shapes of the virtual volume can be computed by a Finite Element solver to handle the geometrical complexity of the source. As a result, it is possible to identify all the acoustic source fields at the real surface of an irregularly shaped structure and irrespective of its acoustic environment. The m-iPTF method is introduced for the first time in this paper. Conversely to the already published u-iPTF method, the m-iPTF method needs only acoustic pressure and avoids particle velocity measurements. This paper is focused on its validation, both with numerical computations and by experiments on a baffled oil pan.

Volume dependence of N-body bound states

NASA Astrophysics Data System (ADS)

König, Sebastian; Lee, Dean

2018-04-01

We derive the finite-volume correction to the binding energy of an N-particle quantum bound state in a cubic periodic volume. Our results are applicable to bound states with arbitrary composition and total angular momentum, and in any number of spatial dimensions. The only assumptions are that the interactions have finite range. The finite-volume correction is a sum of contributions from all possible breakup channels. In the case where the separation is into two bound clusters, our result gives the leading volume dependence up to exponentially small corrections. If the separation is into three or more clusters, there is a power-law factor that is beyond the scope of this work, however our result again determines the leading exponential dependence. We also present two independent methods that use finite-volume data to determine asymptotic normalization coefficients. The coefficients are useful to determine low-energy capture reactions into weakly bound states relevant for nuclear astrophysics. Using the techniques introduced here, one can even extract the infinite-volume energy limit using data from a single-volume calculation. The derived relations are tested using several exactly solvable systems and numerical examples. We anticipate immediate applications to lattice calculations of hadronic, nuclear, and cold atomic systems.

A High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)

2001-01-01

A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.

Stochastic theory of large-scale enzyme-reaction networks: Finite copy number corrections to rate equation models

NASA Astrophysics Data System (ADS)

Thomas, Philipp; Straube, Arthur V.; Grima, Ramon

2010-11-01

Chemical reactions inside cells occur in compartment volumes in the range of atto- to femtoliters. Physiological concentrations realized in such small volumes imply low copy numbers of interacting molecules with the consequence of considerable fluctuations in the concentrations. In contrast, rate equation models are based on the implicit assumption of infinitely large numbers of interacting molecules, or equivalently, that reactions occur in infinite volumes at constant macroscopic concentrations. In this article we compute the finite-volume corrections (or equivalently the finite copy number corrections) to the solutions of the rate equations for chemical reaction networks composed of arbitrarily large numbers of enzyme-catalyzed reactions which are confined inside a small subcellular compartment. This is achieved by applying a mesoscopic version of the quasisteady-state assumption to the exact Fokker-Planck equation associated with the Poisson representation of the chemical master equation. The procedure yields impressively simple and compact expressions for the finite-volume corrections. We prove that the predictions of the rate equations will always underestimate the actual steady-state substrate concentrations for an enzyme-reaction network confined in a small volume. In particular we show that the finite-volume corrections increase with decreasing subcellular volume, decreasing Michaelis-Menten constants, and increasing enzyme saturation. The magnitude of the corrections depends sensitively on the topology of the network. The predictions of the theory are shown to be in excellent agreement with stochastic simulations for two types of networks typically associated with protein methylation and metabolism.

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

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors. Volume 1

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

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.

Lattice study of finite volume effect in HVP for muon g-2

NASA Astrophysics Data System (ADS)

Izubuchi, Taku; Kuramashi, Yoshinobu; Lehner, Christoph; Shintani, Eigo

2018-03-01

We study the finite volume effect of the hadronic vacuum polarization contribution to muon g-2, aμhvp, in lattice QCD by comparison with two different volumes, L4 = (5.4)4 and (8.1)4 fm4, at physical pion. We perform the lattice computation of highly precise vector-vector current correlator with optimized AMA technique on Nf = 2 + 1 PACS gauge configurations in Wilson-clover fermion and stout smeared gluon action at one lattice cut-off, a-1 = 2.33 GeV. We compare two integrals of aμhvp, momentum integral and time-slice summation, on the lattice and numerically show that the different size of finite volume effect appears between two methods. We also discuss the effect of backward-state propagation into the result of aμhvp with the different boundary condition. Our model-independent study suggest that the lattice computation at physical pion is important for correct estimate of finite volume and other lattice systematics in aμhvp.

Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

DOE PAGES

Chen, Zhangxing; Huang, Tianyu; Shao, Yimin; ...

2018-03-15

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE)more » model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is further validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.« less

Investigating cerebral oedema using poroelasticity.

PubMed

Vardakis, John C; Chou, Dean; Tully, Brett J; Hung, Chang C; Lee, Tsong H; Tsui, Po-Hsiang; Ventikos, Yiannis

2016-01-01

Cerebral oedema can be classified as the tangible swelling produced by expansion of the interstitial fluid volume. Hydrocephalus can be succinctly described as the abnormal accumulation of cerebrospinal fluid (CSF) within the brain which ultimately leads to oedema within specific sites of parenchymal tissue. Using hydrocephalus as a test bed, one is able to account for the necessary mechanisms involved in the interaction between oedema formation and cerebral fluid production, transport and drainage. The current state of knowledge about integrative cerebral dynamics and transport phenomena indicates that poroelastic theory may provide a suitable framework to better understand various diseases. In this work, Multiple-Network Poroelastic Theory (MPET) is used to develop a novel spatio-temporal model of fluid regulation and tissue displacement within the various scales of the cerebral environment. The model is applied through two formats, a one-dimensional finite difference - Computational Fluid Dynamics (CFD) coupling framework, as well as a two-dimensional Finite Element Method (FEM) formulation. These are used to investigate the role of endoscopic fourth ventriculostomy in alleviating oedema formation due to fourth ventricle outlet obstruction (1D coupled model) in addition to observing the capability of the FEM template in capturing important characteristics allied to oedema formation, like for instance in the periventricular region (2D model). Copyright © 2015 The Authors. Published by Elsevier Ltd.. All rights reserved.

Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

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

Chen, Zhangxing; Huang, Tianyu; Shao, Yimin

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE)more » model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is further validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.« less

Exact finite volume expectation values of \\overline{Ψ}Ψ in the massive Thirring model from light-cone lattice correlators

NASA Astrophysics Data System (ADS)

Hegedűs, Árpád

2018-03-01

In this paper, using the light-cone lattice regularization, we compute the finite volume expectation values of the composite operator \\overline{Ψ}Ψ between pure fermion states in the Massive Thirring Model. In the light-cone regularized picture, this expectation value is related to 2-point functions of lattice spin operators being located at neighboring sites of the lattice. The operator \\overline{Ψ}Ψ is proportional to the trace of the stress-energy tensor. This is why the continuum finite volume expectation values can be computed also from the set of non-linear integral equations (NLIE) governing the finite volume spectrum of the theory. Our results for the expectation values coming from the computation of lattice correlators agree with those of the NLIE computations. Previous conjectures for the LeClair-Mussardo-type series representation of the expectation values are also checked.

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

Lee, Jin

2014-05-01

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

OpenSeesPy: Python library for the OpenSees finite element framework

NASA Astrophysics Data System (ADS)

Zhu, Minjie; McKenna, Frank; Scott, Michael H.

2018-01-01

OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. The framework allows users to perform finite element analysis with a scripting language and for developers to create both serial and parallel finite element computer applications as interpreters. For the last 15 years, Tcl has been the primary scripting language to which the model building and analysis modules of OpenSees are linked. To provide users with different scripting language options, particularly Python, the OpenSees interpreter interface was refactored to provide multi-interpreter capabilities. This refactoring, resulting in the creation of OpenSeesPy as a Python module, is accomplished through an abstract interface for interpreter calls with concrete implementations for different scripting languages. Through this approach, users are able to develop applications that utilize the unique features of several scripting languages while taking advantage of advanced finite element analysis models and algorithms.

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Slave finite elements for nonlinear analysis of engine structures, volume 1

NASA Technical Reports Server (NTRS)

Gellin, S.

1991-01-01

A 336 degrees of freedom slave finite element processing capability to analyze engine structures under severe thermomechanical loading is presented. Description of the theoretical development and demonstration of that element is presented in this volume.

Numerical simulation of conservation laws

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; To, Wai-Ming

1992-01-01

A new numerical framework for solving conservation laws is being developed. This new approach differs substantially from the well established methods, i.e., finite difference, finite volume, finite element and spectral methods, in both concept and methodology. The key features of the current scheme include: (1) direct discretization of the integral forms of conservation laws, (2) treating space and time on the same footing, (3) flux conservation in space and time, and (4) unified treatment of the convection and diffusion fluxes. The model equation considered in the initial study is the standard one dimensional unsteady constant-coefficient convection-diffusion equation. In a stability study, it is shown that the principal and spurious amplification factors of the current scheme, respectively, are structurally similar to those of the leapfrog/DuFort-Frankel scheme. As a result, the current scheme has no numerical diffusion in the special case of pure convection and is unconditionally stable in the special case of pure diffusion. Assuming smooth initial data, it will be shown theoretically and numerically that, by using an easily determined optimal time step, the accuracy of the current scheme may reach a level which is several orders of magnitude higher than that of the MacCormack scheme, with virtually identical operation count.

Numerical simulation of air hypersonic flows with equilibrium chemical reactions

NASA Astrophysics Data System (ADS)

Emelyanov, Vladislav; Karpenko, Anton; Volkov, Konstantin

2018-05-01

The finite volume method is applied to solve unsteady three-dimensional compressible Navier-Stokes equations on unstructured meshes. High-temperature gas effects altering the aerodynamics of vehicles are taken into account. Possibilities of the use of graphics processor units (GPUs) for the simulation of hypersonic flows are demonstrated. Solutions of some test cases on GPUs are reported, and a comparison between computational results of equilibrium chemically reacting and perfect air flowfields is performed. Speedup of solution on GPUs with respect to the solution on central processor units (CPUs) is compared. The results obtained provide promising perspective for designing a GPU-based software framework for practical applications.

Determination of baryon-baryon elastic scattering phase shift from finite volume spectra in elongated boxes

NASA Astrophysics Data System (ADS)

Li, Ning; Wu, Ya-Jie; Liu, Zhan-Wei

2018-01-01

The relations between the baryon-baryon elastic scattering phase shifts and the two-particle energy spectrum in the elongated box are established. We studied the cases with both the periodic boundary condition and twisted boundary condition in the center of mass frame. The framework is also extended to the system of nonzero total momentum with periodic boundary condition in the moving frame. Moreover, we discussed the sensitivity functions σ (q ) that represent the sensitivity of higher scattering phases. Our analytical results will be helpful to extract the baryon-baryon elastic scattering phase shifts in the continuum from lattice QCD data by using elongated boxes.

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

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

Kong, Bo; Fox, Rodney O.; Feng, Heng

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Euler-euler anisotropic gaussian mesoscale simulation of homogeneous cluster-induced gas-particle turbulence

DOE PAGES

Kong, Bo; Fox, Rodney O.; Feng, Heng; ...

2017-02-16

An Euler–Euler anisotropic Gaussian approach (EE-AG) for simulating gas–particle flows, in which particle velocities are assumed to follow a multivariate anisotropic Gaussian distribution, is used to perform mesoscale simulations of homogeneous cluster-induced turbulence (CIT). A three-dimensional Gauss–Hermite quadrature formulation is used to calculate the kinetic flux for 10 velocity moments in a finite-volume framework. The particle-phase volume-fraction and momentum equations are coupled with the Eulerian solver for the gas phase. This approach is implemented in an open-source CFD package, OpenFOAM, and detailed simulation results are compared with previous Euler–Lagrange simulations in a domain size study of CIT. Here, these resultsmore » demonstrate that the proposed EE-AG methodology is able to produce comparable results to EL simulations, and this moment-based methodology can be used to perform accurate mesoscale simulations of dilute gas–particle flows.« less

Optimization design about gimbal structure of high-precision autonomous celestial navigation tracking mirror system

NASA Astrophysics Data System (ADS)

Huang, Wei; Yang, Xiao-xu; Han, Jun-feng; Wei, Yu; Zhang, Jing; Xie, Mei-lin; Yue, Peng

2016-01-01

High precision tracking platform of celestial navigation with control mirror servo structure form, to solve the disadvantages of big volume and rotational inertia, slow response speed, and so on. It improved the stability and tracking accuracy of platform. Due to optical sensor and mirror are installed on the middle-gimbal, stiffness and resonant frequency requirement for high. Based on the application of finite element modality analysis theory, doing Research on dynamic characteristics of the middle-gimbal, and ANSYS was used for the finite element dynamic emulator analysis. According to the result of the computer to find out the weak links of the structure, and Put forward improvement suggestions and reanalysis. The lowest resonant frequency of optimization middle-gimbal avoid the bandwidth of the platform servo mechanism, and much higher than the disturbance frequency of carrier aircraft, and reduces mechanical resonance of the framework. Reaching provides a theoretical basis for the whole machine structure optimization design of high-precision of autonomous Celestial navigation tracking mirror system.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU

NASA Astrophysics Data System (ADS)

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ˜600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ˜0.25 s/excitation source.

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.

Finite dimensional approximation of a class of constrained nonlinear optimal control problems

NASA Technical Reports Server (NTRS)

Gunzburger, Max D.; Hou, L. S.

1994-01-01

An abstract framework for the analysis and approximation of a class of nonlinear optimal control and optimization problems is constructed. Nonlinearities occur in both the objective functional and in the constraints. The framework includes an abstract nonlinear optimization problem posed on infinite dimensional spaces, and approximate problem posed on finite dimensional spaces, together with a number of hypotheses concerning the two problems. The framework is used to show that optimal solutions exist, to show that Lagrange multipliers may be used to enforce the constraints, to derive an optimality system from which optimal states and controls may be deduced, and to derive existence results and error estimates for solutions of the approximate problem. The abstract framework and the results derived from that framework are then applied to three concrete control or optimization problems and their approximation by finite element methods. The first involves the von Karman plate equations of nonlinear elasticity, the second, the Ginzburg-Landau equations of superconductivity, and the third, the Navier-Stokes equations for incompressible, viscous flows.

Two-particle multichannel systems in a finite volume with arbitrary spin

DOE PAGES

Briceno, Raul A.

2014-04-08

The quantization condition for two-particle systems with arbitrary number of two-body open coupled channels, spin and masses in a finite cubic volume with either periodic or twisted boundary conditions is presented. The condition presented is in agreement with all previous studies of two-body systems in a finite volume. The result is relativistic, holds for all momenta below the three- and four-particle thresholds, and is exact up to exponential volume corrections that are governed by L/r, where L is the spatial extent of the volume and r is the range of the interactions between the particles. With hadronic systems the rangemore » of the interaction is set by the inverse of the pion mass, m π, and as a result the formalism presented is suitable for m πL>>1. Implications of the formalism for the studies of multichannel baryon-baryon systems are discussed.« less

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

Modeling dam-break flows using finite volume method on unstructured grid

USDA-ARS?s Scientific Manuscript database

Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...

Improved Design of Tunnel Supports : Volume 3 : Finite Element Analysis of the Peachtree Center Station in Atlanta

DOT National Transportation Integrated Search

1980-06-01

Volume 3 contains the application of the three-dimensional (3-D) finite element program, Automatic Dynamic Incremental Nonlinear Analysis (ADINA), which was designed to replace the traditional 2-D plane strain analysis, to a specific location. The lo...

Multi-scale Methods in Quantum Field Theory

NASA Astrophysics Data System (ADS)

Polyzou, W. N.; Michlin, Tracie; Bulut, Fatih

2018-05-01

Daubechies wavelets are used to make an exact multi-scale decomposition of quantum fields. For reactions that involve a finite energy that take place in a finite volume, the number of relevant quantum mechanical degrees of freedom is finite. The wavelet decomposition has natural resolution and volume truncations that can be used to isolate the relevant degrees of freedom. The application of flow equation methods to construct effective theories that decouple coarse and fine scale degrees of freedom is examined.

SU(2) lattice gluon propagator: Continuum limit, finite-volume effects, and infrared mass scale m{sub IR}

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

Bornyakov, V. G.; Mitrjushkin, V. K.; Mueller-Preussker, M.

2010-03-01

We study the scaling behavior and finite (physical) volume effects as well as the Gribov copy dependence of the SU(2) Landau gauge gluon propagator on the lattice. Our physical lattice sizes range from (3.0 fm){sup 4} to (7.3 fm){sup 4}. Considering lattices with decreasing lattice spacing but fixed physical volume we confirm (nonperturbative) multiplicative renormalizability and the approach to the continuum limit for the renormalized gluon propagator D{sub ren}(p) at momenta |p| > or approx. 0.6 GeV. The finite-volume effects and Gribov copy influence turn out small in this region. On the contrary, in the deeper infrared we found themore » Gribov copy influence strong and finite-volume effects, which still require special attention. The gluon propagator does not seem to be consistent with a simple polelike behavior {approx}(p{sup 2}+m{sub g}{sup 2}){sup -1} for momenta |p| < or approx. 0.6 GeV. Instead, a Gaussian-type fit works very well in this region. From its width - for a physical volume (5.0 fm){sup 4} - we estimate a corresponding infrared (mass) scale to be m{sub IR{approx}}0.7 GeV.« 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.

Demonstration of finite element simulations in MOOSE using crystallographic models of irradiation hardening and plastic deformation

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

Patra, Anirban; Wen, Wei; Martinez Saez, Enrique

This report describes the implementation of a crystal plasticity framework (VPSC) for irradiation hardening and plastic deformation in the finite element code, MOOSE. Constitutive models for irradiation hardening and the crystal plasticity framework are described in a previous report [1]. Here we describe these models briefly and then describe an algorithm for interfacing VPSC with finite elements. Example applications of tensile deformation of a dog bone specimen and a 3D pre-irradiated bar specimen performed using MOOSE are demonstrated.

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.

The Kπ Interaction in Finite Volume

NASA Astrophysics Data System (ADS)

Zhou, Dan; Cui, Er-Liang; Chen, Hua-Xing; Geng, Li-Sheng; Zhu, Li-Hua

We calculate energy levels of the Kπ scattering in the K∗ channel in finite volume using chiral unitary theory. We use these energy levels to obtain the Kπ phase shifts and the K∗ meson properties. We also investigate their dependence on the pion mass and compare this with Lattice QCD calculations.

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 volume solution of the compressible boundary-layer equations

NASA Technical Reports Server (NTRS)

Loyd, B.; Murman, E. M.

1986-01-01

A box-type finite volume discretization is applied to the integral form of the compressible boundary layer equations. Boundary layer scaling is introduced through the grid construction: streamwise grid lines follow eta = y/h = const., where y is the normal coordinate and h(x) is a scale factor proportional to the boundary layer thickness. With this grid, similarity can be applied explicity to calculate initial conditions. The finite volume method preserves the physical transparency of the integral equations in the discrete approximation. The resulting scheme is accurate, efficient, and conceptually simple. Computations for similar and non-similar flows show excellent agreement with tabulated results, solutions computed with Keller's Box scheme, and experimental data.

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.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 1: Theory and validations

NASA Technical Reports Server (NTRS)

Baker, A. J.; Iannelli, G. S.; Manhardt, Paul D.; Orzechowski, J. A.

1993-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

An arbitrary grid CFD algorithm for configuration aerodynamics analysis. Volume 2: FEMNAS user guide

NASA Technical Reports Server (NTRS)

Manhardt, Paul D.; Orzechowski, J. A.; Baker, A. J.

1992-01-01

This report documents the user input and output data requirements for the FEMNAS finite element Navier-Stokes code for real-gas simulations of external aerodynamics flowfields. This code was developed for the configuration aerodynamics branch of NASA ARC, under SBIR Phase 2 contract NAS2-124568 by Computational Mechanics Corporation (COMCO). This report is in two volumes. Volume 1 contains the theory for the derived finite element algorithm and describes the test cases used to validate the computer program described in the Volume 2 user guide.

A 2D nonlinear multiring model for blood flow in large elastic arteries

NASA Astrophysics Data System (ADS)

Ghigo, Arthur R.; Fullana, Jose-Maria; Lagrée, Pierre-Yves

2017-12-01

In this paper, we propose a two-dimensional nonlinear ;multiring; model to compute blood flow in axisymmetric elastic arteries. This model is designed to overcome the numerical difficulties of three-dimensional fluid-structure interaction simulations of blood flow without using the over-simplifications necessary to obtain one-dimensional blood flow models. This multiring model is derived by integrating over concentric rings of fluid the simplified long-wave Navier-Stokes equations coupled to an elastic model of the arterial wall. The resulting system of balance laws provides a unified framework in which both the motion of the fluid and the displacement of the wall are dealt with simultaneously. The mathematical structure of the multiring model allows us to use a finite volume method that guarantees the conservation of mass and the positivity of the numerical solution and can deal with nonlinear flows and large deformations of the arterial wall. We show that the finite volume numerical solution of the multiring model provides at a reasonable computational cost an asymptotically valid description of blood flow velocity profiles and other averaged quantities (wall shear stress, flow rate, ...) in large elastic and quasi-rigid arteries. In particular, we validate the multiring model against well-known solutions such as the Womersley or the Poiseuille solutions as well as against steady boundary layer solutions in quasi-rigid constricted and expanded tubes.

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.

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.

Nonlinear Conservation Laws and Finite Volume Methods

NASA Astrophysics Data System (ADS)

Leveque, Randall J.

Introduction Software Notation Classification of Differential Equations Derivation of Conservation Laws The Euler Equations of Gas Dynamics Dissipative Fluxes Source Terms Radiative Transfer and Isothermal Equations Multi-dimensional Conservation Laws The Shock Tube Problem Mathematical Theory of Hyperbolic Systems Scalar Equations Linear Hyperbolic Systems Nonlinear Systems The Riemann Problem for the Euler Equations Numerical Methods in One Dimension Finite Difference Theory Finite Volume Methods Importance of Conservation Form - Incorrect Shock Speeds Numerical Flux Functions Godunov's Method Approximate Riemann Solvers High-Resolution Methods Other Approaches Boundary Conditions Source Terms and Fractional Steps Unsplit Methods Fractional Step Methods General Formulation of Fractional Step Methods Stiff Source Terms Quasi-stationary Flow and Gravity Multi-dimensional Problems Dimensional Splitting Multi-dimensional Finite Volume Methods Grids and Adaptive Refinement Computational Difficulties Low-Density Flows Discrete Shocks and Viscous Profiles Start-Up Errors Wall Heating Slow-Moving Shocks Grid Orientation Effects Grid-Aligned Shocks Magnetohydrodynamics The MHD Equations One-Dimensional MHD Solving the Riemann Problem Nonstrict Hyperbolicity Stiffness The Divergence of B Riemann Problems in Multi-dimensional MHD Staggered Grids The 8-Wave Riemann Solver Relativistic Hydrodynamics Conservation Laws in Spacetime The Continuity Equation The 4-Momentum of a Particle The Stress-Energy Tensor Finite Volume Methods Multi-dimensional Relativistic Flow Gravitation and General Relativity References

X-ray EM simulation tool for ptychography dataset construction

NASA Astrophysics Data System (ADS)

Stoevelaar, L. Pjotr; Gerini, Giampiero

2018-03-01

In this paper, we present an electromagnetic full-wave modeling framework, as a support EM tool providing data sets for X-ray ptychographic imaging. Modeling the entire scattering problem with Finite Element Method (FEM) tools is, in fact, a prohibitive task, because of the large area illuminated by the beam (due to the poor focusing power at these wavelengths) and the very small features to be imaged. To overcome this problem, the spectrum of the illumination beam is decomposed into a discrete set of plane waves. This allows reducing the electromagnetic modeling volume to the one enclosing the area to be imaged. The total scattered field is reconstructed by superimposing the solutions for each plane wave illumination.

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.

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.

Numerical approximation for the infinite-dimensional discrete-time optimal linear-quadratic regulator problem

NASA Technical Reports Server (NTRS)

Gibson, J. S.; Rosen, I. G.

1986-01-01

An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.

Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)

2002-01-01

Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve three-dimensional problems for any order of accuracy are then presented. Important aspects of the data structure are discussed. Comparisons with the Discontinuous Galerkin (DG) method are made. Numerical examples for wave propagation problems are presented.

Demonstration Of Ultra HI-FI (UHF) Methods

NASA Technical Reports Server (NTRS)

Dyson, Rodger W.

2004-01-01

Computational aero-acoustics (CAA) requires efficient, high-resolution simulation tools. Most current techniques utilize finite-difference approaches because high order accuracy is considered too difficult or expensive to achieve with finite volume or finite element methods. However, a novel finite volume approach (Ultra HI-FI or UHF) which utilizes Hermite fluxes is presented which can achieve both arbitrary accuracy and fidelity in space and time. The technique can be applied to unstructured grids with some loss of fidelity or with multi-block structured grids for maximum efficiency and resolution. In either paradigm, it is possible to resolve ultra-short waves (less than 2 PPW). This is demonstrated here by solving the 4th CAA workshop Category 1 Problem 1.

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

Chen, Hsi-Hsun; Oh, Se Baek; Zhai, Xiaomin; Tsai, Jui-Chang; Cao, Liang-Cai; Barbastathis, George; Luo, Yuan

2015-01-01

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions. PMID:25836443

Sanity check for NN bound states in lattice QCD with Lüscher's finite volume formula - Disclosing Symptoms of Fake Plateaux -

NASA Astrophysics Data System (ADS)

Aoki, Sinya; Doi, Takumi; Iritani, Takumi

2018-03-01

The sanity check is to rule out certain classes of obviously false results, not to catch every possible error. After reviewing such a sanity check for NN bound states with the Lüscher's finite volume formula [1-3], we give further evidences for the operator dependence of plateaux, a symptom of the fake plateau problem, against the claim [4]. We then present our critical comments on [5] by NPLQCD: (i) Operator dependences of plateaux in NPL2013 [6, 7] exist with the P value of 4-5%. (ii) The volume independence of plateaux in NPL2013 does not prove their correctness. (iii) Effective range expansions (EREs) in NPL2013 violate the physical pole condition. (iv) Their comment is partly based on new data and analysis different from the original ones. (v) Their new ERE does not satisfy the Lüscher's finite volume formula.

pyGIMLi: An open-source library for modelling and inversion in geophysics

NASA Astrophysics Data System (ADS)

Rücker, Carsten; Günther, Thomas; Wagner, Florian M.

2017-12-01

Many tasks in applied geosciences cannot be solved by single measurements, but require the integration of geophysical, geotechnical and hydrological methods. Numerical simulation techniques are essential both for planning and interpretation, as well as for the process understanding of modern geophysical methods. These trends encourage open, simple, and modern software architectures aiming at a uniform interface for interdisciplinary and flexible modelling and inversion approaches. We present pyGIMLi (Python Library for Inversion and Modelling in Geophysics), an open-source framework that provides tools for modelling and inversion of various geophysical but also hydrological methods. The modelling component supplies discretization management and the numerical basis for finite-element and finite-volume solvers in 1D, 2D and 3D on arbitrarily structured meshes. The generalized inversion framework solves the minimization problem with a Gauss-Newton algorithm for any physical forward operator and provides opportunities for uncertainty and resolution analyses. More general requirements, such as flexible regularization strategies, time-lapse processing and different sorts of coupling individual methods are provided independently of the actual methods used. The usage of pyGIMLi is first demonstrated by solving the steady-state heat equation, followed by a demonstration of more complex capabilities for the combination of different geophysical data sets. A fully coupled hydrogeophysical inversion of electrical resistivity tomography (ERT) data of a simulated tracer experiment is presented that allows to directly reconstruct the underlying hydraulic conductivity distribution of the aquifer. Another example demonstrates the improvement of jointly inverting ERT and ultrasonic data with respect to saturation by a new approach that incorporates petrophysical relations in the inversion. Potential applications of the presented framework are manifold and include time-lapse, constrained, joint, and coupled inversions of various geophysical and hydrological data sets.

Methods for High-Order Multi-Scale and Stochastic Problems Analysis, Algorithms, and Applications

DTIC Science & Technology

2016-10-17

finite volume schemes, discontinuous Galerkin finite element method, and related methods, for solving computational fluid dynamics (CFD) problems and...approximation for finite element methods. (3) The development of methods of simulation and analysis for the study of large scale stochastic systems of...laws, finite element method, Bernstein-Bezier finite elements , weakly interacting particle systems, accelerated Monte Carlo, stochastic networks 16

Fourth-Order Conservative Vlasov-Maxwell Solver for Cartesian and Cylindrical Phase Space Coordinates

NASA Astrophysics Data System (ADS)

Vogman, Genia

Plasmas are made up of charged particles whose short-range and long-range interactions give rise to complex behavior that can be difficult to fully characterize experimentally. One of the most complete theoretical descriptions of a plasma is that of kinetic theory, which treats each particle species as a probability distribution function in a six-dimensional position-velocity phase space. Drawing on statistical mechanics, these distribution functions mathematically represent a system of interacting particles without tracking individual ions and electrons. The evolution of the distribution function(s) is governed by the Boltzmann equation coupled to Maxwell's equations, which together describe the dynamics of the plasma and the associated electromagnetic fields. When collisions can be neglected, the Boltzmann equation is reduced to the Vlasov equation. High-fidelity simulation of the rich physics in even a subset of the full six-dimensional phase space calls for low-noise high-accuracy numerical methods. To that end, this dissertation investigates a fourth-order finite-volume discretization of the Vlasov-Maxwell equation system, and addresses some of the fundamental challenges associated with applying these types of computationally intensive enhanced-accuracy numerical methods to phase space simulations. The governing equations of kinetic theory are described in detail, and their conservation-law weak form is derived for Cartesian and cylindrical phase space coordinates. This formulation is well known when it comes to Cartesian geometries, as it is used in finite-volume and finite-element discretizations to guarantee local conservation for numerical solutions. By contrast, the conservation-law weak form of the Vlasov equation in cylindrical phase space coordinates is largely unexplored, and to the author's knowledge has never previously been solved numerically. Thereby the methods described in this dissertation for simulating plasmas in cylindrical phase space coordinates present a new development in the field of computational plasma physics. A fourth-order finite-volume method for solving the Vlasov-Maxwell equation system is presented first for Cartesian and then for cylindrical phase space coordinates. Special attention is given to the treatment of the discrete primary variables and to the quadrature rule for evaluating the surface and line integrals that appear in the governing equations. The finite-volume treatment of conducting wall and axis boundaries is particularly nuanced when it comes to phase space coordinates, and is described in detail. In addition to the mechanics of each part of the finite-volume discretization in the two different coordinate systems, the complete algorithm is also presented. The Cartesian coordinate discretization is applied to several well-known test problems. Since even linear analysis of kinetic theory governing equations is complicated on account of velocity being an independent coordinate, few analytic or semi-analytic predictions exist. Benchmarks are particularly scarce for configurations that have magnetic fields and involve more than two phase space dimensions. Ensuring that simulations are true to the physics thus presents a difficulty in the development of robust numerical methods. The research described in this dissertation addresses this challenge through the development of more complete physics-based benchmarks based on the Dory-Guest-Harris instability. The instability is a special case of perpendicularly-propagating kinetic electrostatic waves in a warm uniformly magnetized plasma. A complete derivation of the closed-form linear theory dispersion relation for the instability is presented. The electric field growth rates and oscillation frequencies specified by the dispersion relation provide concrete measures against which simulation results can be quantitatively compared. Furthermore, a specialized form of perturbation is shown to strongly excite the fastest growing mode. The fourth-order finite-volume algorithm is benchmarked against the instability, and is demonstrated to have good convergence properties and close agreement with theoretical growth rate and oscillation frequency predictions. The Dory-Guest-Harris instability benchmark extends the scope of standard test problems by providing a substantive means of validating continuum kinetic simulations of warm magnetized plasmas in higher-dimensional 3D ( x,vx,vy) phase space. The linear theory analysis, initial conditions, algorithm description, and comparisons between theoretical predictions and simulation results are presented. The cylindrical coordinate finite-volume discretization is applied to model axisymmetric systems. Since mitigating the prohibitive computational cost of simulating six dimensions is another challenge in phase space simulations, the development of a robust means of exploiting symmetry is a major advance when it comes to numerically solving the Vlasov-Maxwell equation system. The discretization is applied to a uniform distribution function to assess the nature of the singularity at the axis, and is demonstrated to converge at fourth-order accuracy. The numerical method is then applied to simulate electrostatic ion confinement in an axisymmetric Z-pinch configuration. To the author's knowledge this presents the first instance of a conservative finite-volume discretization of the cylindrical coordinate Vlasov equation. The computational framework for the Vlasov-Maxwell solver is described, and an outlook for future research is presented.

The New BaBar Data Reconstruction Control System

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

Ceseracciu, Antonio

2003-06-02

The BaBar experiment is characterized by extremely high luminosity, a complex detector, and a huge data volume, with increasing requirements each year. To fulfill these requirements a new control system has been designed and developed for the offline data reconstruction system. The new control system described in this paper provides the performance and flexibility needed to manage a large number of small computing farms, and takes full benefit of OO design. The infrastructure is well isolated from the processing layer, it is generic and flexible, based on a light framework providing message passing and cooperative multitasking. The system is activelymore » distributed, enforces the separation between different processing tiers by using different naming domains, and glues them together by dedicated brokers. It provides a powerful Finite State Machine framework to describe custom processing models in a simple regular language. This paper describes this new control system, currently in use at SLAC and Padova on {approx}450 CPUs organized in 12 farms.« less

The BaBar Data Reconstruction Control System

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

Ceseracciu, A

2005-04-20

The BaBar experiment is characterized by extremely high luminosity and very large volume of data produced and stored, with increasing computing requirements each year. To fulfill these requirements a Control System has been designed and developed for the offline distributed data reconstruction system. The control system described in this paper provides the performance and flexibility needed to manage a large number of small computing farms, and takes full benefit of OO design. The infrastructure is well isolated from the processing layer, it is generic and flexible, based on a light framework providing message passing and cooperative multitasking. The system ismore » distributed in a hierarchical way: the top-level system is organized in farms, farms in services, and services in subservices or code modules. It provides a powerful Finite State Machine framework to describe custom processing models in a simple regular language. This paper describes the design and evolution of this control system, currently in use at SLAC and Padova on {approx}450 CPUs organized in 9 farms.« less

The BaBar Data Reconstruction Control System

NASA Astrophysics Data System (ADS)

Ceseracciu, A.; Piemontese, M.; Tehrani, F. S.; Pulliam, T. M.; Galeazzi, F.

2005-08-01

The BaBar experiment is characterized by extremely high luminosity and very large volume of data produced and stored, with increasing computing requirements each year. To fulfill these requirements a control system has been designed and developed for the offline distributed data reconstruction system. The control system described in this paper provides the performance and flexibility needed to manage a large number of small computing farms, and takes full benefit of object oriented (OO) design. The infrastructure is well isolated from the processing layer, it is generic and flexible, based on a light framework providing message passing and cooperative multitasking. The system is distributed in a hierarchical way: the top-level system is organized in farms, farms in services, and services in subservices or code modules. It provides a powerful finite state machine framework to describe custom processing models in a simple regular language. This paper describes the design and evolution of this control system, currently in use at SLAC and Padova on /spl sim/450 CPUs organized in nine farms.

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Saether, E.; Glaessgen, E.H.; Yamakov, V.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin; Saether, Erik; Glaessgen, Edward H/.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

Dielectric elastomer peristaltic pump module with finite deformation

NASA Astrophysics Data System (ADS)

Mao, Guoyong; Huang, Xiaoqiang; Liu, Junjie; Li, Tiefeng; Qu, Shaoxing; Yang, Wei

2015-07-01

Inspired by various peristaltic structures existing in nature, several bionic peristaltic actuators have been developed. In this study, we propose a novel dielectric elastomer peristaltic pump consisting of short tubular modules, with the saline solution as the electrodes. We investigate the performance of this soft pump module under hydraulic pressure and voltage via experiments and an analytical model based on nonlinear field theory. It is observed that the individual pump module undergoes finite deformation and may experience electromechanical instability during operations. The driving pressure and displaced volume of the peristaltic pump module can be modulated by applied voltage. The efficiency of the pump module is enhanced by alternating current voltage, which can suppress the electromechanical pull-in instability. An analytical model is developed within the framework of the nonlinear field theory, and its predictive capacity is checked by experimental observations. The effects of the prestretch, aspect ratio, and voltage on the performance of the pump modules are characterized by the analytical model. This work can guide the designs of soft active peristaltic pumps in the field of artificial organs and industrial conveying systems.

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

NASA Technical Reports Server (NTRS)

Moghaddam, Masoud Ghorbani; Achuthan, A.; Bednacyk, B. A.; Arnold, S. M.; Pineda, E. J.

2014-01-01

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Toward real-time diffuse optical tomography: accelerating light propagation modeling employing parallel computing on GPU and CPU.

PubMed

Doulgerakis, Matthaios; Eggebrecht, Adam; Wojtkiewicz, Stanislaw; Culver, Joseph; Dehghani, Hamid

2017-12-01

Parameter recovery in diffuse optical tomography is a computationally expensive algorithm, especially when used for large and complex volumes, as in the case of human brain functional imaging. The modeling of light propagation, also known as the forward problem, is the computational bottleneck of the recovery algorithm, whereby the lack of a real-time solution is impeding practical and clinical applications. The objective of this work is the acceleration of the forward model, within a diffusion approximation-based finite-element modeling framework, employing parallelization to expedite the calculation of light propagation in realistic adult head models. The proposed methodology is applicable for modeling both continuous wave and frequency-domain systems with the results demonstrating a 10-fold speed increase when GPU architectures are available, while maintaining high accuracy. It is shown that, for a very high-resolution finite-element model of the adult human head with ∼600,000 nodes, consisting of heterogeneous layers, light propagation can be calculated at ∼0.25  s/excitation source. (2017) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE).

Deformation behaviour of Rheocast A356 Al alloy at microlevel considering approximated RVEs

NASA Astrophysics Data System (ADS)

Islam, Sk. Tanbir; Das, Prosenjit; Das, Santanu

2015-03-01

A micromechanical approach is considered here to predict the deformation behaviour of Rheocast A356 (Al-Si-Mg) alloy. Two representative volume elements (RVEs) are modelled in the finite element (FE) framework. Two dimensional approximated microstructures are generated assuming elliptic grains, based on the grain size, shape factor and area fraction of the primary Al phase of the said alloy at different processing condition. Plastic instability is shown using stress and strain distribution between the Al rich primary and Si rich eutectic phases under different boundary conditions. Boundary conditions are applied on the approximated RVEs in such a manner, so that they represent the real life situation depending on their position on a cylindrical tensile test sample. FE analysis is carried out using commercial finite element code ABAQUS without specifying any damage or failure criteria. Micro-level in-homogeneity leads to incompatible deformation between the constituent phases of the rheocast alloy and steers plastic strain localisation. Plastic stain localised regions within the RVEs are predicted as the favourable sites for void nucleation. Subsequent growth of nucleated voids leads to final failure of the materials under investigation.

High-speed reacting flow simulation using USA-series codes

NASA Astrophysics Data System (ADS)

Chakravarthy, S. R.; Palaniswamy, S.

In this paper, the finite-rate chemistry (FRC) formulation for the USA-series of codes and three sets of validations are presented. USA-series computational fluid dynamics (CFD) codes are based on Unified Solution Algorithms including explicity and implicit formulations, factorization and relaxation approaches, time marching and space marching methodolgies, etc., in order to be able to solve a very wide class of CDF problems using a single framework. Euler or Navier-Stokes equations are solved using a finite-volume treatment with upwind Total Variation Diminishing discretization for the inviscid terms. Perfect and real gas options are available including equilibrium and nonequilibrium chemistry. This capability has been widely used to study various problems including Space Shuttle exhaust plumes, National Aerospace Plane (NASP) designs, etc. (1) Numerical solutions are presented showing the full range of possible solutions to steady detonation wave problems. (2) Comparison between the solution obtained by the USA code and Generalized Kinetics Analysis Program (GKAP) is shown for supersonic combustion in a duct. (3) Simulation of combustion in a supersonic shear layer is shown to have reasonable agreement with experimental observations.

3D highly heterogeneous thermal model of pineal gland in-vitro study for electromagnetic exposure using finite volume method

NASA Astrophysics Data System (ADS)

Cen, Wei; Hoppe, Ralph; Lu, Rongbo; Cai, Zhaoquan; Gu, Ning

2017-08-01

In this paper, the relationship between electromagnetic power absorption and temperature distributions inside highly heterogeneous biological samples was accurately determinated using finite volume method. An in-vitro study on pineal gland that is responsible for physiological activities was for the first time simulated to illustrate effectiveness of the proposed method.

Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics

NASA Technical Reports Server (NTRS)

Wood, William A.

1997-01-01

The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.

Statistical Optics

NASA Astrophysics Data System (ADS)

Goodman, Joseph W.

2000-07-01

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & Norman R. Draper Evolutionary Operation: A Statistical Method for Process Improvement George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I RIchard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold S. M. Coxeter Introduction to Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Cuthbert Daniel Fitting Equations to Data: Computer Analysis of Multifactor Data, Second Edition Bruno de Finetti Theory of Probability, Volume I Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research

Incorporation of an Energy Equation into a Pulsed Inductive Thruster Performance Model

NASA Technical Reports Server (NTRS)

Polzin, Kurt A.; Reneau, Jarred P.; Sankaran, Kameshwaran

2011-01-01

A model for pulsed inductive plasma acceleration containing an energy equation to account for the various sources and sinks in such devices is presented. The model consists of a set of circuit equations coupled to an equation of motion and energy equation for the plasma. The latter two equations are obtained for the plasma current sheet by treating it as a one-element finite volume, integrating the equations over that volume, and then matching known terms or quantities already calculated in the model to the resulting current sheet-averaged terms in the equations. Calculations showing the time-evolution of the various sources and sinks in the system are presented to demonstrate the efficacy of the model, with two separate resistivity models employed to show an example of how the plasma transport properties can affect the calculation. While neither resistivity model is fully accurate, the demonstration shows that it is possible within this modeling framework to time-accurately update various plasma parameters.

Higher order cumulants in colorless partonic plasma

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

Cherif, S.; Laboratoire de Physique et de Mathématiques Appliquées; Ahmed, M. A. A.

2016-06-10

Any physical system considered to study the QCD deconfinement phase transition certainly has a finite volume, so the finite size effects are inevitably present. This renders the location of the phase transition and the determination of its order as an extremely difficult task, even in the simplest known cases. In order to identify and locate the colorless QCD deconfinement transition point in finite volume T{sub 0}(V), a new approach based on the finite-size cumulant expansion of the order parameter and the ℒ{sub m,n}-Method is used. We have shown that both cumulants of higher order and their ratios, associated to themore » thermodynamical fluctuations of the order parameter, in QCD deconfinement phase transition behave in a particular enough way revealing pronounced oscillations in the transition region. The sign structure and the oscillatory behavior of these in the vicinity of the deconfinement phase transition point might be a sensitive probe and may allow one to elucidate their relation to the QCD phase transition point. In the context of our model, we have shown that the finite volume transition point is always associated to the appearance of a particular point in whole higher order cumulants under consideration.« less

plasmaFoam: An OpenFOAM framework for computational plasma physics and chemistry

NASA Astrophysics Data System (ADS)

Venkattraman, Ayyaswamy; Verma, Abhishek Kumar

2016-09-01

As emphasized in the 2012 Roadmap for low temperature plasmas (LTP), scientific computing has emerged as an essential tool for the investigation and prediction of the fundamental physical and chemical processes associated with these systems. While several in-house and commercial codes exist, with each having its own advantages and disadvantages, a common framework that can be developed by researchers from all over the world will likely accelerate the impact of computational studies on advances in low-temperature plasma physics and chemistry. In this regard, we present a finite volume computational toolbox to perform high-fidelity simulations of LTP systems. This framework, primarily based on the OpenFOAM solver suite, allows us to enhance our understanding of multiscale plasma phenomenon by performing massively parallel, three-dimensional simulations on unstructured meshes using well-established high performance computing tools that are widely used in the computational fluid dynamics community. In this talk, we will present preliminary results obtained using the OpenFOAM-based solver suite with benchmark three-dimensional simulations of microplasma devices including both dielectric and plasma regions. We will also discuss the future outlook for the solver suite.

Brittle to ductile transition in a model of sheared granular materials

NASA Astrophysics Data System (ADS)

Elbanna, Ahmed; Ma, Xiao

Understanding the fundamental mechanisms of deformation and failure in sheared fault gouge is critical for the development of physics-based earthquake rupture simulations that are becoming an essential ingredient in next generation hazard and risk models. To that end, we use the shear transformation zone (STZ) theory, a non-equilibrium statistical thermodynamics framework to describe viscoplastic deformation and localization in gouge materials as a first step towards developing multiscale models for earthquake source processes that are informed by high-resolution fault zone physics. We will describe an implementation of this theory in a 2D/3D finite element framework, accounting for finite deformation, under both axial and shear loading and for dry and saturated conditions. We examine conditions under which a localized shear band may form and show that the initial value of disorder plays an important role. In particular, our simulations suggest that if the material is more compact initially, the behavior is more brittle and the plastic deformation localizes with large strength drop. On the other hand, an initially loose material will show a more ductile response and the plastic deformations will be distributed more broadly. We will further show that incorporation of pore fluids alters the localization pattern and changes the stress slip response due to coupling between gouge volume changes (compaction and dilation) and pore pressure build up. Finally, we discuss the implications of our model for gouge friction and dynamic weakening.

Reproducible Hydrogeophysical Inversions through the Open-Source Library pyGIMLi

NASA Astrophysics Data System (ADS)

Wagner, F. M.; Rücker, C.; Günther, T.

2017-12-01

Many tasks in applied geosciences cannot be solved by a single measurement method and require the integration of geophysical, geotechnical and hydrological methods. In the emerging field of hydrogeophysics, researchers strive to gain quantitative information on process-relevant subsurface parameters by means of multi-physical models, which simulate the dynamic process of interest as well as its geophysical response. However, such endeavors are associated with considerable technical challenges, since they require coupling of different numerical models. This represents an obstacle for many practitioners and students. Even technically versatile users tend to build individually tailored solutions by coupling different (and potentially proprietary) forward simulators at the cost of scientific reproducibility. We argue that the reproducibility of studies in computational hydrogeophysics, and therefore the advancement of the field itself, requires versatile open-source software. To this end, we present pyGIMLi - a flexible and computationally efficient framework for modeling and inversion in geophysics. The object-oriented library provides management for structured and unstructured meshes in 2D and 3D, finite-element and finite-volume solvers, various geophysical forward operators, as well as Gauss-Newton based frameworks for constrained, joint and fully-coupled inversions with flexible regularization. In a step-by-step demonstration, it is shown how the hydrogeophysical response of a saline tracer migration can be simulated. Tracer concentration data from boreholes and measured voltages at the surface are subsequently used to estimate the hydraulic conductivity distribution of the aquifer within a single reproducible Python script.

Extrusion Process by Finite Volume Method Using OpenFoam Software

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

Matos Martins, Marcelo; Tonini Button, Sergio; Divo Bressan, Jose

The computational codes are very important tools to solve engineering problems. In the analysis of metal forming process, such as extrusion, this is not different because the computational codes allow analyzing the process with reduced cost. Traditionally, the Finite Element Method is used to solve solid mechanic problems, however, the Finite Volume Method (FVM) have been gaining force in this field of applications. This paper presents the velocity field and friction coefficient variation results, obtained by numerical simulation using the OpenFoam Software and the FVM to solve an aluminum direct cold extrusion process.

A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator on Hilbert Spaces

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

Levajković, Tijana, E-mail: tijana.levajkovic@uibk.ac.at, E-mail: t.levajkovic@sf.bg.ac.rs; Mena, Hermann, E-mail: hermann.mena@uibk.ac.at; Tuffaha, Amjad, E-mail: atufaha@aus.edu

We present an approximation framework for computing the solution of the stochastic linear quadratic control problem on Hilbert spaces. We focus on the finite horizon case and the related differential Riccati equations (DREs). Our approximation framework is concerned with the so-called “singular estimate control systems” (Lasiecka in Optimal control problems and Riccati equations for systems with unbounded controls and partially analytic generators: applications to boundary and point control problems, 2004) which model certain coupled systems of parabolic/hyperbolic mixed partial differential equations with boundary or point control. We prove that the solutions of the approximate finite-dimensional DREs converge to the solutionmore » of the infinite-dimensional DRE. In addition, we prove that the optimal state and control of the approximate finite-dimensional problem converge to the optimal state and control of the corresponding infinite-dimensional problem.« less

Microscopic pressure-cooker model for studying molecules in confinement

NASA Astrophysics Data System (ADS)

Santamaria, Ruben; Adamowicz, Ludwik; Rosas-Acevedo, Hortensia

2015-04-01

A model for a system of a finite number of molecules in confinement is presented and expressions for determining the temperature, pressure, and volume of the system are derived. The present model is a generalisation of the Zwanzig-Langevin model because it includes pressure effects in the system. It also has general validity, preserves the ergodic hypothesis, and provides a formal framework for previous studies of hydrogen clusters in confinement. The application of the model is illustrated by an investigation of a set of prebiotic compounds exposed to varying pressure and temperature. The simulations performed within the model involve the use of a combination of molecular dynamics and density functional theory methods implemented on a computer system with a mixed CPU-GPU architecture.

Finite Volume Methods: Foundation and Analysis

NASA Technical Reports Server (NTRS)

Barth, Timothy; Ohlberger, Mario

2003-01-01

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Robust isotropic super-resolution by maximizing a Laplace posterior for MRI volumes

NASA Astrophysics Data System (ADS)

Han, Xian-Hua; Iwamoto, Yutaro; Shiino, Akihiko; Chen, Yen-Wei

2014-03-01

Magnetic resonance imaging can only acquire volume data with finite resolution due to various factors. In particular, the resolution in one direction (such as the slice direction) is much lower than others (such as the in-plane direction), yielding un-realistic visualizations. This study explores to reconstruct MRI isotropic resolution volumes from three orthogonal scans. This proposed super- resolution reconstruction is formulated as a maximum a posterior (MAP) problem, which relies on the generation model of the acquired scans from the unknown high-resolution volumes. Generally, the deviation ensemble of the reconstructed high-resolution (HR) volume from the available LR ones in the MAP is represented as a Gaussian distribution, which usually results in some noise and artifacts in the reconstructed HR volume. Therefore, this paper investigates a robust super-resolution by formulating the deviation set as a Laplace distribution, which assumes sparsity in the deviation ensemble based on the possible insight of the appeared large values only around some unexpected regions. In addition, in order to achieve reliable HR MRI volume, we integrates the priors such as bilateral total variation (BTV) and non-local mean (NLM) into the proposed MAP framework for suppressing artifacts and enriching visual detail. We validate the proposed robust SR strategy using MRI mouse data with high-definition resolution in two direction and low-resolution in one direction, which are imaged in three orthogonal scans: axial, coronal and sagittal planes. Experiments verifies that the proposed strategy can achieve much better HR MRI volumes than the conventional MAP method even with very high-magnification factor: 10.

Incorporation of Condensation Heat Transfer in a Flow Network Code

NASA Technical Reports Server (NTRS)

Anthony, Miranda; Majumdar, Alok

2002-01-01

Pure water is distilled from waste water in the International Space Station. The distillation assembly consists of an evaporator, a compressor and a condenser. Vapor is periodically purged from the condenser to avoid vapor accumulation. Purged vapor is condensed in a tube by coolant water prior to entering the purge pump. The paper presents a condensation model of purged vapor in a tube. This model is based on the Finite Volume Method. In the Finite Volume Method, the flow domain is discretized into multiple control volumes and a simultaneous analysis is performed.

Thermodynamic evaluation of transonic compressor rotors using the finite volume approach

NASA Technical Reports Server (NTRS)

Moore, John; Nicholson, Stephen; Moore, Joan G.

1986-01-01

The development of a computational capability to handle viscous flow with an explicit time-marching method based on the finite volume approach is summarized. Emphasis is placed on the extensions to the computational procedure which allow the handling of shock induced separation and large regions of strong backflow. Appendices contain abstracts of papers and whole reports generated during the contract period.

Numerical approach for finite volume three-body interaction

NASA Astrophysics Data System (ADS)

Guo, Peng; Gasparian, Vladimir

2018-01-01

In the present work, we study a numerical approach to one dimensional finite volume three-body interaction, the method is demonstrated by considering a toy model of three spinless particles interacting with pair-wise δ -function potentials. The numerical results are compared with the exact solutions of three spinless bosons interaction when the strength of short-range interactions are set equal for all pairs.

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Simulation of all-scale atmospheric dynamics on unstructured meshes

NASA Astrophysics Data System (ADS)

Smolarkiewicz, Piotr K.; Szmelter, Joanna; Xiao, Feng

2016-10-01

The advance of massively parallel computing in the nineteen nineties and beyond encouraged finer grid intervals in numerical weather-prediction models. This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models. This paper first outlines the historical background to a wide range of numerical methods advanced in the process. Next, the trend is illustrated with a technical review of a versatile nonoscillatory forward-in-time finite-volume (NFTFV) approach, proven effective in simulations of atmospheric flows from small-scale dynamics to global circulations and climate. The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible finite-volume median-dual unstructured-mesh discretisation of the spatial differential operators comprising PDEs of atmospheric dynamics. The paper consolidates the concepts leading to a family of generalised nonhydrostatic NFTFV flow solvers that include soundproof PDEs of incompressible Boussinesq, anelastic and pseudo-incompressible systems, common in large-eddy simulation of small- and meso-scale dynamics, as well as all-scale compressible Euler equations. Such a framework naturally extends predictive skills of large-eddy simulation to the global atmosphere, providing a bottom-up alternative to the reverse approach pursued in the weather-prediction models. Theoretical considerations are substantiated by calculations attesting to the versatility and efficacy of the NFTFV approach. Some prospective developments are also discussed.

Finite element simulation of interactions between pelvic organs: predictive model of the prostate motion in the context of radiotherapy.

PubMed

Boubaker, Mohamed Bader; Haboussi, Mohamed; Ganghoffer, Jean-François; Aletti, Pierre

2009-08-25

The setting up of predictive models of the pelvic organ motion and deformation may prove an efficient tool in the framework of prostate cancer radiotherapy, in order to deliver doses more accurately and efficiently to the clinical target volume (CTV). A finite element (FE) model of the prostate, rectum and bladder motion has been developed, investigating more specifically the influence of the rectum and bladder repletions on the gland motion. The required organ geometries are obtained after processing the computed tomography (CT) images, using specific softwares. Due to their structural characteristics, a 3D shell discretization is adopted for the rectum and the bladder, whereas a volume discretization is adopted for the prostate. As for the mechanical behavior modelling, first order Ogden hyperelastic constitutive laws for both the rectum and bladder are identified. The prostate is comparatively considered as more rigid and is accordingly modelled as an elastic tissue undergoing small strains. A FE model is then created, accounting for boundary and contact conditions, internal and applied loadings being selected as close as possible to available anatomic data. The order of magnitude of the prostate motion predicted by the FE simulations is similar to the measurements done on a deceased person, accounting for the delineation errors, with a relative error around 8%. Differences are essentially due to uncertainties in the constitutive parameters, pointing towards the need for the setting up of direct measurement of the organs mechanical behavior.

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.

Simulation-aided constitutive law development - Assessment of low triaxiality void nucleation models via extended finite element method

NASA Astrophysics Data System (ADS)

Zhao, Jifeng; Kontsevoi, Oleg Y.; Xiong, Wei; Smith, Jacob

2017-05-01

In this work, a multi-scale computational framework has been established in order to investigate, refine and validate constitutive behaviors in the context of the Gurson-Tvergaard-Needleman (GTN) void mechanics model. The eXtended Finite Element Method (XFEM) has been implemented in order to (1) develop statistical volume elements (SVE) of a matrix material with subscale inclusions and (2) to simulate the multi-void nucleation process due to interface debonding between the matrix and particle phases. Our analyses strongly suggest that under low stress triaxiality the nucleation rate of the voids f˙ can be well described by a normal distribution function with respect to the matrix equivalent stress (σe), as opposed to that proposed (σbar + 1 / 3σkk) in the original form of the single void GTN model. The modified form of the multi-void nucleation model has been validated based on a series of numerical experiments with different loading conditions, material properties, particle shape/size and spatial distributions. The utilization of XFEM allows for an invariant finite element mesh to represent varying microstructures, which implies suitability for drastically reducing complexity in generating the finite element discretizations for large stochastic arrays of microstructure configurations. The modified form of the multi-void nucleation model is further applied to study high strength steels by incorporating first principles calculations. The necessity of using a phenomenological interface separation law has been fully eliminated and replaced by the physics-based cohesive relationship obtained from Density Functional Theory (DFT) calculations in order to provide an accurate macroscopic material response.

Experimental validation of a numerical 3-D finite model applied to wind turbines design under vibration constraints: TREVISE platform

NASA Astrophysics Data System (ADS)

Sellami, Takwa; Jelassi, Sana; Darcherif, Abdel Moumen; Berriri, Hanen; Mimouni, Med Faouzi

2018-04-01

With the advancement of wind turbines towards complex structures, the requirement of trusty structural models has become more apparent. Hence, the vibration characteristics of the wind turbine components, like the blades and the tower, have to be extracted under vibration constraints. Although extracting the modal properties of blades is a simple task, calculating precise modal data for the whole wind turbine coupled to its tower/foundation is still a perplexing task. In this framework, this paper focuses on the investigation of the structural modeling approach of modern commercial micro-turbines. Thus, the structural model a complex designed wind turbine, which is Rutland 504, is established based on both experimental and numerical methods. A three-dimensional (3-D) numerical model of the structure was set up based on the finite volume method (FVM) using the academic finite element analysis software ANSYS. To validate the created model, experimental vibration tests were carried out using the vibration test system of TREVISE platform at ECAM-EPMI. The tests were based on the experimental modal analysis (EMA) technique, which is one of the most efficient techniques for identifying structures parameters. Indeed, the poles and residues of the frequency response functions (FRF), between input and output spectra, were calculated to extract the mode shapes and the natural frequencies of the structure. Based on the obtained modal parameters, the numerical designed model was up-dated.

Nontrivial thermodynamics in 't Hooft's large-N limit

NASA Astrophysics Data System (ADS)

Cubero, Axel Cortés

2015-05-01

We study the finite volume/temperature correlation functions of the (1 +1 )-dimensional SU (N ) principal chiral sigma model in the planar limit. The exact S-matrix of the sigma model is known to simplify drastically at large N , and this leads to trivial thermodynamic Bethe ansatz (TBA) equations. The partition function, if derived using the TBA, can be shown to be that of free particles. We show that the correlation functions and expectation values of operators at finite volume/temperature are not those of the free theory, and that the TBA does not give enough information to calculate them. Our analysis is done using the Leclair-Mussardo formula for finite-volume correlators, and knowledge of the exact infinite-volume form factors. We present analytical results for the one-point function of the energy-momentum tensor, and the two-point function of the renormalized field operator. The results for the energy-momentum tensor can be used to define a nontrivial partition function.

Simulation studies of vestibular macular afferent-discharge patterns using a new, quasi-3-D finite volume method

NASA Technical Reports Server (NTRS)

Ross, M. D.; Linton, S. W.; Parnas, B. R.

2000-01-01

A quasi-three-dimensional finite-volume numerical simulator was developed to study passive voltage spread in vestibular macular afferents. The method, borrowed from computational fluid dynamics, discretizes events transpiring in small volumes over time. The afferent simulated had three calyces with processes. The number of processes and synapses, and direction and timing of synapse activation, were varied. Simultaneous synapse activation resulted in shortest latency, while directional activation (proximal to distal and distal to proximal) yielded most regular discharges. Color-coded visualizations showed that the simulator discretized events and demonstrated that discharge produced a distal spread of voltage from the spike initiator into the ending. The simulations indicate that directional input, morphology, and timing of synapse activation can affect discharge properties, as must also distal spread of voltage from the spike initiator. The finite volume method has generality and can be applied to more complex neurons to explore discrete synaptic effects in four dimensions.

Recent Developments in Computational Techniques for Applied Hydrodynamics.

DTIC Science & Technology

1979-12-07

by block number) Numerical Method Fluids Incompressible Flow Finite Difference Methods Poisson Equation Convective Equations -MABSTRACT (Continue on...weaknesses of the different approaches are analyzed. Finite - difference techniques have particularly attractive properties in this framework. Hence it will...be worthwhile to correct, at least partially, the difficulties from which Eulerian and Lagrangian finite - difference techniques suffer, discussed in

Finite deformation of incompressible fiber-reinforced elastomers: A computational micromechanics approach

NASA Astrophysics Data System (ADS)

Moraleda, Joaquín; Segurado, Javier; LLorca, Javier

2009-09-01

The in-plane finite deformation of incompressible fiber-reinforced elastomers was studied using computational micromechanics. Composite microstructure was made up of a random and homogeneous dispersion of aligned rigid fibers within a hyperelastic matrix. Different matrices (Neo-Hookean and Gent), fibers (monodisperse or polydisperse, circular or elliptical section) and reinforcement volume fractions (10-40%) were analyzed through the finite element simulation of a representative volume element of the microstructure. A successive remeshing strategy was employed when necessary to reach the large deformation regime in which the evolution of the microstructure influences the effective properties. The simulations provided for the first time "quasi-exact" results of the in-plane finite deformation for this class of composites, which were used to assess the accuracy of the available homogenization estimates for incompressible hyperelastic composites.

Moduli thermalization and finite temperature effects in "big" divisor large volume D3/ D7 Swiss-cheese compactification

NASA Astrophysics Data System (ADS)

Shukla, Pramod

2011-01-01

In the context of Type IIB compactified on a large volume Swiss-Cheese orientifold in the presence of a mobile space-time filling D3-brane and stacks of fluxed D7-branes wrapping the "big" divisor Σ B of a Swiss-Cheese Calabi Yau in WCP 4[1, 1, 1, 6, 9], we explore various implications of moduli dynamics and discuss their couplings and decay into MSSM (-like) matter fields early in the history of universe to reach thermal equilibrium. Like finite temperature effects in O'KKLT, we observe that the local minimum of zero-temperature effective scalar potential is stable against any finite temperature corrections (up to two-loops) in large volume scenarios as well. Also we find that moduli are heavy enough to avoid any cosmological moduli problem.

The unstaggered extension to GFDL's FV3 dynamical core on the cubed-sphere

NASA Astrophysics Data System (ADS)

Chen, X.; Lin, S. J.; Harris, L.

2017-12-01

Finite-volume schemes have become popular for atmospheric transport since they provide intrinsic mass conservation to constituent species. Many CFD codes use unstaggered discretizations for finite volume methods with an approximate Riemann solver. However, this approach is inefficient for geophysical flows due to the complexity of the Riemann solver. We introduce a Low Mach number Approximate Riemann Solver (LMARS) simplified using assumptions appropriate for atmospheric flows: the wind speed is much slower than the sound speed, weak discontinuities, and locally uniform sound wave velocity. LMARS makes possible a Riemann-solver-based dynamical core comparable in computational efficiency to many current dynamical cores. We will present a 3D finite-volume dynamical core using LMARS in a cubed-sphere geometry with a vertically Lagrangian discretization. Results from standard idealized test cases will be discussed.

Optimal protocols for slowly driven quantum systems.

PubMed

Zulkowski, Patrick R; DeWeese, Michael R

2015-09-01

The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

2003-01-01

The use of multi-dimensional finite volume numerical techniques with finite thickness models for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the one-dimensional semi -infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody were investigated. An array of streamwise orientated heating striations were generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients due to the striation patterns two-dimensional heat transfer techniques were necessary to obtain accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates because it did not account for lateral heat conduction in the model.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

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.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

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

Wang, Q.; Sprague, M. A.; Jonkman, J.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context ofmore » LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.« less

Electronic part of the optical correlation function at finite temperature: the S-matrix expansion

NASA Astrophysics Data System (ADS)

Tavares, M.; Marques, G. E.; Tejedor, C.

1998-12-01

We present an extension to finite temperature of the Mahan-Nozières-De Dominicis framework to obtain the electronic part of the current-current correlation function. Its Fourier transform gives the absorption and emission spectra of doped low-dimensional semiconductors. We show the meaning of the new finite-temperature contributions characterizing the electronic part.

A point-value enhanced finite volume method based on approximate delta functions

NASA Astrophysics Data System (ADS)

Xuan, Li-Jun; Majdalani, Joseph

2018-02-01

We revisit the concept of an approximate delta function (ADF), introduced by Huynh (2011) [1], in the form of a finite-order polynomial that holds identical integral properties to the Dirac delta function when used in conjunction with a finite-order polynomial integrand over a finite domain. We show that the use of generic ADF polynomials can be effective at recovering and generalizing several high-order methods, including Taylor-based and nodal-based Discontinuous Galerkin methods, as well as the Correction Procedure via Reconstruction. Based on the ADF concept, we then proceed to formulate a Point-value enhanced Finite Volume (PFV) method, which stores and updates the cell-averaged values inside each element as well as the unknown quantities and, if needed, their derivatives on nodal points. The sharing of nodal information with surrounding elements saves the number of degrees of freedom compared to other compact methods at the same order. To ensure conservation, cell-averaged values are updated using an identical approach to that adopted in the finite volume method. Here, the updating of nodal values and their derivatives is achieved through an ADF concept that leverages all of the elements within the domain of integration that share the same nodal point. The resulting scheme is shown to be very stable at successively increasing orders. Both accuracy and stability of the PFV method are verified using a Fourier analysis and through applications to the linear wave and nonlinear Burgers' equations in one-dimensional space.

Finite-volume method with lattice Boltzmann flux scheme for incompressible porous media flow at the representative-elementary-volume scale.

PubMed

Hu, Yang; Li, Decai; Shu, Shi; Niu, Xiaodong

2016-02-01

Based on the Darcy-Brinkman-Forchheimer equation, a finite-volume computational model with lattice Boltzmann flux scheme is proposed for incompressible porous media flow in this paper. The fluxes across the cell interface are calculated by reconstructing the local solution of the generalized lattice Boltzmann equation for porous media flow. The time-scaled midpoint integration rule is adopted to discretize the governing equation, which makes the time step become limited by the Courant-Friedricks-Lewy condition. The force term which evaluates the effect of the porous medium is added to the discretized governing equation directly. The numerical simulations of the steady Poiseuille flow, the unsteady Womersley flow, the circular Couette flow, and the lid-driven flow are carried out to verify the present computational model. The obtained results show good agreement with the analytical, finite-difference, and/or previously published solutions.

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

DOE PAGES

Wang, Qi; Sprague, Michael A.; Jonkman, Jason; ...

2017-03-14

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

An Integrated Finite Element-based Simulation Framework: From Hole Piercing to Hole Expansion

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

Hu, Xiaohua; Sun, Xin; Golovashchenko, Segey F.

An integrated finite element-based modeling framework is developed to predict the hole expansion ratio (HER) of AA6111-T4 sheet by considering the piercing-induced damages around the hole edge. Using damage models and parameters calibrated from previously reported tensile stretchability studies, the predicted HER correlates well with experimentally measured HER values for different hole piercing clearances. The hole piercing model shows burrs are not generated on the sheared surface for clearances less than 20%, which corresponds well with the experimental data on pierced holes cross-sections. Finite-element-calculated HER also is not especially sensitive to piercing clearances less than this value. However, as clearancesmore » increase to 30% and further to 40%, the HER values are predicted to be considerably smaller, also consistent with experimental measurements. Upon validation, the integrated modeling framework is used to examine the effects of different hole piercing and hole expansion conditions on the critical HERs for AA6111-T4.« less

BeamDyn: a high-fidelity wind turbine blade solver in the FAST modular framework

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

Wang, Qi; Sprague, Michael A.; Jonkman, Jason

Here, this paper presents a numerical implementation of the geometrically exact beam theory based on the Legendre-spectral-finite-element (LSFE) method. The displacement-based geometrically exact beam theory is presented, and the special treatment of three-dimensional rotation parameters is reviewed. An LSFE is a high-order finite element with nodes located at the Gauss-Legendre-Lobatto points. These elements can be an order of magnitude more computationally efficient than low-order finite elements for a given accuracy level. The new module, BeamDyn, is implemented in the FAST modularization framework for dynamic simulation of highly flexible composite-material wind turbine blades within the FAST aeroelastic engineering model. The frameworkmore » allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples are provided to validate BeamDyn and examine the LSFE performance as well as the coupling algorithm in the FAST modularization framework. BeamDyn can also be used as a stand-alone high-fidelity beam tool.« less

Hadronic molecules

NASA Astrophysics Data System (ADS)

Guo, Feng-Kun; Hanhart, Christoph; Meißner, Ulf-G.; Wang, Qian; Zhao, Qiang; Zou, Bing-Song

2018-01-01

A large number of experimental discoveries especially in the heavy quarkonium sector that did not meet the expectations of the until then very successful quark model led to a renaissance of hadron spectroscopy. Among various explanations of the internal structure of these excitations, hadronic molecules, being analogs of light nuclei, play a unique role since for those predictions can be made with controlled uncertainty. Experimental evidence of various candidates of hadronic molecules and methods of identifying such structures are reviewed. Nonrelativistic effective field theories are the suitable framework for studying hadronic molecules and are discussed in both the continuum and finite volumes. Also pertinent lattice QCD results are presented. Further, the production mechanisms and decays of hadronic molecules are discussed and comments are given on the reliability of certain assertions often made in the literature.

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

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

Samaddar, Debasmita; Coster, D. P.; Bonnin, X.

We show that numerical modelling of edge plasma physics may be successfully parallelized in time. The parareal algorithm has been employed for this purpose and the SOLPS code package coupling the B2.5 finite-volume fluid plasma solver with the kinetic Monte-Carlo neutral code Eirene has been used as a test bed. The complex dynamics of the plasma and neutrals in the scrape-off layer (SOL) region makes this a unique application. It is demonstrated that a significant computational gain (more than an order of magnitude) may be obtained with this technique. The use of the IPS framework for event-based parareal implementation optimizesmore » resource utilization and has been shown to significantly contribute to the computational gain.« less

Temporal parallelization of edge plasma simulations using the parareal algorithm and the SOLPS code

DOE PAGES

Samaddar, Debasmita; Coster, D. P.; Bonnin, X.; ...

2017-07-31

We show that numerical modelling of edge plasma physics may be successfully parallelized in time. The parareal algorithm has been employed for this purpose and the SOLPS code package coupling the B2.5 finite-volume fluid plasma solver with the kinetic Monte-Carlo neutral code Eirene has been used as a test bed. The complex dynamics of the plasma and neutrals in the scrape-off layer (SOL) region makes this a unique application. It is demonstrated that a significant computational gain (more than an order of magnitude) may be obtained with this technique. The use of the IPS framework for event-based parareal implementation optimizesmore » resource utilization and has been shown to significantly contribute to the computational gain.« less

FSM-F: Finite State Machine Based Framework for Denial of Service and Intrusion Detection in MANET.

PubMed

N Ahmed, Malik; Abdullah, Abdul Hanan; Kaiwartya, Omprakash

2016-01-01

Due to the continuous advancements in wireless communication in terms of quality of communication and affordability of the technology, the application area of Mobile Adhoc Networks (MANETs) significantly growing particularly in military and disaster management. Considering the sensitivity of the application areas, security in terms of detection of Denial of Service (DoS) and intrusion has become prime concern in research and development in the area. The security systems suggested in the past has state recognition problem where the system is not able to accurately identify the actual state of the network nodes due to the absence of clear definition of states of the nodes. In this context, this paper proposes a framework based on Finite State Machine (FSM) for denial of service and intrusion detection in MANETs. In particular, an Interruption Detection system for Adhoc On-demand Distance Vector (ID-AODV) protocol is presented based on finite state machine. The packet dropping and sequence number attacks are closely investigated and detection systems for both types of attacks are designed. The major functional modules of ID-AODV includes network monitoring system, finite state machine and attack detection model. Simulations are carried out in network simulator NS-2 to evaluate the performance of the proposed framework. A comparative evaluation of the performance is also performed with the state-of-the-art techniques: RIDAN and AODV. The performance evaluations attest the benefits of proposed framework in terms of providing better security for denial of service and intrusion detection attacks.

Relaxation and Preconditioning for High Order Discontinuous Galerkin Methods with Applications to Aeroacoustics and High Speed Flows

NASA Technical Reports Server (NTRS)

Shu, Chi-Wang

2004-01-01

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. Other related issues in high order WENO finite difference and finite volume methods have also been investigated. methods are two classes of high order, high resolution methods suitable for convection dominated simulations with possible discontinuous or sharp gradient solutions. In [18], we first review these two classes of methods, pointing out their similarities and differences in algorithm formulation, theoretical properties, implementation issues, applicability, and relative advantages. We then present some quantitative comparisons of the third order finite volume WENO methods and discontinuous Galerkin methods for a series of test problems to assess their relative merits in accuracy and CPU timing. In [3], we review the development of the Runge-Kutta discontinuous Galerkin (RKDG) methods for non-linear convection-dominated problems. These robust and accurate methods have made their way into the main stream of computational fluid dynamics and are quickly finding use in a wide variety of applications. They combine a special class of Runge-Kutta time discretizations, that allows the method to be non-linearly stable regardless of its accuracy, with a finite element space discretization by discontinuous approximations, that incorporates the ideas of numerical fluxes and slope limiters coined during the remarkable development of the high-resolution finite difference and finite volume schemes. The resulting RKDG methods are stable, high-order accurate, and highly parallelizable schemes that can easily handle complicated geometries and boundary conditions. We review the theoretical and algorithmic aspects of these methods and show several applications including nonlinear conservation laws, the compressible and incompressible Navier-Stokes equations, and Hamilton-Jacobi-like equations.

Flow/Damage Surfaces for Fiber-Reinforced Metals Having Different Periodic Microstructures

NASA Technical Reports Server (NTRS)

Lissenden, Cliff J.; Arnold, Steven M.; Iyer, Saiganesh K.

1998-01-01

Flow/damage surfaces can be defined in terms of stress, inelastic strain rate, and internal variables using a thermodynamics framework. A macroscale definition relevant to thermodynamics and usable in an experimental program is employed to map out surfaces of constant inelastic power in various stress planes. The inelastic flow of a model silicon carbide/ titanium composite system having rectangular, hexagonal, and square diagonal fiber packing arrays subjected to biaxial stresses is quantified by flow/damage surfaces that are determined numerically from micromechanics, using both finite element analysis and the generalized method of cells. Residual stresses from processing are explicitly included and damage in the form of fiber-matrix debonding under transverse tensile and/or shear loading is represented by a simple interface model. The influence of microstructural architecture is largest whenever fiber-matrix debonding is not an issue; for example in the presence of transverse compressive stresses. Additionally, as the fiber volume fraction increases, so does the effect of microstructural architecture. With regard to the micromechanics analysis, the overall inelastic flow predicted by the generalized method of cells is in excellent agreement with that predicted using a large number of displacement-based finite elements.

Flow/Damage Surfaces for Fiber-Reinforced Metals having Different Periodic Microstructures

NASA Technical Reports Server (NTRS)

Lissenden, Cliff J.; Arnold, Steven M.; Iyer, Saiganesh K.

1998-01-01

Flow/damage surfaces can be defined in terms of stress, inelastic strain rate, and internal variables using a thermodynamics framework. A macroscale definition relevant to thermodynamics and usable in an experimental program is employed to map out surfaces of constant inelastic power in various stress planes. The inelastic flow of a model silicon carbide/ titanium composite system having rectangular, hexagonal, and square diagonal fiber packing, arrays subjected to biaxial stresses is quantified by flow/damage surfaces that are determined numerically from micromechanics. using both finite element analysis and the generalized method of cells. Residual stresses from processing are explicitly included and damage in the form of fiber-matrix debonding under transverse tensile and/or shear loading is represented by a simple interface model. The influence of microstructural architecture is largest whenever fiber-matrix debonding is not an issue, for example in the presence of transverse compressive stresses. Additionally, as the fiber volume fraction increases, so does the effect of microstructural architecture. With regard to the micromechanics analysis, the overall inelastic flow predicted by the generalized method of cells is in excellent agreement with that predicted using a large number of displacement-based finite elements.

Elastic properties of paramagnetic austenitic steel at finite temperature: Longitudinal spin fluctuations in multicomponent alloys

NASA Astrophysics Data System (ADS)

Dong, Zhihua; Schönecker, Stephan; Chen, Dengfu; Li, Wei; Long, Mujun; Vitos, Levente

2017-11-01

We propose a first-principles framework for longitudinal spin fluctuations (LSFs) in disordered paramagnetic (PM) multicomponent alloy systems and apply it to investigate the influence of LSFs on the temperature dependence of two elastic constants of PM austenitic stainless steel Fe15Cr15Ni. The magnetic model considers individual fluctuating moments in a static PM medium with first-principles-derived LSF energetics in conjunction with describing chemical disorder and randomness of the transverse magnetic component in the single-site alloy formalism and disordered local moment (DLM) picture. A temperature-sensitive mean magnetic moment is adopted to accurately represent the LSF state in the elastic-constant calculations. We make evident that magnetic interactions between an LSF impurity and the PM medium are weak in the present steel alloy. This allows gaining accurate LSF energetics and mean magnetic moments already through a perturbation from the static DLM moments instead of a tedious self-consistent procedure. We find that LSFs systematically lower the cubic shear elastic constants c' and c44 by ˜6 GPa in the temperature interval 300-1600 K, whereas the predominant mechanism for the softening of both elastic constants with temperature is the magneto-volume coupling due to thermal lattice expansion. We find that non-negligible local magnetic moments of Cr and Ni are thermally induced by LSFs, but they exert only a small influence on the elastic properties. The proposed framework exhibits high flexibility in accurately accounting for finite-temperature magnetism and its impact on the mechanical properties of PM multicomponent alloys.

ChPT loops for the lattice: pion mass and decay constant, HVP at finite volume and nn̅-oscillations

NASA Astrophysics Data System (ADS)

Bijnens, Johan

2018-03-01

I present higher loop order results for several calculations in Chiral perturbation Theory. 1) Two-loop results at finite volume for hadronic vacuum polarization. 2) A three-loop calculation of the pion mass and decay constant in two-flavour ChPT. For the pion mass all needed auxiliary parameters can be determined from lattice calculations of ππ-scattering. 3) Chiral corrections to neutron-anti-neutron oscillations.

Three-Dimensional Viscous Flow Analysis for Moving Bodies Past Fixed Structures

DTIC Science & Technology

1988-05-13

BELLEVUE, WA 98n)05 Research Triangle Park, UC 27709-2211 6Sý. NAME Of FUNDING I PONSORING O Ib. C’FFICE SYMBOL 9 . PROCUREMENT INSTRUMENT IPENTIFICATION...34 otheor sditico Grs IMa ý; pl S- Three- Dimvensio:.iýal Viscrous Flow Analysis for Moving Bodies Past Fixed Structures Fina.11Report, Kelton M. Peery and...Recommendations 40 List of Figures 1 Finite-Volume Mesh ......... ......................... 8 2 Finite-Volume Cell ....... ............................ 9 3

Cell-centered high-order hyperbolic finite volume method for diffusion equation on unstructured grids

NASA Astrophysics Data System (ADS)

Lee, Euntaek; Ahn, Hyung Taek; Luo, Hong

2018-02-01

We apply a hyperbolic cell-centered finite volume method to solve a steady diffusion equation on unstructured meshes. This method, originally proposed by Nishikawa using a node-centered finite volume method, reformulates the elliptic nature of viscous fluxes into a set of augmented equations that makes the entire system hyperbolic. We introduce an efficient and accurate solution strategy for the cell-centered finite volume method. To obtain high-order accuracy for both solution and gradient variables, we use a successive order solution reconstruction: constant, linear, and quadratic (k-exact) reconstruction with an efficient reconstruction stencil, a so-called wrapping stencil. By the virtue of the cell-centered scheme, the source term evaluation was greatly simplified regardless of the solution order. For uniform schemes, we obtain the same order of accuracy, i.e., first, second, and third orders, for both the solution and its gradient variables. For hybrid schemes, recycling the gradient variable information for solution variable reconstruction makes one order of additional accuracy, i.e., second, third, and fourth orders, possible for the solution variable with less computational work than needed for uniform schemes. In general, the hyperbolic method can be an effective solution technique for diffusion problems, but instability is also observed for the discontinuous diffusion coefficient cases, which brings necessity for further investigation about the monotonicity preserving hyperbolic diffusion method.

A multiscale coupled finite-element and phase-field framework to modeling stressed grain growth in polycrystalline thin films

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

Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir; Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar; Thamburaja, P., E-mail: prakash.thamburaja@gmail.com

A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substratemore » and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.« less

Hierarchical bounding structures for efficient virial computations: Towards a realistic molecular description of cholesterics

NASA Astrophysics Data System (ADS)

Tortora, Maxime M. C.; Doye, Jonathan P. K.

2017-12-01

We detail the application of bounding volume hierarchies to accelerate second-virial evaluations for arbitrary complex particles interacting through hard and soft finite-range potentials. This procedure, based on the construction of neighbour lists through the combined use of recursive atom-decomposition techniques and binary overlap search schemes, is shown to scale sub-logarithmically with particle resolution in the case of molecular systems with high aspect ratios. Its implementation within an efficient numerical and theoretical framework based on classical density functional theory enables us to investigate the cholesteric self-assembly of a wide range of experimentally relevant particle models. We illustrate the method through the determination of the cholesteric behavior of hard, structurally resolved twisted cuboids, and report quantitative evidence of the long-predicted phase handedness inversion with increasing particle thread angles near the phenomenological threshold value of 45°. Our results further highlight the complex relationship between microscopic structure and helical twisting power in such model systems, which may be attributed to subtle geometric variations of their chiral excluded-volume manifold.

Transformation-Induced, Geometrically Necessary, Dislocation-Based Flow Curve Modeling of Dual-Phase Steels: Effect of Grain Size

NASA Astrophysics Data System (ADS)

Ramazani, Ali; Mukherjee, Krishnendu; Prahl, Ulrich; Bleck, Wolfgang

2012-10-01

The flow behavior of dual-phase (DP) steels is modeled on the finite-element method (FEM) framework on the microscale, considering the effect of the microstructure through the representative volume element (RVE) approach. Two-dimensional RVEs were created from microstructures of experimentally obtained DP steels with various ferrite grain sizes. The flow behavior of single phases was modeled through the dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was modeled, and the resultant prestrained areas in the ferrite were considered to be the storage place of transformation-induced, geometrically necessary dislocations (GNDs). The flow curves of DP steels with varying ferrite grain sizes, but constant martensite fractions, were obtained from the literature. The flow curves of simulations that take into account the GND are in better agreement with those of experimental flow curves compared with those of predictions without consideration of the GND. The experimental results obeyed the Hall-Petch relationship between yield stress and flow stress and the simulations predicted this as well.

A Finite-Volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction

NASA Astrophysics Data System (ADS)

Daude, F.; Galon, P.

2018-06-01

A Finite-Volume scheme for the numerical computations of compressible single- and two-phase flows in flexible pipelines is proposed based on an approximate Godunov-type approach. The spatial discretization is here obtained using the HLLC scheme. In addition, the numerical treatment of abrupt changes in area and network including several pipelines connected at junctions is also considered. The proposed approach is based on the integral form of the governing equations making it possible to tackle general equations of state. A coupled approach for the resolution of fluid-structure interaction of compressible fluid flowing in flexible pipes is considered. The structural problem is solved using Euler-Bernoulli beam finite elements. The present Finite-Volume method is applied to ideal gas and two-phase steam-water based on the Homogeneous Equilibrium Model (HEM) in conjunction with a tabulated equation of state in order to demonstrate its ability to tackle general equations of state. The extensive application of the scheme for both shock tube and other transient flow problems demonstrates its capability to resolve such problems accurately and robustly. Finally, the proposed 1-D fluid-structure interaction model appears to be computationally efficient.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-07-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved space-times. In this paper, we assume the background space-time to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local time-stepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed space-times. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

ADER discontinuous Galerkin schemes for general-relativistic ideal magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Fambri, F.; Dumbser, M.; Köppel, S.; Rezzolla, L.; Zanotti, O.

2018-03-01

We present a new class of high-order accurate numerical algorithms for solving the equations of general-relativistic ideal magnetohydrodynamics in curved spacetimes. In this paper we assume the background spacetime to be given and static, i.e. we make use of the Cowling approximation. The governing partial differential equations are solved via a new family of fully-discrete and arbitrary high-order accurate path-conservative discontinuous Galerkin (DG) finite-element methods combined with adaptive mesh refinement and time accurate local timestepping. In order to deal with shock waves and other discontinuities, the high-order DG schemes are supplemented with a novel a-posteriori subcell finite-volume limiter, which makes the new algorithms as robust as classical second-order total-variation diminishing finite-volume methods at shocks and discontinuities, but also as accurate as unlimited high-order DG schemes in smooth regions of the flow. We show the advantages of this new approach by means of various classical two- and three-dimensional benchmark problems on fixed spacetimes. Finally, we present a performance and accuracy comparisons between Runge-Kutta DG schemes and ADER high-order finite-volume schemes, showing the higher efficiency of DG schemes.

Finite volume treatment of dispersion-relation-preserving and optimized prefactored compact schemes for wave propagation

NASA Astrophysics Data System (ADS)

Popescu, Mihaela; Shyy, Wei; Garbey, Marc

2005-12-01

In developing suitable numerical techniques for computational aero-acoustics, the dispersion-relation-preserving (DRP) scheme by Tam and co-workers and the optimized prefactored compact (OPC) scheme by Ashcroft and Zhang have shown desirable properties of reducing both dissipative and dispersive errors. These schemes, originally based on the finite difference, attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre-determined formal orders of accuracy. In the present study, finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications. Linear and nonlinear wave equations, with and without viscous dissipation, have been adopted as the test problems. Highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases, the performance of these approaches is documented. For the linear wave equation, there is no major difference between the DRP and OPC schemes. For the nonlinear wave equations, the finite volume version of both DRP and OPC schemes offers substantially better solutions in regions of high gradient or discontinuity.

The CUBLAS and CULA based GPU acceleration of adaptive finite element framework for bioluminescence tomography.

PubMed

Zhang, Bo; Yang, Xiang; Yang, Fei; Yang, Xin; Qin, Chenghu; Han, Dong; Ma, Xibo; Liu, Kai; Tian, Jie

2010-09-13

In molecular imaging (MI), especially the optical molecular imaging, bioluminescence tomography (BLT) emerges as an effective imaging modality for small animal imaging. The finite element methods (FEMs), especially the adaptive finite element (AFE) framework, play an important role in BLT. The processing speed of the FEMs and the AFE framework still needs to be improved, although the multi-thread CPU technology and the multi CPU technology have already been applied. In this paper, we for the first time introduce a new kind of acceleration technology to accelerate the AFE framework for BLT, using the graphics processing unit (GPU). Besides the processing speed, the GPU technology can get a balance between the cost and performance. The CUBLAS and CULA are two main important and powerful libraries for programming on NVIDIA GPUs. With the help of CUBLAS and CULA, it is easy to code on NVIDIA GPU and there is no need to worry about the details about the hardware environment of a specific GPU. The numerical experiments are designed to show the necessity, effect and application of the proposed CUBLAS and CULA based GPU acceleration. From the results of the experiments, we can reach the conclusion that the proposed CUBLAS and CULA based GPU acceleration method can improve the processing speed of the AFE framework very much while getting a balance between cost and performance.

Expansion and improvement of the FORMA system for response and load analysis. Volume 2C: Listings, finite element FORMA subroutines

NASA Technical Reports Server (NTRS)

Wohlen, R. L.

1976-01-01

A listing of the source deck of each finite element FORMA subroutine is given to remove the 'black-box' aura of the subroutines so that the analyst may better understand the detailed operations of each subroutine. The FORTRAN 4 programming language is used in all finite element FORMA subroutines.

Quantum interval-valued probability: Contextuality and the Born rule

NASA Astrophysics Data System (ADS)

Tai, Yu-Tsung; Hanson, Andrew J.; Ortiz, Gerardo; Sabry, Amr

2018-05-01

We present a mathematical framework based on quantum interval-valued probability measures to study the effect of experimental imperfections and finite precision measurements on defining aspects of quantum mechanics such as contextuality and the Born rule. While foundational results such as the Kochen-Specker and Gleason theorems are valid in the context of infinite precision, they fail to hold in general in a world with limited resources. Here we employ an interval-valued framework to establish bounds on the validity of those theorems in realistic experimental environments. In this way, not only can we quantify the idea of finite-precision measurement within our theory, but we can also suggest a possible resolution of the Meyer-Mermin debate on the impact of finite-precision measurement on the Kochen-Specker theorem.

Multiphase fluid-solid coupled analysis of shock-bubble-stone interaction in shockwave lithotripsy.

PubMed

Wang, Kevin G

2017-10-01

A novel multiphase fluid-solid-coupled computational framework is applied to investigate the interaction of a kidney stone immersed in liquid with a lithotripsy shock wave (LSW) and a gas bubble near the stone. The main objective is to elucidate the effects of a bubble in the shock path to the elastic and fracture behaviors of the stone. The computational framework couples a finite volume 2-phase computational fluid dynamics solver with a finite element computational solid dynamics solver. The surface of the stone is represented as a dynamic embedded boundary in the computational fluid dynamics solver. The evolution of the bubble surface is captured by solving the level set equation. The interface conditions at the surfaces of the stone and the bubble are enforced through the construction and solution of local fluid-solid and 2-fluid Riemann problems. This computational framework is first verified for 3 example problems including a 1D multimaterial Riemann problem, a 3D shock-stone interaction problem, and a 3D shock-bubble interaction problem. Next, a series of shock-bubble-stone-coupled simulations are presented. This study suggests that the dynamic response of a bubble to LSW varies dramatically depending on its initial size. Bubbles with an initial radius smaller than a threshold collapse within 1 μs after the passage of LSW, whereas larger bubbles do not. For a typical LSW generated by an electrohydraulic lithotripter (p max  = 35.0MPa, p min  =- 10.1MPa), this threshold is approximately 0.12mm. Moreover, this study suggests that a noncollapsing bubble imposes a negative effect on stone fracture as it shields part of the LSW from the stone. On the other hand, a collapsing bubble may promote fracture on the proximal surface of the stone, yet hinder fracture from stone interior. Copyright © 2016 John Wiley & Sons, Ltd.

Robot Path Planning in Uncertain Environments: A Language-Measure-Theoretic Approach

DTIC Science & Technology

2015-03-01

in the framework of probabilistic finite state automata (PFSA) and language measure from a control-theoretic perspective. The proposed concept has been...DOI: 10.1115/1.4027876] Keywords: path planning, language measure, probabilistic finite state automata 1 Motivation and Introduction In general

GEMPIC: geometric electromagnetic particle-in-cell methods

NASA Astrophysics Data System (ADS)

Kraus, Michael; Kormann, Katharina; Morrison, Philip J.; Sonnendrücker, Eric

2017-08-01

We present a novel framework for finite element particle-in-cell methods based on the discretization of the underlying Hamiltonian structure of the Vlasov-Maxwell system. We derive a semi-discrete Poisson bracket, which retains the defining properties of a bracket, anti-symmetry and the Jacobi identity, as well as conservation of its Casimir invariants, implying that the semi-discrete system is still a Hamiltonian system. In order to obtain a fully discrete Poisson integrator, the semi-discrete bracket is used in conjunction with Hamiltonian splitting methods for integration in time. Techniques from finite element exterior calculus ensure conservation of the divergence of the magnetic field and Gauss' law as well as stability of the field solver. The resulting methods are gauge invariant, feature exact charge conservation and show excellent long-time energy and momentum behaviour. Due to the generality of our framework, these conservation properties are guaranteed independently of a particular choice of the finite element basis, as long as the corresponding finite element spaces satisfy certain compatibility conditions.

Applications and Improvement of a Coupled, Global and Cloud-Resolving Modeling System

NASA Technical Reports Server (NTRS)

Tao, W.-K.; Chern, J.; Atlas, R.

2005-01-01

Recently Grabowski (2001) and Khairoutdinov and Randall (2001) have proposed the use of 2D CFWs as a "super parameterization" [or multi-scale modeling framework (MMF)] to represent cloud processes within atmospheric general circulation models (GCMs). In the MMF, a fine-resolution 2D CRM takes the place of the single-column parameterization used in conventional GCMs. A prototype Goddard MMF based on the 2D Goddard Cumulus Ensemble (GCE) model and the Goddard finite volume general circulation model (fvGCM) is now being developed. The prototype includes the fvGCM run at 2.50 x 20 horizontal resolution with 32 vertical layers from the surface to 1 mb and the 2D (x-z) GCE using 64 horizontal and 32 vertical grid points with 4 km horizontal resolution and a cyclic lateral boundary. The time step for the 2D GCE would be 15 seconds, and the fvGCM-GCE coupling frequency would be 30 minutes (i.e. the fvGCM physical time step). We have successfully developed an fvGCM-GCE coupler for this prototype. Because the vertical coordinate of the fvGCM (a terrain-following floating Lagrangian coordinate) is different from that of the GCE (a z coordinate), vertical interpolations between the two coordinates are needed in the coupler. In interpolating fields from the GCE to fvGCM, we use an existing fvGCM finite- volume piecewise parabolic mapping (PPM) algorithm, which conserves the mass, momentum, and total energy. A new finite-volume PPM algorithm, which conserves the mass, momentum and moist static energy in the z coordinate, is being developed for interpolating fields from the fvGCM to the GCE. In the meeting, we will discuss the major differences between the two MMFs (i.e., the CSU MMF and the Goddard MMF). We will also present performance and critical issues related to the MMFs. In addition, we will present multi-dimensional cloud datasets (i.e., a cloud data library) generated by the Goddard MMF that will be provided to the global modeling community to help improve the representation and performance of moist processes in climate models and to improve our understanding of cloud processes globally (the software tools needed to produce cloud statistics and to identify various types of clouds and cloud systems from both high-resolution satellite and model data will be also presented).

Matrix elements of Δ B =0 operators in heavy hadron chiral perturbation theory

NASA Astrophysics Data System (ADS)

Lee, Jong-Wan

2015-05-01

We study the light-quark mass and spatial volume dependence of the matrix elements of Δ B =0 four-quark operators relevant for the determination of Vu b and the lifetime ratios of single-b hadrons. To this end, one-loop diagrams are computed in the framework of heavy hadron chiral perturbation theory with partially quenched formalism for three light-quark flavors in the isospin limit; flavor-connected and -disconnected diagrams are carefully analyzed. These calculations include the leading light-quark flavor and heavy-quark spin symmetry breaking effects in the heavy hadron spectrum. Our results can be used in the chiral extrapolation of lattice calculations of the matrix elements to the physical light-quark masses and to infinite volume. To provide insight on such chiral extrapolation, we evaluate the one-loop contributions to the matrix elements containing external Bd, Bs mesons and Λb baryon in the QCD limit, where sea and valence quark masses become equal. In particular, we find that the matrix elements of the λ3 flavor-octet operators with an external Bd meson receive the contributions solely from connected diagrams in which current lattice techniques are capable of precise determination of the matrix elements. Finite volume effects are at most a few percent for typical lattice sizes and pion masses.

Fragmentary and incidental behaviour of columns, slabs and crystals

PubMed Central

Whiteley, Walter

2014-01-01

Between the study of small finite frameworks and infinite incidentally periodic frameworks, we find the real materials which are large, but finite, fragments that fit into the infinite periodic frameworks. To understand these materials, we seek insights from both (i) their analysis as large frameworks with associated geometric and combinatorial properties (including the geometric repetitions) and (ii) embedding them into appropriate infinite periodic structures with motions that may break the periodic structure. A review of real materials identifies a number of examples with a local appearance of ‘unit cells’ which repeat under isometries but perhaps in unusual forms. These examples also refocus attention on several new classes of infinite ‘periodic’ frameworks: (i) columns—three-dimensional structures generated with one repeating isometry and (ii) slabs—three-dimensional structures with two independent repeating translations. With this larger vision of structures to be studied, we find some patterns and partial results that suggest new conjectures as well as many additional open questions. These invite a search for new examples and additional theorems. PMID:24379423

Framework Programmable Platform for the Advanced Software Development Workstation (FPP/ASDW). Demonstration framework document. Volume 2: Framework process description

NASA Technical Reports Server (NTRS)

Mayer, Richard J.; Blinn, Thomas M.; Dewitte, Paula S.; Crump, John W.; Ackley, Keith A.

1992-01-01

In the second volume of the Demonstration Framework Document, the graphical representation of the demonstration framework is given. This second document was created to facilitate the reading and comprehension of the demonstration framework. It is designed to be viewed in parallel with Section 4.2 of the first volume to help give a picture of the relationships between the UOB's (Unit of Behavior) of the model. The model is quite large and the design team felt that this form of presentation would make it easier for the reader to get a feel for the processes described in this document. The IDEF3 (Process Description Capture Method) diagrams of the processes of an Information System Development are presented. Volume 1 describes the processes and the agents involved with each process, while this volume graphically shows the precedence relationships among the processes.

FSM-F: Finite State Machine Based Framework for Denial of Service and Intrusion Detection in MANET

PubMed Central

N. Ahmed, Malik; Abdullah, Abdul Hanan; Kaiwartya, Omprakash

2016-01-01

Due to the continuous advancements in wireless communication in terms of quality of communication and affordability of the technology, the application area of Mobile Adhoc Networks (MANETs) significantly growing particularly in military and disaster management. Considering the sensitivity of the application areas, security in terms of detection of Denial of Service (DoS) and intrusion has become prime concern in research and development in the area. The security systems suggested in the past has state recognition problem where the system is not able to accurately identify the actual state of the network nodes due to the absence of clear definition of states of the nodes. In this context, this paper proposes a framework based on Finite State Machine (FSM) for denial of service and intrusion detection in MANETs. In particular, an Interruption Detection system for Adhoc On-demand Distance Vector (ID-AODV) protocol is presented based on finite state machine. The packet dropping and sequence number attacks are closely investigated and detection systems for both types of attacks are designed. The major functional modules of ID-AODV includes network monitoring system, finite state machine and attack detection model. Simulations are carried out in network simulator NS-2 to evaluate the performance of the proposed framework. A comparative evaluation of the performance is also performed with the state-of-the-art techniques: RIDAN and AODV. The performance evaluations attest the benefits of proposed framework in terms of providing better security for denial of service and intrusion detection attacks. PMID:27285146

Comparative Evaluation of a Four-Implant-Supported Polyetherketoneketone Framework Prosthesis: A Three-Dimensional Finite Element Analysis Based on Cone Beam Computed Tomography and Computer-Aided Design.

PubMed

Lee, Ki-Sun; Shin, Sang-Wan; Lee, Sang-Pyo; Kim, Jong-Eun; Kim, Jee-Hwan; Lee, Jeong-Yol

The purpose of this pilot study was to evaluate and compare polyetherketoneketone (PEKK) with different framework materials for implant-supported prostheses by means of a three-dimensional finite element analysis (3D-FEA) based on cone beam computed tomography (CBCT) and computer-aided design (CAD) data. A geometric model that consisted of four maxillary implants supporting a prosthesis framework was constructed from CBCT and CAD data of a treated patient. Three different materials (zirconia, titanium, and PEKK) were selected, and their material properties were simulated using FEA software in the generated geometric model. In the PEKK framework (ie, low elastic modulus) group, the stress transferred to the implant and simulated adjacent tissue was reduced when compressive stress was dominant, but increased when tensile stress was dominant. This study suggests that the shock-absorbing effects of a resilient implant-supported framework are limited in some areas and that rigid framework material shows a favorable stress distribution and safety of overall components of the prosthesis.

Effect of Framework in an Implant-Supported Full-Arch Fixed Prosthesis: 3D Finite Element Analysis.

PubMed

Menini, Maria; Pesce, Paolo; Bevilacqua, Marco; Pera, Francesco; Tealdo, Tiziano; Barberis, Fabrizio; Pera, Paolo

2015-01-01

The aim of this study was to analyze through a three-dimensional finite element analysis (3D-FEA) stress distribution on four implants supporting a full-arch implant-supported fixed prosthesis (FFP) using different prosthesis designs. A 3D edentulous maxillary model was created and four implants were virtually placed into the maxilla and splinted, simulating an FFP without framework, with a cast metal framework, and with a carbon fiber framework. An occlusal load of 150 N was applied, stresses were transmitted into peri-implant bone, and prosthodontic components were recorded. 3D-FEA revealed higher stresses on the implants (up to +55.16%), on peri-implant bone (up to +56.93%), and in the prosthesis (up to +70.71%) when the full-acrylic prosthesis was simulated. The prosthesis with a carbon fiber framework showed an intermediate behavior between that of the other two configurations. This study suggests that the presence of a rigid framework in full-arch fixed prostheses provides a better load distribution that decreases the maximum values of stress at the levels of implants, prosthesis, and maxillary bone.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

Charged hadrons in local finite-volume QED+QCD with C⋆ boundary conditions

NASA Astrophysics Data System (ADS)

Lucini, B.; Patella, A.; Ramos, A.; Tantalo, N.

2016-02-01

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C⋆ boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C⋆ boundary conditions. In particular we learn that a certain class of electrically-charged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

Component mode synthesis and large deflection vibration of complex structures. Volume 3: Multiple-mode nonlinear free and forced vibrations of beams using finite element method

NASA Technical Reports Server (NTRS)

Mei, Chuh; Shen, Mo-How

1987-01-01

Multiple-mode nonlinear forced vibration of a beam was analyzed by the finite element method. Inplane (longitudinal) displacement and inertia (IDI) are considered in the formulation. By combining the finite element method and nonlinear theory, more realistic models of structural response are obtained more easily and faster.

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.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

Pozsgay, B.; Szécsényi, I. M.; Takács, G.

2015-04-01

We present a conjecture for the exact expression of finite volume expectation values in excited states in integrable quantum field theories, which is an extension of an earlier conjecture to the case of general diagonal factorized scattering with bound states and a nontrivial bootstrap structure. The conjectured expression is a spectral expansion which uses the exact form factors and the excited state thermodynamic Bethe Ansatz as building blocks. The conjecture is proven for the case of the trace of the energy-moment tensor. Concerning its validity for more general operators, we provide numerical evidence using the truncated conformal space approach. It is found that the expansion fails to be well-defined for small values of the volume in cases when the singularity structure of the TBA equations undergoes a non-trivial rearrangement under some critical value of the volume. Despite these shortcomings, the conjectured expression is expected to be valid for all volumes for most of the excited states, and as an expansion above the critical volume for the rest.

Hurricane Forecasting with the High-resolution NASA Finite-volume General Circulation Model

NASA Technical Reports Server (NTRS)

Atlas, R.; Reale, O.; Shen, B.-W.; Lin, S.-J.; Chern, J.-D.; Putman, W.; Lee, T.; Yeh, K.-S.; Bosilovich, M.; Radakovich, J.

2004-01-01

A high-resolution finite-volume General Circulation Model (fvGCM), resulting from a development effort of more than ten years, is now being run operationally at the NASA Goddard Space Flight Center and Ames Research Center. The model is based on a finite-volume dynamical core with terrain-following Lagrangian control-volume discretization and performs efficiently on massive parallel architectures. The computational efficiency allows simulations at a resolution of a quarter of a degree, which is double the resolution currently adopted by most global models in operational weather centers. Such fine global resolution brings us closer to overcoming a fundamental barrier in global atmospheric modeling for both weather and climate, because tropical cyclones and even tropical convective clusters can be more realistically represented. In this work, preliminary results of the fvGCM are shown. Fifteen simulations of four Atlantic tropical cyclones in 2002 and 2004 are chosen because of strong and varied difficulties presented to numerical weather forecasting. It is shown that the fvGCM, run at the resolution of a quarter of a degree, can produce very good forecasts of these tropical systems, adequately resolving problems like erratic track, abrupt recurvature, intense extratropical transition, multiple landfall and reintensification, and interaction among vortices.

Nucleon resonance structure in the finite volume of lattice QCD

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

Wu, Jia -Jun; Kamano, H.; Lee, T. -S. H.

An approach for relating the nucleon resonances extracted from πN reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of πN reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance can be related to the probability P N*(E) of finding the bare state, N*, in the πN scattering states in infinite volume. We further demonstrate that the probability P V N*(E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P N*(E) as the volumemore » increases. Our findings suggest that the comparison of P N*(E) and P V N*(E) can be used to examine whether the nucleon resonances extracted from the πN reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P V N*(E) directly from lattice QCD. Furthermore, the practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.« less

Nucleon resonance structure in the finite volume of lattice QCD

DOE PAGES

Wu, Jia -Jun; Kamano, H.; Lee, T. -S. H.; ...

2017-06-19

An approach for relating the nucleon resonances extracted from πN reaction data to lattice QCD calculations has been developed by using the finite-volume Hamiltonian method. Within models of πN reactions, bare states are introduced to parametrize the intrinsic excitations of the nucleon. We show that the resonance can be related to the probability P N*(E) of finding the bare state, N*, in the πN scattering states in infinite volume. We further demonstrate that the probability P V N*(E) of finding the same bare states in the eigenfunctions of the underlying Hamiltonian in finite volume approaches P N*(E) as the volumemore » increases. Our findings suggest that the comparison of P N*(E) and P V N*(E) can be used to examine whether the nucleon resonances extracted from the πN reaction data within the dynamical models are consistent with lattice QCD calculation. We also discuss the measurement of P V N*(E) directly from lattice QCD. Furthermore, the practical differences between our approach and the approach using the Lüscher formalism to relate LQCD calculations to the nucleon resonance poles embedded in the data are also discussed.« less

CFD analysis of a twin scroll radial turbine

NASA Astrophysics Data System (ADS)

Fürst, Jiří; Žák, Zdenĕk

2018-06-01

The contribution deals with the application of coupled implicit solver for compressible flows to CFD analysis of a twin scroll radial turbine. The solver is based on the finite volume method, convective terms are approximated using AUSM+up scheme, viscous terms use central approximation and the time evolution is achieved with lower-upper symmetric Gauss-Seidel (LU-SGS) method. The solver allows steady simulation with the so called frozen rotor approach as well as the fully unsteady solution. Both approaches are at first validated for the case of ERCOFTAC pump [1]. Then the CFD analysis of the flow through a twin scroll radial turbine and the predictions of the efficiency and turbine power is performed and the results are compared to experimental data obtained in the framework of Josef Božek - Competence Centre for Automotive Industry.

Anharmonic effects in the quantum cluster equilibrium method

NASA Astrophysics Data System (ADS)

von Domaros, Michael; Perlt, Eva

2017-03-01

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

The Representation of Tropical Cyclones Within the Global William Putman Non-Hydrostatic Goddard Earth Observing System Model (GEOS-5) at Cloud-Permitting Resolutions

NASA Technical Reports Server (NTRS)

Putman, William M.

2010-01-01

The Goddard Earth Observing System Model (GEOS-S), an earth system model developed in the NASA Global Modeling and Assimilation Office (GMAO), has integrated the non-hydrostatic finite-volume dynamical core on the cubed-sphere grid. The extension to a non-hydrostatic dynamical framework and the quasi-uniform cubed-sphere geometry permits the efficient exploration of global weather and climate modeling at cloud permitting resolutions of 10- to 4-km on today's high performance computing platforms. We have explored a series of incremental increases in global resolution with GEOS-S from irs standard 72-level 27-km resolution (approx.5.5 million cells covering the globe from the surface to 0.1 hPa) down to 3.5-km (approx. 3.6 billion cells).

Multi-grid finite element method used for enhancing the reconstruction accuracy in Cerenkov luminescence tomography

NASA Astrophysics Data System (ADS)

Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie

2017-03-01

Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.

Optimal performance of generalized heat engines with finite-size baths of arbitrary multiple conserved quantities beyond independent-and-identical-distribution scaling

NASA Astrophysics Data System (ADS)

Ito, Kosuke; Hayashi, Masahito

2018-01-01

In quantum thermodynamics, effects of finiteness of the baths have been less considered. In particular, there is no general theory which focuses on finiteness of the baths of multiple conserved quantities. Then, we investigate how the optimal performance of generalized heat engines with multiple conserved quantities alters in response to the size of the baths. In the context of general theories of quantum thermodynamics, the size of the baths has been given in terms of the number of identical copies of a system, which does not cover even such a natural scaling as the volume. In consideration of the asymptotic extensivity, we deal with a generic scaling of the baths to naturally include the volume scaling. Based on it, we derive a bound for the performance of generalized heat engines reflecting finite-size effects of the baths, which we call fine-grained generalized Carnot bound. We also construct a protocol to achieve the optimal performance of the engine given by this bound. Finally, applying the obtained general theory, we deal with simple examples of generalized heat engines. As for an example of non-independent-and-identical-distribution scaling and multiple conserved quantities, we investigate a heat engine with two baths composed of an ideal gas exchanging particles, where the volume scaling is applied. The result implies that the mass of the particle explicitly affects the performance of this engine with finite-size baths.

On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1987-01-01

This Annual Status Report presents the results of work performed during the third year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes that permit more accurate and efficient three-dimensional analysis of selected hot section components, i.e., combustor liners, turbine blades, and turbine vanes. The computer codes embody a progression of mathematical models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. This report is presented in two volumes. Volume 1 describes effort performed under Task 4B, Special Finite Element Special Function Models, while Volume 2 concentrates on Task 4C, Advanced Special Functions Models.

Effects of Pore Distributions on Ductility of Thin-Walled High Pressure Die-Cast Magnesium

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

Choi, Kyoo Sil; Li, Dongsheng; Sun, Xin

2013-06-01

In this paper, a microstructure-based three-dimensional (3D) finite element modeling method is adopted to investigate the effects of porosity in thin-walled high pressure die-cast (HPDC) Magnesium alloys on their ductility. For this purpose, the cross-sections of AM60 casting samples are first examined using optical microscope and X-ray tomography to obtain the general information on the pore distribution features. The experimentally observed pore distribution features are then used to generate a series of synthetic microstructure-based 3D finite element models with different pore volume fractions and pore distribution features. Shear and ductile damage models are adopted in the finite element analyses tomore » induce the fracture by element removal, leading to the prediction of ductility. The results in this study show that the ductility monotonically decreases as the pore volume fraction increases and that the effect of ‘skin region’ on the ductility is noticeable under the condition of same local pore volume fraction in the center region of the sample and its existence can be beneficial for the improvement of ductility. The further synthetic microstructure-based 3D finite element analyses are planned to investigate the effects of pore size and pore size distribution.« less

Computing Reliabilities Of Ceramic Components Subject To Fracture

NASA Technical Reports Server (NTRS)

Nemeth, N. N.; Gyekenyesi, J. P.; Manderscheid, J. M.

1992-01-01

CARES calculates fast-fracture reliability or failure probability of macroscopically isotropic ceramic components. Program uses results from commercial structural-analysis program (MSC/NASTRAN or ANSYS) to evaluate reliability of component in presence of inherent surface- and/or volume-type flaws. Computes measure of reliability by use of finite-element mathematical model applicable to multiple materials in sense model made function of statistical characterizations of many ceramic materials. Reliability analysis uses element stress, temperature, area, and volume outputs, obtained from two-dimensional shell and three-dimensional solid isoparametric or axisymmetric finite elements. Written in FORTRAN 77.

An integrated algorithm for hypersonic fluid-thermal-structural numerical simulation

NASA Astrophysics Data System (ADS)

Li, Jia-Wei; Wang, Jiang-Feng

2018-05-01

In this paper, a fluid-structural-thermal integrated method is presented based on finite volume method. A unified integral equations system is developed as the control equations for physical process of aero-heating and structural heat transfer. The whole physical field is discretized by using an up-wind finite volume method. To demonstrate its capability, the numerical simulation of Mach 6.47 flow over stainless steel cylinder shows a good agreement with measured values, and this method dynamically simulates the objective physical processes. Thus, the integrated algorithm proves to be efficient and reliable.

Finite-volume effects and the electromagnetic contributions to kaon and pion masses

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

Basak, Subhasish; Bazavov, Alexei; Bernard, Claude

2014-09-25

We report on the MILC Collaboration calculation of electromagnetic effects on light pseudoscalar mesons. The simulations employ asqtad staggered dynamical quarks in QCD plus quenched photons, with lattice spacings varying from 0.12 to 0.06 fm. Finite volume corrections for the MILC realization of lattice electrodynamics have been calculated in chiral perturbation theory and applied to the lattice data. These corrections differ from those calculated by Hayakawa and Uno because our treatment of zero modes differs from theirs. Updated results for the corrections to "Dashen's theorem" are presented.

FLUX-CORRECTED TRANSPORT TECHNIQUE FOR OPEN CHANNEL FLOW. (R825200)

EPA Science Inventory

In modeling flow in open channels, the traditional finite difference/finite volume schemes become inefficient and warrant special numerical treatment in the presence of shocks and discontinuities. The numerical oscillations that arise by making use of a second- and higher-order s...

Definition of NASTRAN sets by use of parametric geometry

NASA Technical Reports Server (NTRS)

Baughn, Terry V.; Tiv, Mehran

1989-01-01

Many finite element preprocessors describe finite element model geometry with points, lines, surfaces and volumes. One method for describing these basic geometric entities is by use of parametric cubics which are useful for representing complex shapes. The lines, surfaces and volumes may be discretized for follow on finite element analysis. The ability to limit or selectively recover results from the finite element model is extremely important to the analyst. Equally important is the ability to easily apply boundary conditions. Although graphical preprocessors have made these tasks easier, model complexity may not lend itself to easily identify a group of grid points desired for data recovery or application of constraints. A methodology is presented which makes use of the assignment of grid point locations in parametric coordinates. The parametric coordinates provide a convenient ordering of the grid point locations and a method for retrieving the grid point ID's from the parent geometry. The selected grid points may then be used for the generation of the appropriate set and constraint cards.

Application of numerical methods to heat transfer and thermal stress analysis of aerospace vehicles

NASA Technical Reports Server (NTRS)

Wieting, A. R.

1979-01-01

The paper describes a thermal-structural design analysis study of a fuel-injection strut for a hydrogen-cooled scramjet engine for a supersonic transport, utilizing finite-element methodology. Applications of finite-element and finite-difference codes to the thermal-structural design-analysis of space transports and structures are discussed. The interaction between the thermal and structural analyses has led to development of finite-element thermal methodology to improve the integration between these two disciplines. The integrated thermal-structural analysis capability developed within the framework of a computer code is outlined.

The Effect of Fiber Strength Stochastics and Local Fiber Volume Fraction on Multiscale Progressive Failure of Composites

NASA Technical Reports Server (NTRS)

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

2013-01-01

Continuous fiber unidirectional polymer matrix composites (PMCs) can exhibit significant local variations in fiber volume fraction as a result of processing conditions that can lead to further local differences in material properties and failure behavior. In this work, the coupled effects of both local variations in fiber volume fraction and the empirically-based statistical distribution of fiber strengths on the predicted longitudinal modulus and local tensile strength of a unidirectional AS4 carbon fiber/ Hercules 3502 epoxy composite were investigated using the special purpose NASA Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC); local effective composite properties were obtained by homogenizing the material behavior over repeating units cells (RUCs). The predicted effective longitudinal modulus was relatively insensitive to small (8%) variations in local fiber volume fraction. The composite tensile strength, however, was highly dependent on the local distribution in fiber strengths. The RUC-averaged constitutive response can be used to characterize lower length scale material behavior within a multiscale analysis framework that couples the NASA code FEAMAC and the ABAQUS finite element solver. Such an approach can be effectively used to analyze the progressive failure of PMC structures whose failure initiates at the RUC level. Consideration of the effect of local variations in constituent properties and morphologies on progressive failure of PMCs is a central aspect of the application of Integrated Computational Materials Engineering (ICME) principles for composite materials.

Three-Dimensional Imaging and Numerical Reconstruction of Graphite/Epoxy Composite Microstructure Based on Ultra-High Resolution X-Ray Computed Tomography

NASA Technical Reports Server (NTRS)

Czabaj, M. W.; Riccio, M. L.; Whitacre, W. W.

2014-01-01

A combined experimental and computational study aimed at high-resolution 3D imaging, visualization, and numerical reconstruction of fiber-reinforced polymer microstructures at the fiber length scale is presented. To this end, a sample of graphite/epoxy composite was imaged at sub-micron resolution using a 3D X-ray computed tomography microscope. Next, a novel segmentation algorithm was developed, based on concepts adopted from computer vision and multi-target tracking, to detect and estimate, with high accuracy, the position of individual fibers in a volume of the imaged composite. In the current implementation, the segmentation algorithm was based on Global Nearest Neighbor data-association architecture, a Kalman filter estimator, and several novel algorithms for virtualfiber stitching, smoothing, and overlap removal. The segmentation algorithm was used on a sub-volume of the imaged composite, detecting 508 individual fibers. The segmentation data were qualitatively compared to the tomographic data, demonstrating high accuracy of the numerical reconstruction. Moreover, the data were used to quantify a) the relative distribution of individual-fiber cross sections within the imaged sub-volume, and b) the local fiber misorientation relative to the global fiber axis. Finally, the segmentation data were converted using commercially available finite element (FE) software to generate a detailed FE mesh of the composite volume. The methodology described herein demonstrates the feasibility of realizing an FE-based, virtual-testing framework for graphite/fiber composites at the constituent level.

A mapping from the unitary to doubly stochastic matrices and symbols on a finite set

NASA Astrophysics Data System (ADS)

Karabegov, Alexander V.

2008-11-01

We prove that the mapping from the unitary to doubly stochastic matrices that maps a unitary matrix (ukl) to the doubly stochastic matrix (|ukl|2) is a submersion at a generic unitary matrix. The proof uses the framework of operator symbols on a finite set.

The Global Modeling and Assimilation Office (GMAO) 4d-Var and its Adjoint-based Tools

NASA Technical Reports Server (NTRS)

Todling, Ricardo; Tremolet, Yannick

2008-01-01

The fifth generation of the Goddard Earth Observing System (GEOS-5) Data Assimilation System (DAS) is a 3d-var system that uses the Grid-point Statistical Interpolation (GSI) system developed in collaboration with NCEP, and a general circulation model developed at Goddard, that includes the finite-volume hydrodynamics of GEOS-4 wrapped in the Earth System Modeling Framework and physical packages tuned to provide a reliable hydrological cycle for the integration of the Modern Era Retrospective-analysis for Research and Applications (MERRA). This MERRA system is essentially complete and the next generation GEOS is under intense development. A prototype next generation system is now complete and has been producing preliminary results. This prototype system replaces the GSI-based Incremental Analysis Update procedure with a GSI-based 4d-var which uses the adjoint of the finite-volume hydrodynamics of GEOS-4 together with a vertical diffusing scheme for simplified physics. As part of this development we have kept the GEOS-5 IAU procedure as an option and have added the capability to experiment with a First Guess at the Appropriate Time (FGAT) procedure, thus allowing for at least three modes of running the data assimilation experiments. The prototype system is a large extension of GEOS-5 as it also includes various adjoint-based tools, namely, a forecast sensitivity tool, a singular vector tool, and an observation impact tool, that combines the model sensitivity tool with a GSI-based adjoint tool. These features bring the global data assimilation effort at Goddard up to date with technologies used in data assimilation systems at major meteorological centers elsewhere. Various aspects of the next generation GEOS will be discussed during the presentation at the Workshop, and preliminary results will illustrate the discussion.

Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

DOE PAGES

Norman, Matthew R.

2014-11-24

New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existingmore » HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.« less

Application of an unstructured 3D finite volume numerical model to flows and salinity dynamics in the San Francisco Bay-Delta

USGS Publications Warehouse

Martyr-Koller, R.C.; Kernkamp, H.W.J.; Van Dam, Anne A.; Mick van der Wegen,; Lucas, Lisa; Knowles, N.; Jaffe, B.; Fregoso, T.A.

2017-01-01

A linked modeling approach has been undertaken to understand the impacts of climate and infrastructure on aquatic ecology and water quality in the San Francisco Bay-Delta region. The Delft3D Flexible Mesh modeling suite is used in this effort for its 3D hydrodynamics, salinity, temperature and sediment dynamics, phytoplankton and water-quality coupling infrastructure, and linkage to a habitat suitability model. The hydrodynamic model component of the suite is D-Flow FM, a new 3D unstructured finite-volume model based on the Delft3D model. In this paper, D-Flow FM is applied to the San Francisco Bay-Delta to investigate tidal, seasonal and annual dynamics of water levels, river flows and salinity under historical environmental and infrastructural conditions. The model is driven by historical winds, tides, ocean salinity, and river flows, and includes federal, state, and local freshwater withdrawals, and regional gate and barrier operations. The model is calibrated over a 9-month period, and subsequently validated for water levels, flows, and 3D salinity dynamics over a 2 year period.Model performance was quantified using several model assessment metrics and visualized through target diagrams. These metrics indicate that the model accurately estimated water levels, flows, and salinity over wide-ranging tidal and fluvial conditions, and the model can be used to investigate detailed circulation and salinity patterns throughout the Bay-Delta. The hydrodynamics produced through this effort will be used to drive affiliated sediment, phytoplankton, and contaminant hindcast efforts and habitat suitability assessments for fish and bivalves. The modeling framework applied here will serve as a baseline to ultimately shed light on potential ecosystem change over the current century.

Application of an unstructured 3D finite volume numerical model to flows and salinity dynamics in the San Francisco Bay-Delta

NASA Astrophysics Data System (ADS)

Martyr-Koller, R. C.; Kernkamp, H. W. J.; van Dam, A.; van der Wegen, M.; Lucas, L. V.; Knowles, N.; Jaffe, B.; Fregoso, T. A.

2017-06-01

A linked modeling approach has been undertaken to understand the impacts of climate and infrastructure on aquatic ecology and water quality in the San Francisco Bay-Delta region. The Delft3D Flexible Mesh modeling suite is used in this effort for its 3D hydrodynamics, salinity, temperature and sediment dynamics, phytoplankton and water-quality coupling infrastructure, and linkage to a habitat suitability model. The hydrodynamic model component of the suite is D-Flow FM, a new 3D unstructured finite-volume model based on the Delft3D model. In this paper, D-Flow FM is applied to the San Francisco Bay-Delta to investigate tidal, seasonal and annual dynamics of water levels, river flows and salinity under historical environmental and infrastructural conditions. The model is driven by historical winds, tides, ocean salinity, and river flows, and includes federal, state, and local freshwater withdrawals, and regional gate and barrier operations. The model is calibrated over a 9-month period, and subsequently validated for water levels, flows, and 3D salinity dynamics over a 2 year period. Model performance was quantified using several model assessment metrics and visualized through target diagrams. These metrics indicate that the model accurately estimated water levels, flows, and salinity over wide-ranging tidal and fluvial conditions, and the model can be used to investigate detailed circulation and salinity patterns throughout the Bay-Delta. The hydrodynamics produced through this effort will be used to drive affiliated sediment, phytoplankton, and contaminant hindcast efforts and habitat suitability assessments for fish and bivalves. The modeling framework applied here will serve as a baseline to ultimately shed light on potential ecosystem change over the current century.

The Finite-Surface Method for incompressible flow: a step beyond staggered grid

NASA Astrophysics Data System (ADS)

Hokpunna, Arpiruk; Misaka, Takashi; Obayashi, Shigeru

2017-11-01

We present a newly developed higher-order finite surface method for the incompressible Navier-Stokes equations (NSE). This method defines the velocities as a surface-averaged value on the surfaces of the pressure cells. Consequently, the mass conservation on the pressure cells becomes an exact equation. The only things left to approximate is the momentum equation and the pressure at the new time step. At certain conditions, the exact mass conservation enables the explicit n-th order accurate NSE solver to be used with the pressure treatment that is two or four order less accurate without loosing the apparent convergence rate. This feature was not possible with finite volume of finite difference methods. We use Fourier analysis with a model spectrum to determine the condition and found that the range covers standard boundary layer flows. The formal convergence and the performance of the proposed scheme is compared with a sixth-order finite volume method. Finally, the accuracy and performance of the method is evaluated in turbulent channel flows. This work is partially funded by a research colloaboration from IFS, Tohoku university and ASEAN+3 funding scheme from CMUIC, Chiang Mai University.

Study on Edge Thickening Flow Forming Using the Finite Elements Analysis

NASA Astrophysics Data System (ADS)

Kim, Young Jin; Park, Jin Sung; Cho, Chongdu

2011-08-01

This study is to examine the forming features of flow stress property and the incremental forming method with increasing the thickness of material. Recently, the optimized forming method is widely studied through the finite element analysis to optimize forming process conditions in many different forming fields. The optimal forming method should be adopted to meet geometric requirements as the reduction in volume per unit length of material such as forging, rolling, spinning etc. However conventional studies have not dealt with issue regarding volume per unit length. For the study we use the finite element method and model a gear part of an automotive engine flywheel as the study model, which is a weld assembly of a plate and a gear with respective different thickness. In simulation of the present study, a optimized forming condition for gear machining, considering the thickness of the outer edge of flywheel is studied using the finite elements analysis for the increasing thickness of the forming method. It is concluded from the study that forming method to increase the thickness per unit length for gear machining is reasonable using the finite elements analysis and forming test.

The Role of Multiphysics Simulation in Multidisciplinary Analysis

NASA Technical Reports Server (NTRS)

Rifai, Steven M.; Ferencz, Robert M.; Wang, Wen-Ping; Spyropoulos, Evangelos T.; Lawrence, Charles; Melis, Matthew E.

1998-01-01

This article describes the applications of the Spectrum(Tm) Solver in Multidisciplinary Analysis (MDA). Spectrum, a multiphysics simulation software based on the finite element method, addresses compressible and incompressible fluid flow, structural, and thermal modeling as well as the interaction between these disciplines. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena. Interaction constraints are enforced in a fully-coupled manner using the augmented-Lagrangian method. Within the multiphysics framework, the finite element treatment of fluids is based on Galerkin-Least-Squares (GLS) method with discontinuity capturing operators. The arbitrary-Lagrangian-Eulerian method is utilized to account for deformable fluid domains. The finite element treatment of solids and structures is based on the Hu-Washizu variational principle. The multiphysics architecture lends itself naturally to high-performance parallel computing. Aeroelastic, propulsion, thermal management and manufacturing applications are presented.

A discrete model to study reaction-diffusion-mechanics systems.

PubMed

Weise, Louis D; Nash, Martyn P; Panfilov, Alexander V

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects.

A Discrete Model to Study Reaction-Diffusion-Mechanics Systems

PubMed Central

Weise, Louis D.; Nash, Martyn P.; Panfilov, Alexander V.

2011-01-01

This article introduces a discrete reaction-diffusion-mechanics (dRDM) model to study the effects of deformation on reaction-diffusion (RD) processes. The dRDM framework employs a FitzHugh-Nagumo type RD model coupled to a mass-lattice model, that undergoes finite deformations. The dRDM model describes a material whose elastic properties are described by a generalized Hooke's law for finite deformations (Seth material). Numerically, the dRDM approach combines a finite difference approach for the RD equations with a Verlet integration scheme for the equations of the mass-lattice system. Using this framework results were reproduced on self-organized pacemaking activity that have been previously found with a continuous RD mechanics model. Mechanisms that determine the period of pacemakers and its dependency on the medium size are identified. Finally it is shown how the drift direction of pacemakers in RDM systems is related to the spatial distribution of deformation and curvature effects. PMID:21804911

Self-consistent field theory simulations of polymers on arbitrary domains

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

Ouaknin, Gaddiel, E-mail: gaddielouaknin@umail.ucsb.edu; Laachi, Nabil; Delaney, Kris

2016-12-15

We introduce a framework for simulating the mesoscale self-assembly of block copolymers in arbitrary confined geometries subject to Neumann boundary conditions. We employ a hybrid finite difference/volume approach to discretize the mean-field equations on an irregular domain represented implicitly by a level-set function. The numerical treatment of the Neumann boundary conditions is sharp, i.e. it avoids an artificial smearing in the irregular domain boundary. This strategy enables the study of self-assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface. In addition, we employ adaptive grids encoded with Quad-/Oc-trees in parallel to automatically refinemore » the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain. This approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement. Finally, in the case of regular periodic domains, where pseudo-spectral approaches are superior to finite differences in terms of CPU time and accuracy, we use the adaptive strategy to store chain propagators, reducing the memory footprint without loss of accuracy in computed physical observables.« less

Probabilistic homogenization of random composite with ellipsoidal particle reinforcement by the iterative stochastic finite element method

NASA Astrophysics Data System (ADS)

Sokołowski, Damian; Kamiński, Marcin

2018-01-01

This study proposes a framework for determination of basic probabilistic characteristics of the orthotropic homogenized elastic properties of the periodic composite reinforced with ellipsoidal particles and a high stiffness contrast between the reinforcement and the matrix. Homogenization problem, solved by the Iterative Stochastic Finite Element Method (ISFEM) is implemented according to the stochastic perturbation, Monte Carlo simulation and semi-analytical techniques with the use of cubic Representative Volume Element (RVE) of this composite containing single particle. The given input Gaussian random variable is Young modulus of the matrix, while 3D homogenization scheme is based on numerical determination of the strain energy of the RVE under uniform unit stretches carried out in the FEM system ABAQUS. The entire series of several deterministic solutions with varying Young modulus of the matrix serves for the Weighted Least Squares Method (WLSM) recovery of polynomial response functions finally used in stochastic Taylor expansions inherent for the ISFEM. A numerical example consists of the High Density Polyurethane (HDPU) reinforced with the Carbon Black particle. It is numerically investigated (1) if the resulting homogenized characteristics are also Gaussian and (2) how the uncertainty in matrix Young modulus affects the effective stiffness tensor components and their PDF (Probability Density Function).

Fluctuating hydrodynamics for multiscale modeling and simulation: energy and heat transfer in molecular fluids.

PubMed

Shang, Barry Z; Voulgarakis, Nikolaos K; Chu, Jhih-Wei

2012-07-28

This work illustrates that fluctuating hydrodynamics (FHD) simulations can be used to capture the thermodynamic and hydrodynamic responses of molecular fluids at the nanoscale, including those associated with energy and heat transfer. Using all-atom molecular dynamics (MD) trajectories as the reference data, the atomistic coordinates of each snapshot are mapped onto mass, momentum, and energy density fields on Eulerian grids to generate a corresponding field trajectory. The molecular length-scale associated with finite molecule size is explicitly imposed during this coarse-graining by requiring that the variances of density fields scale inversely with the grid volume. From the fluctuations of field variables, the response functions and transport coefficients encoded in the all-atom MD trajectory are computed. By using the extracted fluid properties in FHD simulations, we show that the fluctuations and relaxation of hydrodynamic fields quantitatively match with those observed in the reference all-atom MD trajectory, hence establishing compatibility between the atomistic and field representations. We also show that inclusion of energy transfer in the FHD equations can more accurately capture the thermodynamic and hydrodynamic responses of molecular fluids. The results indicate that the proposed MD-to-FHD mapping with explicit consideration of finite molecule size provides a robust framework for coarse-graining the solution phase of complex molecular systems.

A finite difference method for off-fault plasticity throughout the earthquake cycle

NASA Astrophysics Data System (ADS)

Erickson, Brittany A.; Dunham, Eric M.; Khosravifar, Arash

2017-12-01

We have developed an efficient computational framework for simulating multiple earthquake cycles with off-fault plasticity. The method is developed for the classical antiplane problem of a vertical strike-slip fault governed by rate-and-state friction, with inertial effects captured through the radiation-damping approximation. Both rate-independent plasticity and viscoplasticity are considered, where stresses are constrained by a Drucker-Prager yield condition. The off-fault volume is discretized using finite differences and tectonic loading is imposed by displacing the remote side boundaries at a constant rate. Time-stepping combines an adaptive Runge-Kutta method with an incremental solution process which makes use of an elastoplastic tangent stiffness tensor and the return-mapping algorithm. Solutions are verified by convergence tests and comparison to a finite element solution. We quantify how viscosity, isotropic hardening, and cohesion affect the magnitude and off-fault extent of plastic strain that develops over many ruptures. If hardening is included, plastic strain saturates after the first event and the response during subsequent ruptures is effectively elastic. For viscoplasticity without hardening, however, successive ruptures continue to generate additional plastic strain. In all cases, coseismic slip in the shallow sub-surface is diminished compared to slip accumulated at depth during interseismic loading. The evolution of this slip deficit with each subsequent event, however, is dictated by the plasticity model. Integration of the off-fault plastic strain from the viscoplastic model reveals that a significant amount of tectonic offset is accommodated by inelastic deformation ( ∼ 0.1 m per rupture, or ∼ 10% of the tectonic deformation budget).

Application of variational principles and adjoint integrating factors for constructing numerical GFD models

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Tsvetova, Elena; Penenko, Alexey

2015-04-01

The proposed method is considered on an example of hydrothermodynamics and atmospheric chemistry models [1,2]. In the development of the existing methods for constructing numerical schemes possessing the properties of total approximation for operators of multiscale process models, we have developed a new variational technique, which uses the concept of adjoint integrating factors. The technique is as follows. First, a basic functional of the variational principle (the integral identity that unites the model equations, initial and boundary conditions) is transformed using Lagrange's identity and the second Green's formula. As a result, the action of the operators of main problem in the space of state functions is transferred to the adjoint operators defined in the space of sufficiently smooth adjoint functions. By the choice of adjoint functions the order of the derivatives becomes lower by one than those in the original equations. We obtain a set of new balance relationships that take into account the sources and boundary conditions. Next, we introduce the decomposition of the model domain into a set of finite volumes. For multi-dimensional non-stationary problems, this technique is applied in the framework of the variational principle and schemes of decomposition and splitting on the set of physical processes for each coordinate directions successively at each time step. For each direction within the finite volume, the analytical solutions of one-dimensional homogeneous adjoint equations are constructed. In this case, the solutions of adjoint equations serve as integrating factors. The results are the hybrid discrete-analytical schemes. They have the properties of stability, approximation and unconditional monotony for convection-diffusion operators. These schemes are discrete in time and analytic in the spatial variables. They are exact in case of piecewise-constant coefficients within the finite volume and along the coordinate lines of the grid area in each direction on a time step. In each direction, they have tridiagonal structure. They are solved by the sweep method. An important advantage of the discrete-analytical schemes is that the values of derivatives at the boundaries of finite volume are calculated together with the values of the unknown functions. This technique is particularly attractive for problems with dominant convection, as it does not require artificial monotonization and limiters. The same idea of integrating factors is applied in temporal dimension to the stiff systems of equations describing chemical transformation models [2]. The proposed method is applicable for the problems involving convection-diffusion-reaction operators. The work has been partially supported by the Presidium of RAS under Program 43, and by the RFBR grants 14-01-00125 and 14-01-31482. References: 1. V.V. Penenko, E.A. Tsvetova, A.V. Penenko. Variational approach and Euler's integrating factors for environmental studies// Computers and Mathematics with Applications, (2014) V.67, Issue 12, P. 2240-2256. 2. V.V.Penenko, E.A.Tsvetova. Variational methods of constructing monotone approximations for atmospheric chemistry models // Numerical analysis and applications, 2013, V. 6, Issue 3, pp 210-220.

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

DOE PAGES

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

2017-04-18

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

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

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

Data-driven reduced order models for effective yield strength and partitioning of strain in multiphase materials

NASA Astrophysics Data System (ADS)

Latypov, Marat I.; Kalidindi, Surya R.

2017-10-01

There is a critical need for the development and verification of practically useful multiscale modeling strategies for simulating the mechanical response of multiphase metallic materials with heterogeneous microstructures. In this contribution, we present data-driven reduced order models for effective yield strength and strain partitioning in such microstructures. These models are built employing the recently developed framework of Materials Knowledge Systems that employ 2-point spatial correlations (or 2-point statistics) for the quantification of the heterostructures and principal component analyses for their low-dimensional representation. The models are calibrated to a large collection of finite element (FE) results obtained for a diverse range of microstructures with various sizes, shapes, and volume fractions of the phases. The performance of the models is evaluated by comparing the predictions of yield strength and strain partitioning in two-phase materials with the corresponding predictions from a classical self-consistent model as well as results of full-field FE simulations. The reduced-order models developed in this work show an excellent combination of accuracy and computational efficiency, and therefore present an important advance towards computationally efficient microstructure-sensitive multiscale modeling frameworks.

Thermalization dynamics in a quenched many-body state

NASA Astrophysics Data System (ADS)

Kaufman, Adam; Preiss, Philipp; Tai, Eric; Lukin, Alex; Rispoli, Matthew; Schittko, Robert; Greiner, Markus

2016-05-01

Quantum and classical many-body systems appear to have disparate behavior due to the different mechanisms that govern their evolution. The dynamics of a classical many-body system equilibrate to maximally entropic states and quickly re-thermalize when perturbed. The assumptions of ergodicity and unbiased configurations lead to a successful framework of describing classical systems by a sampling of thermal ensembles that are blind to the system's microscopic details. By contrast, an isolated quantum many-body system is governed by unitary evolution: the system retains memory of past dynamics and constant global entropy. However, even with differing characteristics, the long-term behavior for local observables in quenched, non-integrable quantum systems are often well described by the same thermal framework. We explore the onset of this convergence in a many-body system of bosonic atoms in an optical lattice. Our system's finite size allows us to verify full state purity and measure local observables. We observe rapid growth and saturation of the entanglement entropy with constant global purity. The combination of global purity and thermalized local observables agree with the Eigenstate Thermalization Hypothesis in the presence of a near-volume law in the entanglement entropy.

A numerical multi-scale model to predict macroscopic material anisotropy of multi-phase steels from crystal plasticity material definitions

NASA Astrophysics Data System (ADS)

Ravi, Sathish Kumar; Gawad, Jerzy; Seefeldt, Marc; Van Bael, Albert; Roose, Dirk

2017-10-01

A numerical multi-scale model is being developed to predict the anisotropic macroscopic material response of multi-phase steel. The embedded microstructure is given by a meso-scale Representative Volume Element (RVE), which holds the most relevant features like phase distribution, grain orientation, morphology etc., in sufficient detail to describe the multi-phase behavior of the material. A Finite Element (FE) mesh of the RVE is constructed using statistical information from individual phases such as grain size distribution and ODF. The material response of the RVE is obtained for selected loading/deformation modes through numerical FE simulations in Abaqus. For the elasto-plastic response of the individual grains, single crystal plasticity based plastic potential functions are proposed as Abaqus material definitions. The plastic potential functions are derived using the Facet method for individual phases in the microstructure at the level of single grains. The proposed method is a new modeling framework and the results presented in terms of macroscopic flow curves are based on the building blocks of the approach, while the model would eventually facilitate the construction of an anisotropic yield locus of the underlying multi-phase microstructure derived from a crystal plasticity based framework.

Calculation of Derivative Thermodynamic Hydration and Aqueous Partial Molar Properties of Ions Based on Atomistic Simulations.

PubMed

Dahlgren, Björn; Reif, Maria M; Hünenberger, Philippe H; Hansen, Niels

2012-10-09

The raw ionic solvation free energies calculated on the basis of atomistic (explicit-solvent) simulations are extremely sensitive to the boundary conditions and treatment of electrostatic interactions used during these simulations. However, as shown recently [Kastenholz, M. A.; Hünenberger, P. H. J. Chem. Phys.2006, 124, 224501 and Reif, M. M.; Hünenberger, P. H. J. Chem. Phys.2011, 134, 144104], the application of an appropriate correction scheme allows for a conversion of the methodology-dependent raw data into methodology-independent results. In this work, methodology-independent derivative thermodynamic hydration and aqueous partial molar properties are calculated for the Na(+) and Cl(-) ions at P° = 1 bar and T(-) = 298.15 K, based on the SPC water model and on ion-solvent Lennard-Jones interaction coefficients previously reoptimized against experimental hydration free energies. The hydration parameters considered are the hydration free energy and enthalpy. The aqueous partial molar parameters considered are the partial molar entropy, volume, heat capacity, volume-compressibility, and volume-expansivity. Two alternative calculation methods are employed to access these properties. Method I relies on the difference in average volume and energy between two aqueous systems involving the same number of water molecules, either in the absence or in the presence of the ion, along with variations of these differences corresponding to finite pressure or/and temperature changes. Method II relies on the calculation of the hydration free energy of the ion, along with variations of this free energy corresponding to finite pressure or/and temperature changes. Both methods are used considering two distinct variants in the application of the correction scheme. In variant A, the raw values from the simulations are corrected after the application of finite difference in pressure or/and temperature, based on correction terms specifically designed for derivative parameters at P° and T(-). In variant B, these raw values are corrected prior to differentiation, based on corresponding correction terms appropriate for the different simulation pressures P and temperatures T. The results corresponding to the different calculation schemes show that, except for the hydration free energy itself, accurate methodological independence and quantitative agreement with even the most reliable experimental parameters (ion-pair properties) are not yet reached. Nevertheless, approximate internal consistency and qualitative agreement with experimental results can be achieved, but only when an appropriate correction scheme is applied, along with a careful consideration of standard-state issues. In this sense, the main merit of the present study is to set a clear framework for these types of calculations and to point toward directions for future improvements, with the ultimate goal of reaching a consistent and quantitative description of single-ion hydration thermodynamics in molecular dynamics simulations.

Application of Local Discretization Methods in the NASA Finite-Volume General Circulation Model

NASA Technical Reports Server (NTRS)

Yeh, Kao-San; Lin, Shian-Jiann; Rood, Richard B.

2002-01-01

We present the basic ideas of the dynamics system of the finite-volume General Circulation Model developed at NASA Goddard Space Flight Center for climate simulations and other applications in meteorology. The dynamics of this model is designed with emphases on conservative and monotonic transport, where the property of Lagrangian conservation is used to maintain the physical consistency of the computational fluid for long-term simulations. As the model benefits from the noise-free solutions of monotonic finite-volume transport schemes, the property of Lagrangian conservation also partly compensates the accuracy of transport for the diffusion effects due to the treatment of monotonicity. By faithfully maintaining the fundamental laws of physics during the computation, this model is able to achieve sufficient accuracy for the global consistency of climate processes. Because the computing algorithms are based on local memory, this model has the advantage of efficiency in parallel computation with distributed memory. Further research is yet desirable to reduce the diffusion effects of monotonic transport for better accuracy, and to mitigate the limitation due to fast-moving gravity waves for better efficiency.

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.

Multichannel 0 → 2 and 1 → 2 transition amplitudes for arbitrary spin particles in a finite volume

DOE PAGES

Hansen, Maxwell; Briceno, Raul

2015-10-01

We present a model-independent, non-perturbative relation between finite-volume matrix elements and infinite-volumemore » $$\\textbf{0}\\rightarrow\\textbf{2}$$ and $$\\textbf{1}\\rightarrow\\textbf{2}$$ transition amplitudes. Our result accommodates theories in which the final two-particle state is coupled to any number of other two-body channels, with all angular momentum states included. The derivation uses generic, fully relativistic field theory, and is exact up to exponentially suppressed corrections in the lightest particle mass times the box size. This work distinguishes itself from previous studies by accommodating particles with any intrinsic spin. To illustrate the utility of our general result, we discuss how it can be implemented for studies of $$N+\\mathcal{J}~\\rightarrow~(N\\pi,N\\eta,N\\eta',\\Sigma K,\\Lambda K)$$ transitions, where $$\\mathcal{J}$$ is a generic external current. The reduction of rotational symmetry, due to the cubic finite volume, manifests in this example through the mixing of S- and P-waves when the system has nonzero total momentum.« less

Generalized source Finite Volume Method for radiative transfer equation in participating media

NASA Astrophysics Data System (ADS)

Zhang, Biao; Xu, Chuan-Long; Wang, Shi-Min

2017-03-01

Temperature monitoring is very important in a combustion system. In recent years, non-intrusive temperature reconstruction has been explored intensively on the basis of calculating arbitrary directional radiative intensities. In this paper, a new method named Generalized Source Finite Volume Method (GSFVM) was proposed. It was based on radiative transfer equation and Finite Volume Method (FVM). This method can be used to calculate arbitrary directional radiative intensities and is proven to be accurate and efficient. To verify the performance of this method, six test cases of 1D, 2D, and 3D radiative transfer problems were investigated. The numerical results show that the efficiency of this method is close to the radial basis function interpolation method, but the accuracy and stability is higher than that of the interpolation method. The accuracy of the GSFVM is similar to that of the Backward Monte Carlo (BMC) algorithm, while the time required by the GSFVM is much shorter than that of the BMC algorithm. Therefore, the GSFVM can be used in temperature reconstruction and improvement on the accuracy of the FVM.

Hybrid finite volume-finite element model for the numerical analysis of furrow irrigation and fertigation

USDA-ARS?s Scientific Manuscript database

Although slowly abandoned in developed countries, furrow irrigation systems continue to be a dominant irrigation method in developing countries. Numerical models represent powerful tools to assess irrigation and fertigation efficiency. While several models have been proposed in the past, the develop...

Very Large Data Volumes Analysis of Collaborative Systems with Finite Number of States

ERIC Educational Resources Information Center

Ivan, Ion; Ciurea, Cristian; Pavel, Sorin

2010-01-01

The collaborative system with finite number of states is defined. A very large database is structured. Operations on large databases are identified. Repetitive procedures for collaborative systems operations are derived. The efficiency of such procedures is analyzed. (Contains 6 tables, 5 footnotes and 3 figures.)

Algebraic signal processing theory: 2-D spatial hexagonal lattice.

PubMed

Pünschel, Markus; Rötteler, Martin

2007-06-01

We develop the framework for signal processing on a spatial, or undirected, 2-D hexagonal lattice for both an infinite and a finite array of signal samples. This framework includes the proper notions of z-transform, boundary conditions, filtering or convolution, spectrum, frequency response, and Fourier transform. In the finite case, the Fourier transform is called discrete triangle transform. Like the hexagonal lattice, this transform is nonseparable. The derivation of the framework makes it a natural extension of the algebraic signal processing theory that we recently introduced. Namely, we construct the proper signal models, given by polynomial algebras, bottom-up from a suitable definition of hexagonal space shifts using a procedure provided by the algebraic theory. These signal models, in turn, then provide all the basic signal processing concepts. The framework developed in this paper is related to Mersereau's early work on hexagonal lattices in the same way as the discrete cosine and sine transforms are related to the discrete Fourier transform-a fact that will be made rigorous in this paper.

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%.

Finite-volume and partial quenching effects in the magnetic polarizability of the neutron

NASA Astrophysics Data System (ADS)

Hall, J. M. M.; Leinweber, D. B.; Young, R. D.

2014-03-01

There has been much progress in the experimental measurement of the electric and magnetic polarizabilities of the nucleon. Similarly, lattice QCD simulations have recently produced dynamical QCD results for the magnetic polarizability of the neutron approaching the chiral regime. In order to compare the lattice simulations with experiment, calculation of partial quenching and finite-volume effects is required prior to an extrapolation in quark mass to the physical point. These dependencies are described using chiral effective field theory. Corrections to the partial quenching effects associated with the sea-quark-loop electric charges are estimated by modeling corrections to the pion cloud. These are compared to the uncorrected lattice results. In addition, the behavior of the finite-volume corrections as a function of pion mass is explored. Box sizes of approximately 7 fm are required to achieve a result within 5% of the infinite-volume result at the physical pion mass. A variety of extrapolations are shown at different box sizes, providing a benchmark to guide future lattice QCD calculations of the magnetic polarizabilities. A relatively precise value for the physical magnetic polarizability of the neutron is presented, βn=1.93(11)stat(11)sys×10-4 fm3, which is in agreement with current experimental results.

Nonlinear mesomechanics of composites with periodic microstructure

NASA Technical Reports Server (NTRS)

Walker, Kevin P.; Jordan, Eric H.; Freed, Alan D.

1989-01-01

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Quantum Monte Carlo calculations of two neutrons in finite volume

DOE PAGES

Klos, P.; Lynn, J. E.; Tews, I.; ...

2016-11-18

Ab initio calculations provide direct access to the properties of pure neutron systems that are challenging to study experimentally. In addition to their importance for fundamental physics, their properties are required as input for effective field theories of the strong interaction. In this work, we perform auxiliary-field diffusion Monte Carlo calculations of the ground state and first excited state of two neutrons in a finite box, considering a simple contact potential as well as chiral effective field theory interactions. We compare the results against exact diagonalizations and present a detailed analysis of the finite-volume effects, whose understanding is crucial formore » determining observables from the calculated energies. Finally, using the Lüscher formula, we extract the low-energy S-wave scattering parameters from ground- and excited-state energies for different box sizes.« less

A multitasking finite state architecture for computer control of an electric powertrain

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

Burba, J.C.

1984-01-01

Finite state techniques provide a common design language between the control engineer and the computer engineer for event driven computer control systems. They simplify communication and provide a highly maintainable control system understandable by both. This paper describes the development of a control system for an electric vehicle powertrain utilizing finite state concepts. The basics of finite state automata are provided as a framework to discuss a unique multitasking software architecture developed for this application. The architecture employs conventional time-sliced techniques with task scheduling controlled by a finite state machine representation of the control strategy of the powertrain. The complexitiesmore » of excitation variable sampling in this environment are also considered.« less

Global Inventory of Regional and National Qualifications Frameworks. Volume II: National and Regional Cases

ERIC Educational Resources Information Center

UNESCO Institute for Lifelong Learning, 2015

2015-01-01

This second volume of the "Global Inventory of Regional and National Qualifications Frameworks" focuses on national and regional cases of national qualifications frameworks for eighty- six countries from Afghanistan to Uzbekistan and seven regional qualifications frameworks. Each country profile provides a thorough review of the main…

Stress distribution in fixed-partial prosthesis and peri-implant bone tissue with different framework materials and vertical misfit levels: a three-dimensional finite element analysis.

PubMed

Bacchi, Ataís; Consani, Rafael L X; Mesquita, Marcelo F; dos Santos, Mateus B F

2013-09-01

The purpose of this study was to evaluate the influence of superstructure material and vertical misfits on the stresses created in an implant-supported partial prosthesis. A three-dimensional (3-D) finite element model was prepared based on common clinical data. The posterior part of a severely resorbed jaw with two osseointegrated implants at the second premolar and second molar regions was modeled using specific modeling software (SolidWorks 2010). Finite element models were created by importing the solid model into mechanical simulation software (ANSYS Workbench 11). The models were divided into groups according to the prosthesis framework material (type IV gold alloy, silver-palladium alloy, commercially pure titanium, cobalt-chromium alloy, or zirconia) and vertical misfit level (10 µm, 50 µm, and 100 µm) created at one implant-prosthesis interface. The gap of the vertical misfit was set to be closed and the stress values were measured in the framework, porcelain veneer, retention screw, and bone tissue. Stiffer materials led to higher stress concentration in the framework and increased stress values in the retention screw, while in the same circumstances, the porcelain veneer showed lower stress values, and there was no significant difference in stress in the peri-implant bone tissue. A considerable increase in stress concentration was observed in all the structures evaluated within the misfit amplification. The framework material influenced the stress concentration in the prosthetic structures and retention screw, but not that in bone tissue. All the structures were significantly influenced by the increase in the misfit levels.

New numerical approach for the modelling of machining applied to aeronautical structural parts

NASA Astrophysics Data System (ADS)

Rambaud, Pierrick; Mocellin, Katia

2018-05-01

The manufacturing of aluminium alloy structural aerospace parts involves several steps: forming (rolling, forging …etc), heat treatments and machining. Before machining, the manufacturing processes have embedded residual stresses into the workpiece. The final geometry is obtained during this last step, when up to 90% of the raw material volume is removed by machining. During this operation, the mechanical equilibrium of the part is in constant evolution due to the redistribution of the initial stresses. This redistribution is the main cause for workpiece deflections during machining and for distortions - after unclamping. Both may lead to non-conformity of the part regarding the geometrical and dimensional specifications and therefore to rejection of the part or additional conforming steps. In order to improve the machining accuracy and the robustness of the process, the effect of the residual stresses has to be considered for the definition of the machining process plan and even in the geometrical definition of the part. In this paper, the authors present two new numerical approaches concerning the modelling of machining of aeronautical structural parts. The first deals with the use of an immersed volume framework to model the cutting step, improving the robustness and the quality of the resulting mesh compared to the previous version. The second is about the mechanical modelling of the machining problem. The authors thus show that in the framework of rolled aluminium parts the use of a linear elasticity model is functional in the finite element formulation and promising regarding the reduction of computation times.

Coevolutionary dynamics in large, but finite populations

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph

2006-07-01

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

Computational methods for vortex dominated compressible flows

NASA Technical Reports Server (NTRS)

Murman, Earll M.

1987-01-01

The principal objectives were to: understand the mechanisms by which Euler equation computations model leading edge vortex flows; understand the vortical and shock wave structures that may exist for different wing shapes, angles of incidence, and Mach numbers; and compare calculations with experiments in order to ascertain the limitations and advantages of Euler equation models. The initial approach utilized the cell centered finite volume Jameson scheme. The final calculation utilized a cell vertex finite volume method on an unstructured grid. Both methods used Runge-Kutta four stage schemes for integrating the equations. The principal findings are briefly summarized.

A dynamic model of the piezoelectric traveling wave rotary ultrasonic motor stator with the finite volume method.

PubMed

Renteria Marquez, I A; Bolborici, V

2017-05-01

This manuscript presents a method to model in detail the piezoelectric traveling wave rotary ultrasonic motor (PTRUSM) stator response under the action of DC and AC voltages. The stator is modeled with a discrete two dimensional system of equations using the finite volume method (FVM). In order to obtain accurate results, a model of the stator bridge is included into the stator model. The model of the stator under the action of DC voltage is presented first, and the results of the model are compared versus a similar model using the commercial finite element software COMSOL Multiphysics. One can observe that there is a difference of less than 5% between the displacements of the stator using the proposed model and the one with COMSOL Multiphysics. After that, the model of the stator under the action of AC voltages is presented. The time domain analysis shows the generation of the traveling wave in the stator surface. One can use this model to accurately calculate the stator surface velocities, elliptical motion of the stator surface and the amplitude and shape of the stator traveling wave. A system of equations discretized with the finite volume method can easily be transformed into electrical circuits, because of that, FVM may be a better choice to develop a model-based control strategy for the PTRUSM. Copyright © 2017 Elsevier B.V. All rights reserved.

A low-dissipation monotonicity-preserving scheme for turbulent flows in hydraulic turbines

NASA Astrophysics Data System (ADS)

Yang, L.; Nadarajah, S.

2016-11-01

The objective of this work is to improve the inherent dissipation of the numerical schemes under the framework of a Reynolds-averaged Navier-Stokes (RANS) simulation. The governing equations are solved by the finite volume method with the k-ω SST turbulence model. Instead of the van Albada limiter, a novel eddy-preserving limiter is employed in the MUSCL reconstructions to minimize the dissipation of the vortex. The eddy-preserving procedure inactivates the van Albada limiter in the swirl plane and reduces the artificial dissipation to better preserve vortical flow structures. Steady and unsteady simulations of turbulent flows in a straight channel and a straight asymmetric diffuser are demonstrated. Profiles of velocity, Reynolds shear stress and turbulent kinetic energy are presented and compared against large eddy simulation (LES) and/or experimental data. Finally, comparisons are made to demonstrate the capability of the eddy-preserving limiter scheme.

Observation of organ-pipe acoustic excitations in supported thin films

NASA Astrophysics Data System (ADS)

Zhang, X.; Sooryakumar, R.; Every, A. G.; Manghnani, M. H.

2001-08-01

Brillouin light scattering from supported silicon oxynitride films reveal an extended series of acoustic excitations occurring at regular frequency intervals when the mode wave vector is perpendicular to the film surface. These periodic peaks are identified as distinct standing wave excitations that, similar to harmonics of an open-ended organ pipe, occur due to the boundary conditions imposed by the free surface and substrate-film interface. The surface ripple and volume elasto-optic scattering mechanisms contribute to the scattering cross sections and lead to dramatic interference effects at low frequencies where the surface corrugations play a dominant role. The transformation of these standing wave excitations to modes with finite in-plane wave vectors is also investigated. The results are discussed in the framework of a Green's-function formalism that reproduces the experimental features and illustrate the importance of the standing modes in evaluating the longitudinal elastic properties of the films.

A numerical study on bow shocks around the lightning return stroke channel

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

Chen, Qiang, E-mail: cq0405@126.com; Chen, Bin, E-mail: emcchen@163.com; Yi, Yun

2015-03-15

Bow shock structures are important to various hydrodynamics and magnetohydrodynamics (MHD) phenomena in geophysics and astrophysics. The formation and propagation of bow shocks around the lightning return stroke channel are investigated based on the self-similar motion theory and simulated with a two-dimensional Eulerian finite volume resistive radiation MHD code. In this framework, as verification of theoretical models, the evolving structures of many quantities, such as the plasma density, temperature, pressure, shock velocity, and magnetic field, can be obtained, which present all the characteristics of bow shocks in the lightning return stroke processes. The evolution characteristics and the configuration of themore » curved return stroke channels, e.g., the non-ideal effects and the scaling laws, are discussed in detail. The results may have applications for some observed features of the return stroke channels and other phenomena in the lightning discharge plasmas.« less

Biomedical Simulation Models of Human Auditory Processes

NASA Technical Reports Server (NTRS)

Bicak, Mehmet M. A.

2012-01-01

Detailed acoustic engineering models that explore noise propagation mechanisms associated with noise attenuation and transmission paths created when using hearing protectors such as earplugs and headsets in high noise environments. Biomedical finite element (FE) models are developed based on volume Computed Tomography scan data which provides explicit external ear, ear canal, middle ear ossicular bones and cochlea geometry. Results from these studies have enabled a greater understanding of hearing protector to flesh dynamics as well as prioritizing noise propagation mechanisms. Prioritization of noise mechanisms can form an essential framework for exploration of new design principles and methods in both earplug and earcup applications. These models are currently being used in development of a novel hearing protection evaluation system that can provide experimentally correlated psychoacoustic noise attenuation. Moreover, these FE models can be used to simulate the effects of blast related impulse noise on human auditory mechanisms and brain tissue.

A Cartesian grid approach with hierarchical refinement for compressible flows

NASA Technical Reports Server (NTRS)

Quirk, James J.

1994-01-01

Many numerical studies of flows that involve complex geometries are limited by the difficulties in generating suitable grids. We present a Cartesian boundary scheme for two-dimensional, compressible flows that is unfettered by the need to generate a computational grid and so it may be used, routinely, even for the most awkward of geometries. In essence, an arbitrary-shaped body is allowed to blank out some region of a background Cartesian mesh and the resultant cut-cells are singled out for special treatment. This is done within a finite-volume framework and so, in principle, any explicit flux-based integration scheme can take advantage of this method for enforcing solid boundary conditions. For best effect, the present Cartesian boundary scheme has been combined with a sophisticated, local mesh refinement scheme, and a number of examples are shown in order to demonstrate the efficacy of the combined algorithm for simulations of shock interaction phenomena.

Solar Corona Simulation Model With Positivity-preserving Property

NASA Astrophysics Data System (ADS)

Feng, X. S.

2015-12-01

Positivity-preserving is one of crucial problems in solar corona simulation. In such numerical simulation of low plasma β region, keeping density and pressure is a first of all matter to obtain physical sound solution. In the present paper, we utilize the maximum-principle-preserving flux limiting technique to develop a class of second order positivity-preserving Godunov finite volume HLL methods for the solar wind plasma MHD equations. Based on the underlying first order building block of positivity preserving Lax-Friedrichs, our schemes, under the constrained transport (CT) and generalized Lagrange multiplier (GLM) framework, can achieve high order accuracy, a discrete divergence-free condition and positivity of the numerical solution simultaneously without extra CFL constraints. Numerical results in four Carrington rotation during the declining, rising, minimum and maximum solar activity phases are provided to demonstrate the performance of modeling small plasma beta with positivity-preserving property of the proposed method.

Experimental and Numerical Analysis of Microstructures and Stress States of Shot-Peened GH4169 Superalloys

NASA Astrophysics Data System (ADS)

Hu, Dianyin; Gao, Ye; Meng, Fanchao; Song, Jun; Wang, Rongqiao

2018-04-01

Combining experiments and finite element analysis (FEA), a systematic study was performed to analyze the microstructural evolution and stress states of shot-peened GH4169 superalloy over a variety of peening intensities and coverages. A dislocation density evolution model was integrated into the representative volume FEA model to quantitatively predict microstructural evolution in the surface layers and compared with experimental results. It was found that surface roughness and through-depth residual stress profile are more sensitive to shot-peening intensity compared to coverage due to the high kinetic energy involved. Moreover, a surface nanocrystallization layer was discovered in the top surface region of GH4169 for all shot-peening conditions. However, the grain refinement was more intensified under high shot-peening coverage, under which enough time was permitted for grain refinement. The grain size gradient predicted by the numerical framework showed good agreement with experimental observations.

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.

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE PAGES

Doring, M.; Hammer, H. -W.; Mai, M.; ...

2018-06-15

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Three-body spectrum in a finite volume: The role of cubic symmetry

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

Doring, M.; Hammer, H. -W.; Mai, M.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics.

PubMed

Brocchini, Maurizio

2013-12-08

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention.

A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics

PubMed Central

Brocchini, Maurizio

2013-01-01

This paper, which is largely the fruit of an invited talk on the topic at the latest International Conference on Coastal Engineering, describes the state of the art of modelling by means of Boussinesq-type models (BTMs). Motivations for using BTMs as well as their fundamentals are illustrated, with special attention to the interplay between the physics to be described, the chosen model equations and the numerics in use. The perspective of the analysis is that of a physicist/engineer rather than of an applied mathematician. The chronological progress of the currently available BTMs from the pioneering models of the late 1960s is given. The main applications of BTMs are illustrated, with reference to specific models and methods. The evolution in time of the numerical methods used to solve BTMs (e.g. finite differences, finite elements, finite volumes) is described, with specific focus on finite volumes. Finally, an overview of the most important BTMs currently available is presented, as well as some indications on improvements required and fields of applications that call for attention. PMID:24353475

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

DOE PAGES

Xia, Yidong; Wang, Chuanjin; Luo, Hong; ...

2015-12-15

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

Assessment of a hybrid finite element and finite volume code for turbulent incompressible flows

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

Xia, Yidong; Wang, Chuanjin; Luo, Hong

Hydra-TH is a hybrid finite-element/finite-volume incompressible/low-Mach flow simulation code based on the Hydra multiphysics toolkit being developed and used for thermal-hydraulics applications. In the present work, a suite of verification and validation (V&V) test problems for Hydra-TH was defined to meet the design requirements of the Consortium for Advanced Simulation of Light Water Reactors (CASL). The intent for this test problem suite is to provide baseline comparison data that demonstrates the performance of the Hydra-TH solution methods. The simulation problems vary in complexity from laminar to turbulent flows. A set of RANS and LES turbulence models were used in themore » simulation of four classical test problems. Numerical results obtained by Hydra-TH agreed well with either the available analytical solution or experimental data, indicating the verified and validated implementation of these turbulence models in Hydra-TH. Where possible, we have attempted some form of solution verification to identify sensitivities in the solution methods, and to suggest best practices when using the Hydra-TH code.« less

OFF, Open source Finite volume Fluid dynamics code: A free, high-order solver based on parallel, modular, object-oriented Fortran API

NASA Astrophysics Data System (ADS)

Zaghi, S.

2014-07-01

OFF, an open source (free software) code for performing fluid dynamics simulations, is presented. The aim of OFF is to solve, numerically, the unsteady (and steady) compressible Navier-Stokes equations of fluid dynamics by means of finite volume techniques: the research background is mainly focused on high-order (WENO) schemes for multi-fluids, multi-phase flows over complex geometries. To this purpose a highly modular, object-oriented application program interface (API) has been developed. In particular, the concepts of data encapsulation and inheritance available within Fortran language (from standard 2003) have been stressed in order to represent each fluid dynamics "entity" (e.g. the conservative variables of a finite volume, its geometry, etc…) by a single object so that a large variety of computational libraries can be easily (and efficiently) developed upon these objects. The main features of OFF can be summarized as follows: Programming LanguageOFF is written in standard (compliant) Fortran 2003; its design is highly modular in order to enhance simplicity of use and maintenance without compromising the efficiency; Parallel Frameworks Supported the development of OFF has been also targeted to maximize the computational efficiency: the code is designed to run on shared-memory multi-cores workstations and distributed-memory clusters of shared-memory nodes (supercomputers); the code's parallelization is based on Open Multiprocessing (OpenMP) and Message Passing Interface (MPI) paradigms; Usability, Maintenance and Enhancement in order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account; the documentation is built upon comprehensive comments placed directly into the source files (no external documentation files needed): these comments are parsed by means of doxygen free software producing high quality html and latex documentation pages; the distributed versioning system referred as git has been adopted in order to facilitate the collaborative maintenance and improvement of the code; CopyrightsOFF is a free software that anyone can use, copy, distribute, study, change and improve under the GNU Public License version 3. The present paper is a manifesto of OFF code and presents the currently implemented features and ongoing developments. This work is focused on the computational techniques adopted and a detailed description of the main API characteristics is reported. OFF capabilities are demonstrated by means of one and two dimensional examples and a three dimensional real application.

Movies of Finite Deformation within Western North American Plate Boundary Zone

NASA Astrophysics Data System (ADS)

Holt, W. E.; Birkes, B.; Richard, G. A.

2004-12-01

Animations of finite strain within deforming continental zones can be an important tool for both education and research. We present finite strain models for western North America. We have found that these moving images, which portray plate motions, landform uplift, and subsidence, are highly useful for enabling students to conceptualize the dramatic changes that can occur within plate boundary zones over geologic time. These models use instantaneous rates of strain inferred from both space geodetic observations and Quaternary fault slip rates. Geodetic velocities and Quaternary strain rates are interpolated to define a continuous, instantaneous velocity field for western North America. This velocity field is then used to track topography points and fault locations through time (both backward and forward in time), using small time steps, to produce a 6 million year image. The strain rate solution is updated at each time step, accounting for changes in boundary conditions of plate motion, and changes in fault orientation. Assuming zero volume change, Airy isostasy, and a ratio of erosion rate to tectonic uplift rate, the topography is also calculated as a function of time. The animations provide interesting moving images of the transform boundary, highlighting ongoing extension and subsidence, convergence and uplift, and large translations taking place within the strike-slip regime. Moving images of the strain components, uplift volume through time, and inferred erosion volume through time, have also been produced. These animations are an excellent demonstration for education purposes and also hold potential as an important tool for research enabling the quantification of finite rotations of fault blocks, potential erosion volume, uplift volume, and the influence of climate on these parameters. The models, however, point to numerous shortcomings of taking constraints from instantaneous calculations to provide insight into time evolution and reconstruction models. More rigorous calculations are needed to account for changes in dynamics (body forces) through time and resultant changes in fault behavior and crustal rheology.

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.

Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings

NASA Astrophysics Data System (ADS)

Berthelsen, Rolf; Denzer, Ralf; Oppermann, Philip; Menzel, Andreas

2017-11-01

Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples.

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

USGS Publications Warehouse

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

1993-01-01

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

A real-time control framework for urban water reservoirs operation

NASA Astrophysics Data System (ADS)

Galelli, S.; Goedbloed, A.; Schwanenberg, D.

2012-04-01

Drinking water demand in urban areas is growing parallel to the worldwide urban population, and it is acquiring an increasing part of the total water consumption. Since the delivery of sufficient water volumes in urban areas represents a difficult logistic and economical problem, different metropolitan areas are evaluating the opportunity of constructing relatively small reservoirs within urban areas. Singapore, for example, is developing the so-called 'Four National Taps Strategies', which detects the maximization of water yields from local, urban catchments as one of the most important water sources. However, the peculiar location of these reservoirs can provide a certain advantage from the logistical point of view, but it can pose serious difficulties in their daily management. Urban catchments are indeed characterized by large impervious areas: this results in a change of the hydrological cycle, with decreased infiltration and groundwater recharge, and increased patterns of surface and river discharges, with higher peak flows, volumes and concentration time. Moreover, the high concentrations of nutrients and sediments characterizing urban discharges can cause further water quality problems. In this critical hydrological context, the effective operation of urban water reservoirs must rely on real-time control techniques, which can exploit hydro-meteorological information available in real-time from hydrological and nowcasting models. This work proposes a novel framework for the real-time control of combined water quality and quantity objectives in urban reservoirs. The core of this framework is a non-linear Model Predictive Control (MPC) scheme, which employs the current state of the system, the future discharges furnished by a predictive model and a further model describing the internal dynamics of the controlled sub-system to determine an optimal control sequence over a finite prediction horizon. The main advantage of this scheme stands in its reduced computational requests and the capability of exploiting real-time hydro-meteorological information, which are crucial for an effective operation of these fast-varying hydrological systems. The framework is here demonstrated on the operation of Marina Reservoir (Singapore), whose recent construction in late 2008 increased the effective catchment area to about 50% of the total available. Its operation, which accounts for drinking water supply, flash floods control and water quality standards, is here designed by combining the MPC scheme with the process-based hydrological model SOBEK. Extensive simulation experiments show the validity of the proposed framework.

A general observatory control software framework design for existing small and mid-size telescopes

NASA Astrophysics Data System (ADS)

Ge, Liang; Lu, Xiao-Meng; Jiang, Xiao-Jun

2015-07-01

A general framework for observatory control software would help to improve the efficiency of observation and operation of telescopes, and would also be advantageous for remote and joint observations. We describe a general framework for observatory control software, which considers principles of flexibility and inheritance to meet the expectations from observers and technical personnel. This framework includes observation scheduling, device control and data storage. The design is based on a finite state machine that controls the whole process.

Modelling and finite-time stability analysis of psoriasis pathogenesis

NASA Astrophysics Data System (ADS)

Oza, Harshal B.; Pandey, Rakesh; Roper, Daniel; Al-Nuaimi, Yusur; Spurgeon, Sarah K.; Goodfellow, Marc

2017-08-01

A new systems model of psoriasis is presented and analysed from the perspective of control theory. Cytokines are treated as actuators to the plant model that govern the cell population under the reasonable assumption that cytokine dynamics are faster than the cell population dynamics. The analysis of various equilibria is undertaken based on singular perturbation theory. Finite-time stability and stabilisation have been studied in various engineering applications where the principal paradigm uses non-Lipschitz functions of the states. A comprehensive study of the finite-time stability properties of the proposed psoriasis dynamics is carried out. It is demonstrated that the dynamics are finite-time convergent to certain equilibrium points rather than asymptotically or exponentially convergent. This feature of finite-time convergence motivates the development of a modified version of the Michaelis-Menten function, frequently used in biology. This framework is used to model cytokines as fast finite-time actuators.

Damage tolerance in filament-wound graphite/epoxy pressure vessels

NASA Technical Reports Server (NTRS)

Simon, William E.; Ngueyen, Vinh D.; Chenna, Ravi K.

1995-01-01

Graphite/epoxy composites are extensively used in the aerospace and sporting goods industries due to their superior engineering properties compared to those of metals. However, graphite/epoxy is extremely susceptible to impact damage which can cause considerable and sometimes undetected reduction in strength. An inelastic impact model was developed to predict damage due to low-velocity impact. A transient dynamic finite element formulation was used in conjunction with the 3D Tsai-Wu failure criterion to determine and incorporate failure in the materials during impact. Material degradation can be adjusted from no degradation to partial degradation to full degradation. The developed software is based on an object-oriented implementation framework called Extensible Implementation Framework for Finite Elements (EIFFE).

An Open Source Framework for Coupled Hydro-Hydrogeo-Chemical Systems in Catchment Research

NASA Astrophysics Data System (ADS)

Delfs, J.; Sachse, A.; Gayler, S.; Grathwohl, P.; He, W.; Jang, E.; Kalbacher, T.; Klein, C.; Kolditz, O.; Maier, U.; Priesack, E.; Rink, K.; Selle, B.; Shao, H.; Singh, A. K.; Streck, T.; Sun, Y.; Wang, W.; Walther, M.

2013-12-01

This poster presents an open-source framework designed to assist water scientists in the study of catchment hydraulic functions with associated chemical processes, e.g. contaminant degradation, plant nutrient turnover. The model successfully calculates the feedbacks between surface water, subsurface water and air in standard benchmarks. In specific model applications to heterogeneous catchments, subsurface water is driven by density variations and runs through double porous media. Software codes of water science are tightly coupled by iteration, namely the Storm Water Management Model (SWMM) for urban runoff, Expert-N for simulating water fluxes and nutrient turnover in agricultural and forested soils, and OpenGeoSys (OGS) for groundwater. The coupled model calculates flow of hydrostatic shallow water over the land surface with finite volume and difference methods. The flow equations for water in the porous subsurface are discretized in space with finite elements. Chemical components are transferred through 1D, 2D or 3D watershed representations with advection-dispersion solvers or, as an alternative, random walk particle tracking. A transport solver can be in sequence with a chemical solver, e.g. PHREEQ-C, BRNS, additionally. Besides coupled partial differential equations, the concept of hydrological response units is employed in simulations at regional scale with scarce data availability. In this case, a conceptual hydrological model, specifically the Jena Adaptable Modeling System (JAMS), passes groundwater recharge through a software interface into OGS, which solves the partial differential equations of groundwater flow. Most components of the modeling framework are open source and can be modified for individual purposes. Applications range from temperate climate regions in Germany (Ammer catchment and Hessian Ried) to arid regions in the Middle East (Oman and Dead See). Some of the presented examples originate from intensively monitored research sites of the WESS research centre and the monitoring initiative TERENO. Other examples originate from the IWAS project on integrated water resources management. The model applications are primarily concerned with groundwater resources, which are endangered by overexploitation, intrusion of saltwater, and nitrate loads.

Distributed robust finite-time nonlinear consensus protocols for multi-agent systems

NASA Astrophysics Data System (ADS)

Zuo, Zongyu; Tie, Lin

2016-04-01

This paper investigates the robust finite-time consensus problem of multi-agent systems in networks with undirected topology. Global nonlinear consensus protocols augmented with a variable structure are constructed with the aid of Lyapunov functions for each single-integrator agent dynamics in the presence of external disturbances. In particular, it is shown that the finite settling time of the proposed general framework for robust consensus design is upper bounded for any initial condition. This makes it possible for network consensus problems to design and estimate the convergence time offline for a multi-agent team with a given undirected information flow. Finally, simulation results are presented to demonstrate the performance and effectiveness of our finite-time protocols.

Linear quadratic tracking problems in Hilbert space - Application to optimal active noise suppression

NASA Technical Reports Server (NTRS)

Banks, H. T.; Silcox, R. J.; Keeling, S. L.; Wang, C.

1989-01-01

A unified treatment of the linear quadratic tracking (LQT) problem, in which a control system's dynamics are modeled by a linear evolution equation with a nonhomogeneous component that is linearly dependent on the control function u, is presented; the treatment proceeds from the theoretical formulation to a numerical approximation framework. Attention is given to two categories of LQT problems in an infinite time interval: the finite energy and the finite average energy. The behavior of the optimal solution for finite time-interval problems as the length of the interval tends to infinity is discussed. Also presented are the formulations and properties of LQT problems in a finite time interval.

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

NASA Astrophysics Data System (ADS)

Blum, Thomas; Christ, Norman; Hayakawa, Masashi; Izubuchi, Taku; Jin, Luchang; Jung, Chulwoo; Lehner, Christoph

2017-08-01

In our previous work, Blum et al. [Phys. Rev. Lett. 118, 022005 (2017), 10.1103/PhysRevLett.118.022005], the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g -2 ) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1 /L2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

DOE PAGES

Blum, Thomas; Christ, Norman; Hayakawa, Masashi; ...

2017-08-22

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L 2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy.more » We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.« less

Using infinite-volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment

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

Blum, Thomas; Christ, Norman; Hayakawa, Masashi

In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g — 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD Collaboration. However, the calculation is expected to suffer from a significant finite-volume error that scales like 1/L 2 where L is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite-volume, continuum QED, resulting in a weighting function that is precomputed and saved with affordable cost and sufficient accuracy.more » We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. Here, we have implemented an improved weighting function which reduces both discretization and finite-volume effects arising from the hadronic part of the amplitude.« 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.

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.

Nucleon axial charge in (2+1)-flavor dynamical-lattice QCD with domain-wall fermions.

PubMed

Yamazaki, T; Aoki, Y; Blum, T; Lin, H W; Lin, M F; Ohta, S; Sasaki, S; Tweedie, R J; Zanotti, J M

2008-05-02

We present results for the nucleon axial charge g{A} at a fixed lattice spacing of 1/a=1.73(3) GeV using 2+1 flavors of domain wall fermions on size 16;{3} x 32 and 24;{3} x 64 lattices (L=1.8 and 2.7 fm) with length 16 in the fifth dimension. The length of the Monte Carlo trajectory at the lightest m_{pi} is 7360 units, including 900 for thermalization. We find finite volume effects are larger than the pion mass dependence at m{pi}=330 MeV. We also find a scaling with the single variable m{pi}L which can also be seen in previous two-flavor domain wall and Wilson fermion calculations. Using this scaling to eliminate the finite-volume effect, we obtain g{A}=1.20(6)(4) at the physical pion mass, m_{pi}=135 MeV, where the first and second errors are statistical and systematic. The observed finite-volume scaling also appears in similar quenched simulations, but disappear when V>or=(2.4 fm);{3}. We argue this is a dynamical quark effect.

Finite Volume Numerical Methods for Aeroheating Rate Calculations from Infrared Thermographic Data

NASA Technical Reports Server (NTRS)

Daryabeigi, Kamran; Berry, Scott A.; Horvath, Thomas J.; Nowak, Robert J.

2006-01-01

The use of multi-dimensional finite volume heat conduction techniques for calculating aeroheating rates from measured global surface temperatures on hypersonic wind tunnel models was investigated. Both direct and inverse finite volume techniques were investigated and compared with the standard one-dimensional semi-infinite technique. Global transient surface temperatures were measured using an infrared thermographic technique on a 0.333-scale model of the Hyper-X forebody in the NASA Langley Research Center 20-Inch Mach 6 Air tunnel. In these tests the effectiveness of vortices generated via gas injection for initiating hypersonic transition on the Hyper-X forebody was investigated. An array of streamwise-orientated heating striations was generated and visualized downstream of the gas injection sites. In regions without significant spatial temperature gradients, one-dimensional techniques provided accurate aeroheating rates. In regions with sharp temperature gradients caused by striation patterns multi-dimensional heat transfer techniques were necessary to obtain more accurate heating rates. The use of the one-dimensional technique resulted in differences of 20% in the calculated heating rates compared to 2-D analysis because it did not account for lateral heat conduction in the model.

Simplified equation for Young's modulus of CNT reinforced concrete

NASA Astrophysics Data System (ADS)

Chandran, RameshBabu; Gifty Honeyta A, Maria

2017-12-01

This research investigation focuses on finite element modeling of carbon nanotube (CNT) reinforced concrete matrix for three grades of concrete namely M40, M60 and M120. Representative volume element (RVE) was adopted and one-eighth model depicting the CNT reinforced concrete matrix was simulated using FEA software ANSYS17.2. Adopting random orientation of CNTs, with nine fibre volume fractions from 0.1% to 0.9%, finite element modeling simulations replicated exactly the CNT reinforced concrete matrix. Upon evaluations of the model, the longitudinal and transverse Young's modulus of elasticity of the CNT reinforced concrete was arrived. The graphical plots between various fibre volume fractions and the concrete grade revealed simplified equation for estimating the young's modulus. It also exploited the fact that the concrete grade does not have significant impact in CNT reinforced concrete matrix.

Hamiltonian Effective Field Theory Study of the N^{*}(1535) Resonance in Lattice QCD.

PubMed

Liu, Zhan-Wei; Kamleh, Waseem; Leinweber, Derek B; Stokes, Finn M; Thomas, Anthony W; Wu, Jia-Jun

2016-02-26

Drawing on experimental data for baryon resonances, Hamiltonian effective field theory (HEFT) is used to predict the positions of the finite-volume energy levels to be observed in lattice QCD simulations of the lowest-lying J^{P}=1/2^{-} nucleon excitation. In the initial analysis, the phenomenological parameters of the Hamiltonian model are constrained by experiment and the finite-volume eigenstate energies are a prediction of the model. The agreement between HEFT predictions and lattice QCD results obtained on volumes with spatial lengths of 2 and 3 fm is excellent. These lattice results also admit a more conventional analysis where the low-energy coefficients are constrained by lattice QCD results, enabling a determination of resonance properties from lattice QCD itself. Finally, the role and importance of various components of the Hamiltonian model are examined.

Principles of Considering the Effect of the Limited Volume of a System on Its Thermodynamic State

NASA Astrophysics Data System (ADS)

Tovbin, Yu. K.

2018-01-01

The features of a system with a finite volume that affect its thermodynamic state are considered in comparison to describing small bodies in macroscopic phases. Equations for unary and pair distribution functions are obtained using difference derivatives of a discrete statistical sum. The structure of the equation for the free energy of a system consisting of an ensemble of volume-limited regions with different sizes and a full set of equations describing a macroscopic polydisperse system are discussed. It is found that the equations can be applied to molecular adsorption on small faces of microcrystals, to bound and isolated pores of a polydisperse material, and to describe the spinodal decomposition of a fluid in brief periods of time and high supersaturations of the bulk phase when each local region functions the same on average. It is shown that as the size of a system diminishes, corrections must be introduced for the finiteness of the system volume and fluctuations of the unary and pair distribution functions.

Perturbative expansions from Monte Carlo simulations at weak coupling: Wilson loops and the static-quark self-energy

NASA Astrophysics Data System (ADS)

Trottier, H. D.; Shakespeare, N. H.; Lepage, G. P.; MacKenzie, P. B.

2002-05-01

Perturbative coefficients for Wilson loops and the static-quark self-energy are extracted from Monte Carlo simulations at weak coupling. The lattice volumes and couplings are chosen to ensure that the lattice momenta are all perturbative. Twisted boundary conditions are used to eliminate the effects of lattice zero modes and to suppress nonperturbative finite-volume effects due to Z(3) phases. Simulations of the Wilson gluon action are done with both periodic and twisted boundary conditions, and over a wide range of lattice volumes (from 34 to 164) and couplings (from β~9 to β~60). A high precision comparison is made between the simulation data and results from finite-volume lattice perturbation theory. The Monte Carlo results are shown to be in excellent agreement with perturbation theory through second order. New results for third-order coefficients for a number of Wilson loops and the static-quark self-energy are reported.

A Vertically Lagrangian Finite-Volume Dynamical Core for Global Models

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann

2003-01-01

A finite-volume dynamical core with a terrain-following Lagrangian control-volume discretization is described. The vertically Lagrangian discretization reduces the dimensionality of the physical problem from three to two with the resulting dynamical system closely resembling that of the shallow water dynamical system. The 2D horizontal-to-Lagrangian-surface transport and dynamical processes are then discretized using the genuinely conservative flux-form semi-Lagrangian algorithm. Time marching is split- explicit, with large-time-step for scalar transport, and small fractional time step for the Lagrangian dynamics, which permits the accurate propagation of fast waves. A mass, momentum, and total energy conserving algorithm is developed for mapping the state variables periodically from the floating Lagrangian control-volume to an Eulerian terrain-following coordinate for dealing with physical parameterizations and to prevent severe distortion of the Lagrangian surfaces. Deterministic baroclinic wave growth tests and long-term integrations using the Held-Suarez forcing are presented. Impact of the monotonicity constraint is discussed.

Storm Water Infiltration and Focused Groundwater Recharge in a Rain Garden: Finite Volume Model and Numerical Simulations for Different Configurations and Climates

NASA Astrophysics Data System (ADS)

Aravena, J.; Dussaillant, A. R.

2006-12-01

Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).

Optimizing Wartime Materiel Delivery: An Overview of DoD containerization. Volume 2. Framework for Action to Address DoD Containerization Issues

DOT National Transportation Integrated Search

1988-10-01

This second volume of the study entitled, Optimizing Wartime Materiel Delivery: An Overview of DOD Containerization Efforts, -outlines a framework for action to address containerization issues identified in Volume I. The objectives of the study inclu...

Implant-Supported Fixed Partial Prostheses With Different Prosthetic Materials: A Three-Dimensional Finite Element Stress Analysis.

PubMed

Arinc, Hakan

2018-06-01

To evaluate the effects of prosthetic material on the degree of stress to the cortical bone, trabecular bone, framework, and implants using finite element analysis (FEA). A mandibular implant-supported fixed prosthesis was designed. Different prosthetic materials [cobalt-chromium-supported ceramic, zirconia-supported ceramic, and zirconia-reinforced polymethyl methacrylate (ZRPMMA)-supported resin] were used. FEA was used to evaluate stress under different loading conditions. Maximum principal (σmax), minimum principal (σmin), and von Mises (σvM) stress values were obtained. Similar σmax, σmin, and σvM values were observed in the cortical and trabecular bones and in implants under both loading conditions, with the exception of the ZRPMMA model, which showed the highest σmax, σmin, and σvM values in oblique loading. The ZRPMMA model had the lowest σvM value in the framework under both loading conditions. ZRPMMA had the lowest stress values in the framework, with increased stress values in the implants and bone tissue. Framework and veneering materials may influence stress values under different loading conditions.

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

Endres, Michael G.; Shindler, Andrea; Tiburzi, Brian C.

The commonly adopted approach for including electromagnetic interactions in lattice QCD simulations relies on using finite volume as the infrared regularization for QED. The long-range nature of the electromagnetic interaction, however, implies that physical quantities are susceptible to power-law finite volume corrections, which must be removed by performing costly simulations at multiple lattice volumes, followed by an extrapolation to the infinite volume limit. In this work, we introduce a photon mass as an alternative means for gaining control over infrared effects associated with electromagnetic interactions. We present findings for hadron mass shifts due to electromagnetic interactions (i.e., for the proton,more » neutron, charged and neutral kaon) and corresponding mass splittings, and compare the results with those obtained from conventional QCD+QED calculations. Results are reported for numerical studies of three flavor electroquenched QCD using ensembles corresponding to 800 MeV pions, ensuring that the only appreciable volume corrections arise from QED effects. The calculations are performed with three lattice volumes with spatial extents ranging from 3.4 - 6.7 fm. As a result, we find that for equal computing time (not including the generation of the lattice configurations), the electromagnetic mass shifts can be extracted from computations on a single (our smallest) lattice volume with comparable or better precision than the conventional approach.« less

Massive photons: An infrared regularization scheme for lattice QCD + QED

DOE PAGES

Endres, Michael G.; Shindler, Andrea; Tiburzi, Brian C.; ...

2016-08-10

The commonly adopted approach for including electromagnetic interactions in lattice QCD simulations relies on using finite volume as the infrared regularization for QED. The long-range nature of the electromagnetic interaction, however, implies that physical quantities are susceptible to power-law finite volume corrections, which must be removed by performing costly simulations at multiple lattice volumes, followed by an extrapolation to the infinite volume limit. In this work, we introduce a photon mass as an alternative means for gaining control over infrared effects associated with electromagnetic interactions. We present findings for hadron mass shifts due to electromagnetic interactions (i.e., for the proton,more » neutron, charged and neutral kaon) and corresponding mass splittings, and compare the results with those obtained from conventional QCD+QED calculations. Results are reported for numerical studies of three flavor electroquenched QCD using ensembles corresponding to 800 MeV pions, ensuring that the only appreciable volume corrections arise from QED effects. The calculations are performed with three lattice volumes with spatial extents ranging from 3.4 - 6.7 fm. As a result, we find that for equal computing time (not including the generation of the lattice configurations), the electromagnetic mass shifts can be extracted from computations on a single (our smallest) lattice volume with comparable or better precision than the conventional approach.« less

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.

Liftings and stresses for planar periodic frameworks

PubMed Central

Borcea, Ciprian; Streinu, Ileana

2015-01-01

We formulate and prove a periodic analog of Maxwell’s theorem relating stressed planar frameworks and their liftings to polyhedral surfaces with spherical topology. We use our lifting theorem to prove deformation and rigidity-theoretic properties for planar periodic pseudo-triangulations, generalizing features known for their finite counterparts. These properties are then applied to questions originating in mathematical crystallography and materials science, concerning planar periodic auxetic structures and ultrarigid periodic frameworks. PMID:26973370

Functional validation and comparison framework for EIT lung imaging.

PubMed

Grychtol, Bartłomiej; Elke, Gunnar; Meybohm, Patrick; Weiler, Norbert; Frerichs, Inéz; Adler, Andy

2014-01-01

Electrical impedance tomography (EIT) is an emerging clinical tool for monitoring ventilation distribution in mechanically ventilated patients, for which many image reconstruction algorithms have been suggested. We propose an experimental framework to assess such algorithms with respect to their ability to correctly represent well-defined physiological changes. We defined a set of clinically relevant ventilation conditions and induced them experimentally in 8 pigs by controlling three ventilator settings (tidal volume, positive end-expiratory pressure and the fraction of inspired oxygen). In this way, large and discrete shifts in global and regional lung air content were elicited. We use the framework to compare twelve 2D EIT reconstruction algorithms, including backprojection (the original and still most frequently used algorithm), GREIT (a more recent consensus algorithm for lung imaging), truncated singular value decomposition (TSVD), several variants of the one-step Gauss-Newton approach and two iterative algorithms. We consider the effects of using a 3D finite element model, assuming non-uniform background conductivity, noise modeling, reconstructing for electrode movement, total variation (TV) reconstruction, robust error norms, smoothing priors, and using difference vs. normalized difference data. Our results indicate that, while variation in appearance of images reconstructed from the same data is not negligible, clinically relevant parameters do not vary considerably among the advanced algorithms. Among the analysed algorithms, several advanced algorithms perform well, while some others are significantly worse. Given its vintage and ad-hoc formulation backprojection works surprisingly well, supporting the validity of previous studies in lung EIT.

Influence of finish line in the distribution of stress trough an all ceramic implant-supported crown.

PubMed Central

SANNINO, G.; GLORIA, F.; OTTRIA, L.; BARLATTANI, A.

2010-01-01

SUMMARY Porpose. The aim of this study was to evaluate, by finite element analysis (FEA), the influence of finish line on stress distribution and resistance to the loads of a ZrO2 crown and porcelain in implant-supported. Material and methods. The object of this analysis consisted of a fxture, an abutment, a passing screw, a layer of cement, a framework crown, a feldspatic porcelain veneering. The abutment’s marginal design was used in 3 different types of preparation: feather edge, slight chamfer and 50°, each of them was of 1 mm depth over the entire circumference. The ZrO2Y-TZP coping was 0.6 mm thick. Two material matching for the abutment and the framework was used for the simulations: ZrO2 framework and ZrO2 abutment, ZrO2 framework and T abutment. A 600 N axial force distributed over the entire surface of the crown was applied. The numerical simulations with finite elements were used to verify the different distribution of equivalent von Mises stress for three different geometries of abutment and framework. Results Slight chamfer on the matching ZrO2 - ZrO2 is the geometry with minimum equivalent stress of von Mises. Even for T abutment and ZrO2 framework slight chamfer is the best configuration to minimize the localized stress. Geometry that has the highest average stress is one with abutment at 50°, we see a downward trend for all three configurations using only zirconium for both components. Conclusions Finite element analysis. performed for the manifacturing of implant-supported crown, gives exact geometric guide lines about the choice of chamfer preparation, while the analysis of other marginal geometries suggests a possible improved behavior of the mating between ZrO2 abutment and ZrO2 coping. for three different geometries of the abutment and the coping. PMID:23285359

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

NASA Technical Reports Server (NTRS)

Liu, Yen; Vinokur, Marcel

2004-01-01

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Joint Seismic-Geodetic Algorithm for Finite-Fault Detection and Slip Inversion in the West Coast ShakeAlert System

NASA Astrophysics Data System (ADS)

Smith, D. E.; Felizardo, C.; Minson, S. E.; Boese, M.; Langbein, J. O.; Murray, J. R.

2016-12-01

Finite-fault source algorithms can greatly benefit earthquake early warning (EEW) systems. Estimates of finite-fault parameters provide spatial information, which can significantly improve real-time shaking calculations and help with disaster response. In this project, we have focused on integrating a finite-fault seismic-geodetic algorithm into the West Coast ShakeAlert framework. The seismic part is FinDer 2, a C++ version of the algorithm developed by Böse et al. (2012). It interpolates peak ground accelerations and calculates the best fault length and strike from template matching. The geodetic part is a C++ version of BEFORES, the algorithm developed by Minson et al. (2014) that uses a Bayesian methodology to search for the most probable slip distribution on a fault of unknown orientation. Ultimately, these two will be used together where FinDer generates a Bayesian prior for BEFORES via the methodology of Minson et al. (2015), and the joint solution will generate estimates of finite-fault extent, strike, dip, best slip distribution, and magnitude. We have created C++ versions of both FinDer and BEFORES using open source libraries and have developed a C++ Application Protocol Interface (API) for them both. Their APIs allow FinDer and BEFORES to contribute to the ShakeAlert system via an open source messaging system, ActiveMQ. FinDer has been receiving real-time data, detecting earthquakes, and reporting messages on the development system for several months. We are also testing FinDer extensively with Earthworm tankplayer files. BEFORES has been tested with ActiveMQ messaging in the ShakeAlert framework, and works off a FinDer trigger. We are finishing the FinDer-BEFORES connections in this framework, and testing this system via seismic-geodetic tankplayer files. This will include actual and simulated data.

Recent numerical and algorithmic advances within the volume tracking framework for modeling interfacial flows

DOE PAGES

François, Marianne M.

2015-05-28

A review of recent advances made in numerical methods and algorithms within the volume tracking framework is presented. The volume tracking method, also known as the volume-of-fluid method has become an established numerical approach to model and simulate interfacial flows. Its advantage is its strict mass conservation. However, because the interface is not explicitly tracked but captured via the material volume fraction on a fixed mesh, accurate estimation of the interface position, its geometric properties and modeling of interfacial physics in the volume tracking framework remain difficult. Several improvements have been made over the last decade to address these challenges.more » In this study, the multimaterial interface reconstruction method via power diagram, curvature estimation via heights and mean values and the balanced-force algorithm for surface tension are highlighted.« less

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 3: Systems' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

The internal structure is discussed of the MHOST finite element program designed for 3-D inelastic analysis of gas turbine hot section components. The computer code is the first implementation of the mixed iterative solution strategy for improved efficiency and accuracy over the conventional finite element method. The control structure of the program is covered along with the data storage scheme and the memory allocation procedure and the file handling facilities including the read and/or write sequences.

Characteristics of the Shuttle Orbiter Leeside Flow During A Reentry Condition

NASA Technical Reports Server (NTRS)

Kleb, William L.; Weilmuenster, K. James

1992-01-01

A study of the leeside flow characteristics of the Shuttle Orbiter is presented for a reentry flight condition. The flow is computed using a point-implicit, finite-volume scheme known as the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). LAURA is a second-order accurate, laminar Navier-Stokes solver, incorporating finite-rate chemistry with a radiative equilibrium wall temperature distribution and finite-rate wall catalysis. The resulting computational solution is analyzed in terms of salient flow features and the surface quantities are compared with flight data.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

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

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE PAGES

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.; ...

2017-09-13

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Partial volume correction and image analysis methods for intersubject comparison of FDG-PET studies

NASA Astrophysics Data System (ADS)

Yang, Jun

2000-12-01

Partial volume effect is an artifact mainly due to the limited imaging sensor resolution. It creates bias in the measured activity in small structures and around tissue boundaries. In brain FDG-PET studies, especially for Alzheimer's disease study where there is serious gray matter atrophy, accurate estimate of cerebral metabolic rate of glucose is even more problematic due to large amount of partial volume effect. In this dissertation, we developed a framework enabling inter-subject comparison of partial volume corrected brain FDG-PET studies. The framework is composed of the following image processing steps: (1)MRI segmentation, (2)MR-PET registration, (3)MR based PVE correction, (4)MR 3D inter-subject elastic mapping. Through simulation studies, we showed that the newly developed partial volume correction methods, either pixel based or ROI based, performed better than previous methods. By applying this framework to a real Alzheimer's disease study, we demonstrated that the partial volume corrected glucose rates vary significantly among the control, at risk and disease patient groups and this framework is a promising tool useful for assisting early identification of Alzheimer's patients.

Nonperturbative evaluation for anomalous dimension in 2-dimensional O (3 ) sigma model

NASA Astrophysics Data System (ADS)

Calle Jimenez, Sergio; Oka, Makoto; Sasaki, Kiyoshi

2018-06-01

We nonperturbatively calculate the wave-function renormalization in the two-dimensional O (3 ) sigma model. It is evaluated in a box with a finite spatial extent. We determine the anomalous dimension in the finite-volume scheme through an analysis of the step-scaling function. Results are compared with a perturbative evaluation, and reasonable behavior is observed.

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.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1986-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

An analysis of finite-difference and finite-volume formulations of conservation laws

NASA Technical Reports Server (NTRS)

Vinokur, Marcel

1989-01-01

Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.

Finite-size analysis of a continuous-variable quantum key distribution

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

Leverrier, Anthony; Grosshans, Frederic; Grangier, Philippe

2010-06-15

The goal of this paper is to extend the framework of finite-size analysis recently developed for quantum key distribution to continuous-variable protocols. We do not solve this problem completely here, and we mainly consider the finite-size effects on the parameter estimation procedure. Despite the fact that some questions are left open, we are able to give an estimation of the secret key rate for protocols which do not contain a postselection procedure. As expected, these results are significantly more pessimistic than those obtained in the asymptotic regime. However, we show that recent continuous-variable protocols are able to provide fully securemore » secret keys in the finite-size scenario, over distances larger than 50 km.« less

Finite gradient elasticity and plasticity: a constitutive thermodynamical framework

NASA Astrophysics Data System (ADS)

Bertram, Albrecht

2016-05-01

In Bertram (Continuum Mech Thermodyn. doi: 10.1007/s00161-014-0387-0 , 2015), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius-Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion.

Nonlinear analysis of structures. [within framework of finite element method

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H.; Pifko, A.; Levy, A.

1974-01-01

The development of nonlinear analysis techniques within the framework of the finite-element method is reported. Although the emphasis is concerned with those nonlinearities associated with material behavior, a general treatment of geometric nonlinearity, alone or in combination with plasticity is included, and applications presented for a class of problems categorized as axisymmetric shells of revolution. The scope of the nonlinear analysis capabilities includes: (1) a membrane stress analysis, (2) bending and membrane stress analysis, (3) analysis of thick and thin axisymmetric bodies of revolution, (4) a general three dimensional analysis, and (5) analysis of laminated composites. Applications of the methods are made to a number of sample structures. Correlation with available analytic or experimental data range from good to excellent.

A framework for grand scale parallelization of the combined finite discrete element method in 2d

NASA Astrophysics Data System (ADS)

Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.

2014-09-01

Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.

The MHOST finite element program: 3-D inelastic analysis methods for hot section components. Volume 2: User's manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

The user options available for running the MHOST finite element analysis package is described. MHOST is a solid and structural analysis program based on the mixed finite element technology, and is specifically designed for 3-D inelastic analysis. A family of 2- and 3-D continuum elements along with beam and shell structural elements can be utilized, many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. The outline of solution algorithms is discussed along with the data input and output, analysis options including the user subroutines and the definition of the finite elements implemented in the program package.

Improving NASA's Multiscale Modeling Framework for Tropical Cyclone Climate Study

NASA Technical Reports Server (NTRS)

Shen, Bo-Wen; Nelson, Bron; Cheung, Samson; Tao, Wei-Kuo

2013-01-01

One of the current challenges in tropical cyclone (TC) research is how to improve our understanding of TC interannual variability and the impact of climate change on TCs. Recent advances in global modeling, visualization, and supercomputing technologies at NASA show potential for such studies. In this article, the authors discuss recent scalability improvement to the multiscale modeling framework (MMF) that makes it feasible to perform long-term TC-resolving simulations. The MMF consists of the finite-volume general circulation model (fvGCM), supplemented by a copy of the Goddard cumulus ensemble model (GCE) at each of the fvGCM grid points, giving 13,104 GCE copies. The original fvGCM implementation has a 1D data decomposition; the revised MMF implementation retains the 1D decomposition for most of the code, but uses a 2D decomposition for the massive copies of GCEs. Because the vast majority of computation time in the MMF is spent computing the GCEs, this approach can achieve excellent speedup without incurring the cost of modifying the entire code. Intelligent process mapping allows differing numbers of processes to be assigned to each domain for load balancing. The revised parallel implementation shows highly promising scalability, obtaining a nearly 80-fold speedup by increasing the number of cores from 30 to 3,335.

A discontinuous control volume finite element method for multi-phase flow in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Salinas, P.; Pavlidis, D.; Xie, Z.; Osman, H.; Pain, C. C.; Jackson, M. D.

2018-01-01

We present a new, high-order, control-volume-finite-element (CVFE) method for multiphase porous media flow with discontinuous 1st-order representation for pressure and discontinuous 2nd-order representation for velocity. The method has been implemented using unstructured tetrahedral meshes to discretize space. The method locally and globally conserves mass. However, unlike conventional CVFE formulations, the method presented here does not require the use of control volumes (CVs) that span the boundaries between domains with differing material properties. We demonstrate that the approach accurately preserves discontinuous saturation changes caused by permeability variations across such boundaries, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than using conventional CVFE methods. We resolve a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media.

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

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.

We consider the sign problem for classical spin models at complexmore » $$\\beta =1/g_0^2$$ on $$L\\times L$$ lattices. We show that the tensor renormalization group method allows reliable calculations for larger Im$$\\beta$$ than the reweighting Monte Carlo method. For the Ising model with complex $$\\beta$$ we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the TRG method. We check the convergence of the TRG method for the O(2) model on $$L\\times L$$ lattices when the number of states $$D_s$$ increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.« less

The diffusive finite state projection algorithm for efficient simulation of the stochastic reaction-diffusion master equation.

PubMed

Drawert, Brian; Lawson, Michael J; Petzold, Linda; Khammash, Mustafa

2010-02-21

We have developed a computational framework for accurate and efficient simulation of stochastic spatially inhomogeneous biochemical systems. The new computational method employs a fractional step hybrid strategy. A novel formulation of the finite state projection (FSP) method, called the diffusive FSP method, is introduced for the efficient and accurate simulation of diffusive transport. Reactions are handled by the stochastic simulation algorithm.

Finite temperature grand canonical ensemble study of the minimum electrophilicity principle.

PubMed

Miranda-Quintana, Ramón Alain; Chattaraj, Pratim K; Ayers, Paul W

2017-09-28

We analyze the minimum electrophilicity principle of conceptual density functional theory using the framework of the finite temperature grand canonical ensemble. We provide support for this principle, both for the cases of systems evolving from a non-equilibrium to an equilibrium state and for the change from one equilibrium state to another. In doing so, we clearly delineate the cases where this principle can, or cannot, be used.

Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory

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

Ghosh, Swarnava; Suryanarayana, Phanish, E-mail: phanish.suryanarayana@ce.gatech.edu

2016-02-15

We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization.more » We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.« less

An object-oriented framework for medical image registration, fusion, and visualization.

PubMed

Zhu, Yang-Ming; Cochoff, Steven M

2006-06-01

An object-oriented framework for image registration, fusion, and visualization was developed based on the classic model-view-controller paradigm. The framework employs many design patterns to facilitate legacy code reuse, manage software complexity, and enhance the maintainability and portability of the framework. Three sample applications built a-top of this framework are illustrated to show the effectiveness of this framework: the first one is for volume image grouping and re-sampling, the second one is for 2D registration and fusion, and the last one is for visualization of single images as well as registered volume images.

Optimal nonlinear filtering using the finite-volume method

NASA Astrophysics Data System (ADS)

Fox, Colin; Morrison, Malcolm E. K.; Norton, Richard A.; Molteno, Timothy C. A.

2018-01-01

Optimal sequential inference, or filtering, for the state of a deterministic dynamical system requires simulation of the Frobenius-Perron operator, that can be formulated as the solution of a continuity equation. For low-dimensional, smooth systems, the finite-volume numerical method provides a solution that conserves probability and gives estimates that converge to the optimal continuous-time values, while a Courant-Friedrichs-Lewy-type condition assures that intermediate discretized solutions remain positive density functions. This method is demonstrated in an example of nonlinear filtering for the state of a simple pendulum, with comparison to results using the unscented Kalman filter, and for a case where rank-deficient observations lead to multimodal probability distributions.

Extracting observables from lattice data in the three-particle sector

NASA Astrophysics Data System (ADS)

Rusetsky, Akaki; Hammer, Hans-Werner; Pang, Jin-Yi

2018-03-01

The three-particle quantization condition is derived, using the particle-dimer picture in the non-relativistic effective field theory. The procedure for the extraction of various observables in the three-particle sector (the particle-dimer scattering amplitudes, breakup amplitudes, etc.) from the finite-volume lattice spectrum is discussed in detail. As an illustration of the general formalism, the expression for the finite-volume energy shift of the three-body bound-state in the unitary limit is re-derived. The role of the threebody force, which is essential for the renormalization, is highlighted, and the extension of the result beyond the unitary limit is studied. Comparison with other approaches, known in the literature, is carried out.

Notes on Accuracy of Finite-Volume Discretization Schemes on Irregular Grids

NASA Technical Reports Server (NTRS)

Diskin, Boris; Thomas, James L.

2011-01-01

Truncation-error analysis is a reliable tool in predicting convergence rates of discretization errors on regular smooth grids. However, it is often misleading in application to finite-volume discretization schemes on irregular (e.g., unstructured) grids. Convergence of truncation errors severely degrades on general irregular grids; a design-order convergence can be achieved only on grids with a certain degree of geometric regularity. Such degradation of truncation-error convergence does not necessarily imply a lower-order convergence of discretization errors. In these notes, irregular-grid computations demonstrate that the design-order discretization-error convergence can be achieved even when truncation errors exhibit a lower-order convergence or, in some cases, do not converge at all.

SToRM: A Model for Unsteady Surface Hydraulics Over Complex Terrain

USGS Publications Warehouse

Simoes, Francisco J.

2014-01-01

A two-dimensional (depth-averaged) finite volume Godunov-type shallow water model developed for flow over complex topography is presented. The model is based on an unstructured cellcentered finite volume formulation and a nonlinear strong stability preserving Runge-Kutta time stepping scheme. The numerical discretization is founded on the classical and well established shallow water equations in hyperbolic conservative form, but the convective fluxes are calculated using auto-switching Riemann and diffusive numerical fluxes. The model’s implementation within a graphical user interface is discussed. Field application of the model is illustrated by utilizing it to estimate peak flow discharges in a flooding event of historic significance in Colorado, U.S.A., in 2013.

A Distributed GPU-Based Framework for Real-Time 3D Volume Rendering of Large Astronomical Data Cubes

NASA Astrophysics Data System (ADS)

Hassan, A. H.; Fluke, C. J.; Barnes, D. G.

2012-05-01

We present a framework to volume-render three-dimensional data cubes interactively using distributed ray-casting and volume-bricking over a cluster of workstations powered by one or more graphics processing units (GPUs) and a multi-core central processing unit (CPU). The main design target for this framework is to provide an in-core visualization solution able to provide three-dimensional interactive views of terabyte-sized data cubes. We tested the presented framework using a computing cluster comprising 64 nodes with a total of 128GPUs. The framework proved to be scalable to render a 204GB data cube with an average of 30 frames per second. Our performance analyses also compare the use of NVIDIA Tesla 1060 and 2050GPU architectures and the effect of increasing the visualization output resolution on the rendering performance. Although our initial focus, as shown in the examples presented in this work, is volume rendering of spectral data cubes from radio astronomy, we contend that our approach has applicability to other disciplines where close to real-time volume rendering of terabyte-order three-dimensional data sets is a requirement.

Development of a theoretical framework for analyzing cerebrospinal fluid dynamics

PubMed Central

Cohen, Benjamin; Voorhees, Abram; Vedel, Søren; Wei, Timothy

2009-01-01

Background To date hydrocephalus researchers acknowledge the need for rigorous but utilitarian fluid mechanics understanding and methodologies in studying normal and hydrocephalic intracranial dynamics. Pressure volume models and electric circuit analogs introduced pressure into volume conservation; but control volume analysis enforces independent conditions on pressure and volume. Previously, utilization of clinical measurements has been limited to understanding of the relative amplitude and timing of flow, volume and pressure waveforms; qualitative approaches without a clear framework for meaningful quantitative comparison. Methods Control volume analysis is presented to introduce the reader to the theoretical background of this foundational fluid mechanics technique for application to general control volumes. This approach is able to directly incorporate the diverse measurements obtained by clinicians to better elucidate intracranial dynamics and progression to disorder. Results Several examples of meaningful intracranial control volumes and the particular measurement sets needed for the analysis are discussed. Conclusion Control volume analysis provides a framework to guide the type and location of measurements and also a way to interpret the resulting data within a fundamental fluid physics analysis. PMID:19772652

Nucleon form factors with 2+1 flavor dynamical domain-wall fermions

NASA Astrophysics Data System (ADS)

Yamazaki, Takeshi; Aoki, Yasumichi; Blum, Tom; Lin, Huey-Wen; Ohta, Shigemi; Sasaki, Shoichi; Tweedie, Robert; Zanotti, James

2009-06-01

We report our numerical lattice QCD calculations of the isovector nucleon form factors for the vector and axial-vector currents: the vector, induced tensor, axial-vector, and induced pseudoscalar form factors. The calculation is carried out with the gauge configurations generated with Nf=2+1 dynamical domain-wall fermions and Iwasaki gauge actions at β=2.13, corresponding to a cutoff a-1=1.73GeV, and a spatial volume of (2.7fm)3. The up and down-quark masses are varied so the pion mass lies between 0.33 and 0.67 GeV while the strange quark mass is about 12% heavier than the physical one. We calculate the form factors in the range of momentum transfers, 0.26 is required to ensure that finite-volume effects are below 1%.

The MUSIC algorithm for impedance tomography of small inclusions from discrete data

NASA Astrophysics Data System (ADS)

Lechleiter, A.

2015-09-01

We consider a point-electrode model for electrical impedance tomography and show that current-to-voltage measurements from finitely many electrodes are sufficient to characterize the positions of a finite number of point-like inclusions. More precisely, we consider an asymptotic expansion with respect to the size of the small inclusions of the relative Neumann-to-Dirichlet operator in the framework of the point electrode model. This operator is naturally finite-dimensional and models difference measurements by finitely many small electrodes of the electric potential with and without the small inclusions. Moreover, its leading-order term explicitly characterizes the centers of the small inclusions if the (finite) number of point electrodes is large enough. This characterization is based on finite-dimensional test vectors and leads naturally to a MUSIC algorithm for imaging the inclusion centers. We show both the feasibility and limitations of this imaging technique via two-dimensional numerical experiments, considering in particular the influence of the number of point electrodes on the algorithm’s images.

Noncontact diffuse correlation tomography of human breast tumor

PubMed Central

He, Lian; Lin, Yu; Huang, Chong; Irwin, Daniel; Szabunio, Margaret M.; Yu, Guoqiang

2015-01-01

Abstract. Our first step to adapt our recently developed noncontact diffuse correlation tomography (ncDCT) system for three-dimensional (3-D) imaging of blood flow distribution in human breast tumors is reported. A commercial 3-D camera was used to obtain breast surface geometry, which was then converted to a solid volume mesh. An ncDCT probe scanned over a region of interest on the mesh surface and the measured boundary data were combined with a finite element framework for 3-D image reconstruction of blood flow distribution. This technique was tested in computer simulations and in vivo human breasts with low-grade carcinoma. Results from computer simulations suggest that relatively high accuracy can be achieved when the entire tumor is within the sensitive region of diffuse light. Image reconstruction with a priori knowledge of the tumor volume and location can significantly improve the accuracy in recovery of tumor blood flow contrasts. In vivo imaging results from two breast carcinomas show higher average blood flow contrasts (5.9- and 10.9-fold) in the tumor regions compared to the surrounding tissues, which are comparable with previous findings using diffuse correlation spectroscopy. The ncDCT system has the potential to image blood flow distributions in soft and vulnerable tissues without distorting tissue hemodynamics. PMID:26259706

Finite element simulation of texture evolution and Swift effect in NiAl under torsion

NASA Astrophysics Data System (ADS)

Böhlke, Thomas; Glüge, Rainer; Klöden, Burghardt; Skrotzki, Werner; Bertram, Albrecht

2007-09-01

The texture evolution and the Swift effect in NiAl under torsion at 727 °C are studied by finite element simulations for two different initial textures. The material behaviour is modelled by an elastic-viscoplastic Taylor model. In order to overcome the well-known shortcomings of Taylor's approach, the texture evolution is also investigated by a representative volume element (RVE) with periodic boundary conditions and a compatible microstructure at the opposite faces of the RVE. Such a representative volume element takes into account the grain morphology and the grain interaction. The numerical results are compared with experimental data. It is shown that the modelling of a finite element based RVE leads to a better prediction of the final textures. However, the texture evolution path is not accounted for correctly. The simulated Swift effect depends much more on the initial orientation distribution than observed in experiment. Deviations between simulation and experiment may be due to continuous dynamic recrystallization.

Investigation of smoothness-increasing accuracy-conserving filters for improving streamline integration through discontinuous fields.

PubMed

Steffen, Michael; Curtis, Sean; Kirby, Robert M; Ryan, Jennifer K

2008-01-01

Streamline integration of fields produced by computational fluid mechanics simulations is a commonly used tool for the investigation and analysis of fluid flow phenomena. Integration is often accomplished through the application of ordinary differential equation (ODE) integrators--integrators whose error characteristics are predicated on the smoothness of the field through which the streamline is being integrated--smoothness which is not available at the inter-element level of finite volume and finite element data. Adaptive error control techniques are often used to ameliorate the challenge posed by inter-element discontinuities. As the root of the difficulties is the discontinuous nature of the data, we present a complementary approach of applying smoothness-enhancing accuracy-conserving filters to the data prior to streamline integration. We investigate whether such an approach applied to uniform quadrilateral discontinuous Galerkin (high-order finite volume) data can be used to augment current adaptive error control approaches. We discuss and demonstrate through numerical example the computational trade-offs exhibited when one applies such a strategy.

A 3-D enlarged cell technique (ECT) for elastic wave modelling of a curved free surface

NASA Astrophysics Data System (ADS)

Wei, Songlin; Zhou, Jianyang; Zhuang, Mingwei; Liu, Qing Huo

2016-09-01

The conventional finite-difference time-domain (FDTD) method for elastic waves suffers from the staircasing error when applied to model a curved free surface because of its structured grid. In this work, an improved, stable and accurate 3-D FDTD method for elastic wave modelling on a curved free surface is developed based on the finite volume method and enlarged cell technique (ECT). To achieve a sufficiently accurate implementation, a finite volume scheme is applied to the curved free surface to remove the staircasing error; in the mean time, to achieve the same stability as the FDTD method without reducing the time step increment, the ECT is introduced to preserve the solution stability by enlarging small irregular cells into adjacent cells under the condition of conservation of force. This method is verified by several 3-D numerical examples. Results show that the method is stable at the Courant stability limit for a regular FDTD grid, and has much higher accuracy than the conventional FDTD method.

Structure of the Nucleon and its Excitations

NASA Astrophysics Data System (ADS)

Kamleh, Waseem; Leinweber, Derek; Liu, Zhan-wei; Stokes, Finn; Thomas, Anthony; Thomas, Samuel; Wu, Jia-jun

2018-03-01

The structure of the ground state nucleon and its finite-volume excitations are examined from three different perspectives. Using new techniques to extract the relativistic components of the nucleon wave function, the node structure of both the upper and lower components of the nucleon wave function are illustrated. A non-trivial role for gluonic components is manifest. In the second approach, the parity-expanded variational analysis (PEVA) technique is utilised to isolate states at finite momenta, enabling a novel examination of the electric and magnetic form factors of nucleon excitations. Here the magnetic form factors of low-lying odd-parity nucleons are particularly interesting. Finally, the structure of the nucleon spectrum is examined in a Hamiltonian effective field theory analysis incorporating recent lattice-QCD determinations of low-lying two-particle scattering-state energies in the finite volume. The Roper resonance of Nature is observed to originate from multi-particle coupled-channel interactions while the first radial excitation of the nucleon sits much higher at approximately 1.9 GeV.

The influence of injection volume and capsular bag contraction on the refractive power of polymer refilled lenses - a finite element modelling simulation study.

PubMed

Martin, Heiner; Guthoff, Rudolf; Schmitz, Klaus-Peter

2011-09-01

Polymer injection into the capsular bag after phakoemulsification is an interesting and promising approach to lens surgery. Safe clinical application of this technique will require an appropriate estimate of the effect of implantation variables on the lens power. This article details the results of finite element investigations into the effects of the injected polymer volume and capsular bag contraction on the resultant lens power and accommodation amplitude. An axisymmetric finite element model was created from literature sources. Polymer injection and the capsular contraction were simulated, and their effect on the lens power was calculated. The simulations show that overfilling during polymer injection leads to a refractive power increase of the lens. Capsular bag contraction also results in a power increase. The calculated accommodative amplitude of the lens is minimally affected by capsular bag contraction but decreases significantly with increased capsular bag stiffness as a result of fibrosis. © 2010 The Authors. Journal compilation © 2010 Acta Ophthalmol.

High order finite volume WENO schemes for the Euler equations under gravitational fields

NASA Astrophysics Data System (ADS)

Li, Gang; Xing, Yulong

2016-07-01

Euler equations with gravitational source terms are used to model many astrophysical and atmospheric phenomena. This system admits hydrostatic balance where the flux produced by the pressure is exactly canceled by the gravitational source term, and two commonly seen equilibria are the isothermal and polytropic hydrostatic solutions. Exact preservation of these equilibria is desirable as many practical problems are small perturbations of such balance. High order finite difference weighted essentially non-oscillatory (WENO) schemes have been proposed in [22], but only for the isothermal equilibrium state. In this paper, we design high order well-balanced finite volume WENO schemes, which can preserve not only the isothermal equilibrium but also the polytropic hydrostatic balance state exactly, and maintain genuine high order accuracy for general solutions. The well-balanced property is obtained by novel source term reformulation and discretization, combined with well-balanced numerical fluxes. Extensive one- and two-dimensional simulations are performed to verify well-balanced property, high order accuracy, as well as good resolution for smooth and discontinuous solutions.

Infinity Computer and Calculus

NASA Astrophysics Data System (ADS)

Sergeyev, Yaroslav D.

2007-09-01

Traditional computers work with finite numbers. Situations where the usage of infinite or infinitesimal quantities is required are studied mainly theoretically. In this survey talk, a new computational methodology (that is not related to nonstandard analysis) is described. It is based on the principle `The part is less than the whole' applied to all numbers (finite, infinite, and infinitesimal) and to all sets and processes (finite and infinite). It is shown that it becomes possible to write down finite, infinite, and infinitesimal numbers by a finite number of symbols as particular cases of a unique framework. The new methodology allows us to introduce the Infinity Computer working with all these numbers (its simulator is presented during the lecture). The new computational paradigm both gives possibilities to execute computations of a new type and simplifies fields of mathematics where infinity and/or infinitesimals are encountered. Numerous examples of the usage of the introduced computational tools are given during the lecture.

The dynamics of discrete-time computation, with application to recurrent neural networks and finite state machine extraction.

PubMed

Casey, M

1996-08-15

Recurrent neural networks (RNNs) can learn to perform finite state computations. It is shown that an RNN performing a finite state computation must organize its state space to mimic the states in the minimal deterministic finite state machine that can perform that computation, and a precise description of the attractor structure of such systems is given. This knowledge effectively predicts activation space dynamics, which allows one to understand RNN computation dynamics in spite of complexity in activation dynamics. This theory provides a theoretical framework for understanding finite state machine (FSM) extraction techniques and can be used to improve training methods for RNNs performing FSM computations. This provides an example of a successful approach to understanding a general class of complex systems that has not been explicitly designed, e.g., systems that have evolved or learned their internal structure.

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

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

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

A Finite Element Framework for Studying the Mechanical Response of Macromolecules: Application to the Gating of the Mechanosensitive Channel MscL

PubMed Central

Tang, Yuye; Cao, Guoxin; Chen, Xi; Yoo, Jejoong; Yethiraj, Arun; Cui, Qiang

2006-01-01

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom-based techniques such as targeted or steered molecular-dynamics simulations, the finite element method-based continuum-mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scales and long timescales. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction. PMID:16731564

An Object-Oriented Finite Element Framework for Multiphysics Phase Field Simulations

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

Michael R Tonks; Derek R Gaston; Paul C Millett

2012-01-01

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a phase field framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory's finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in phase fields models to facilitate development of newmore » models with very little written code. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are included to demonstrate the muliphysics capability.« less

A Second Law Based Unstructured Finite Volume Procedure for Generalized Flow Simulation

NASA Technical Reports Server (NTRS)

Majumdar, Alok

1998-01-01

An unstructured finite volume procedure has been developed for steady and transient thermo-fluid dynamic analysis of fluid systems and components. The procedure is applicable for a flow network consisting of pipes and various fittings where flow is assumed to be one dimensional. It can also be used to simulate flow in a component by modeling a multi-dimensional flow using the same numerical scheme. The flow domain is discretized into a number of interconnected control volumes located arbitrarily in space. The conservation equations for each control volume account for the transport of mass, momentum and entropy from the neighboring control volumes. In addition, they also include the sources of each conserved variable and time dependent terms. The source term of entropy equation contains entropy generation due to heat transfer and fluid friction. Thermodynamic properties are computed from the equation of state of a real fluid. The system of equations is solved by a hybrid numerical method which is a combination of simultaneous Newton-Raphson and successive substitution schemes. The paper also describes the application and verification of the procedure by comparing its predictions with the analytical and numerical solution of several benchmark problems.

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.

Evaluation of β-blocker gel and effect of dosing volume for topical delivery.

PubMed

Zhang, Qian; Chantasart, Doungdaw; Li, S Kevin

2015-05-01

Although topical administration of β-blockers is desired because of the improved therapeutic efficacy and reduced systemic adverse effects compared with systemic administration in the treatment of infantile hemangioma, the permeation of β-blockers across skin under finite dose conditions has not been systematically studied and an effective topical β-blocker formulation for skin application is not available. The present study evaluated the permeation of β-blockers propranolol, betaxolol, and timolol across human epidermal membrane (HEM) from a topical gel in Franz diffusion cells in vitro under various dosing conditions. The effects of occlusion and dosing volume on percutaneous absorption of β-blockers from the gel were studied. The permeation data were compared with those of finite dose diffusion theory. The results showed that skin permeation of β-blockers generally could be enhanced two to three times by skin occlusion. The cumulative amounts of β-blockers permeated across HEM increased with increasing dosing volume. An adequate fit was obtained between the theoretical curve and experimental permeation data, indicating that the experimental results of the gel are consistent with finite dose diffusion theory. In conclusion, the findings suggest the feasibility of using topical gels of β-blockers for infantile hemangioma treatment and topical application with skin occlusion is preferred. © 2015 Wiley Periodicals, Inc. and the American Pharmacists Association.

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.

Modeling of electrical impedance tomography to detect breast cancer by finite volume methods

NASA Astrophysics Data System (ADS)

Ain, K.; Wibowo, R. A.; Soelistiono, S.

2017-05-01

The properties of the electrical impedance of tissue are an interesting study, because changes of the electrical impedance of organs are related to physiological and pathological. Both physiological and pathological properties are strongly associated with disease information. Several experiments shown that the breast cancer has a lower impedance than the normal breast tissue. Thus, the imaging based on impedance can be used as an alternative equipment to detect the breast cancer. This research carries out by modelling of Electrical Impedance Tomography to detect the breast cancer by finite volume methods. The research includes development of a mathematical model of the electric potential field by 2D Finite Volume Method, solving the forward problem and inverse problem by linear reconstruction method. The scanning is done by 16 channel electrode with neighbors method to collect data. The scanning is performed at a frequency of 10 kHz and 100 kHz with three objects numeric includes an anomaly at the surface, an anomaly at the depth and an anomaly at the surface and at depth. The simulation has been successfully to reconstruct image of functional anomalies of the breast cancer at the surface position, the depth position or a combination of surface and the depth.

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 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

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

A finite-volume ELLAM for three-dimensional solute-transport modeling

USGS Publications Warehouse

Russell, T.F.; Heberton, C.I.; Konikow, Leonard F.; Hornberger, G.Z.

2003-01-01

A three-dimensional finite-volume ELLAM method has been developed, tested, and successfully implemented as part of the U.S. Geological Survey (USGS) MODFLOW-2000 ground water modeling package. It is included as a solver option for the Ground Water Transport process. The FVELLAM uses space-time finite volumes oriented along the streamlines of the flow field to solve an integral form of the solute-transport equation, thus combining local and global mass conservation with the advantages of Eulerian-Lagrangian characteristic methods. The USGS FVELLAM code simulates solute transport in flowing ground water for a single dissolved solute constituent and represents the processes of advective transport, hydrodynamic dispersion, mixing from fluid sources, retardation, and decay. Implicit time discretization of the dispersive and source/sink terms is combined with a Lagrangian treatment of advection, in which forward tracking moves mass to the new time level, distributing mass among destination cells using approximate indicator functions. This allows the use of large transport time increments (large Courant numbers) with accurate results, even for advection-dominated systems (large Peclet numbers). Four test cases, including comparisons with analytical solutions and benchmarking against other numerical codes, are presented that indicate that the FVELLAM can usually yield excellent results, even if relatively few transport time steps are used, although the quality of the results is problem-dependent.

Nonlinear Computational Aeroelasticity: Formulations and Solution Algorithms

DTIC Science & Technology

2003-03-01

problem is proposed. Fluid-structure coupling algorithms are then discussed with some emphasis on distributed computing strategies. Numerical results...the structure and the exchange of structure motion to the fluid. The computational fluid dynamics code PFES is our finite element code for the numerical ...unstructured meshes). It was numerically demonstrated [1-3] that EBS can be less diffusive than SUPG [4-6] and the standard Finite Volume schemes

Brittle to ductile transition in a model of sheared granular materials

NASA Astrophysics Data System (ADS)

Ma, X.; Elbanna, A. E.

2016-12-01

Understanding the fundamental mechanisms of deformation and failure in sheared fault gouge is critical for the development of physics-based earthquake rupture simulations that are becoming an essential ingredient in next generation hazard and risk models. To that end, we use the shear transformation zone (STZ) theory, a non-equilibrium statistical thermodynamics framework to describe viscoplastic deformation and localization in gouge materials as a first step towards developing multiscale models for earthquake source processes that are informed by high-resolution fault zone physics. The primary ingredient of the STZ theory is that inelastic deformation occurs at rare and local non-interacting soft zones known as the shear transformation zones. The larger the number of these STZs the more disordered (the more loose) the layer is. We will describe an implementation of this theory in a 2D/3D finite element framework, accounting for finite deformation, under both axial and shear loading and for dry and saturated conditions. We examine conditions under which a localized shear band may form and show that the initial value of disorder (or the initial porosity) plays an important role. In particular, our simulations suggest that if the material is more compact initially, the behavior is more brittle and the plastic deformation localizes with generating large strength drop. On the other hand, an initially loose material will show a more ductile response and the plastic deformations will be distributed more broadly. We will further show that incorporation of pore fluids alters the localization pattern and changes the stress slip response due to coupling between gouge volume changes (compaction and dilation) and pore pressure build up. We validate the model predictions by comparing them to available experimental observations on strain localization and fault gouge strength evolution. Finally, we discuss the implications of our model for gouge friction and dynamic weakening.

Stochastic interpretation of the advection-diffusion equation and its relevance to bed load transport

NASA Astrophysics Data System (ADS)

Ancey, C.; Bohorquez, P.; Heyman, J.

2015-12-01

The advection-diffusion equation is one of the most widespread equations in physics. It arises quite often in the context of sediment transport, e.g., for describing time and space variations in the particle activity (the solid volume of particles in motion per unit streambed area). Phenomenological laws are usually sufficient to derive this equation and interpret its terms. Stochastic models can also be used to derive it, with the significant advantage that they provide information on the statistical properties of particle activity. These models are quite useful when sediment transport exhibits large fluctuations (typically at low transport rates), making the measurement of mean values difficult. Among these stochastic models, the most common approach consists of random walk models. For instance, they have been used to model the random displacement of tracers in rivers. Here we explore an alternative approach, which involves monitoring the evolution of the number of particles moving within an array of cells of finite length. Birth-death Markov processes are well suited to this objective. While the topic has been explored in detail for diffusion-reaction systems, the treatment of advection has received no attention. We therefore look into the possibility of deriving the advection-diffusion equation (with a source term) within the framework of birth-death Markov processes. We show that in the continuum limit (when the cell size becomes vanishingly small), we can derive an advection-diffusion equation for particle activity. Yet while this derivation is formally valid in the continuum limit, it runs into difficulty in practical applications involving cells or meshes of finite length. Indeed, within our stochastic framework, particle advection produces nonlocal effects, which are more or less significant depending on the cell size and particle velocity. Albeit nonlocal, these effects look like (local) diffusion and add to the intrinsic particle diffusion (dispersal due to velocity fluctuations), with the important consequence that local measurements depend on both the intrinsic properties of particle displacement and the dimensions of the measurement system.

Algebraic Semantics for Narrative

ERIC Educational Resources Information Center

Kahn, E.

1974-01-01

This paper uses discussion of Edmund Spenser's "The Faerie Queene" to present a theoretical framework for explaining the semantics of narrative discourse. The algebraic theory of finite automata is used. (CK)

Solution of Eshelby's inclusion problem with a bounded domain and Eshelby's tensor for a spherical inclusion in a finite spherical matrix based on a simplified strain gradient elasticity theory

NASA Astrophysics Data System (ADS)

Gao, X.-L.; Ma, H. M.

2010-05-01

A solution for Eshelby's inclusion problem of a finite homogeneous isotropic elastic body containing an inclusion prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is derived in a general form using a simplified strain gradient elasticity theory (SSGET). An extended Betti's reciprocal theorem and an extended Somigliana's identity based on the SSGET are proposed and utilized to solve the finite-domain inclusion problem. The solution for the disturbed displacement field is expressed in terms of the Green's function for an infinite three-dimensional elastic body in the SSGET. It contains a volume integral term and a surface integral term. The former is the same as that for the infinite-domain inclusion problem based on the SSGET, while the latter represents the boundary effect. The solution reduces to that of the infinite-domain inclusion problem when the boundary effect is not considered. The problem of a spherical inclusion embedded concentrically in a finite spherical elastic body is analytically solved by applying the general solution, with the Eshelby tensor and its volume average obtained in closed forms. This Eshelby tensor depends on the position, inclusion size, matrix size, and material length scale parameter, and, as a result, can capture the inclusion size and boundary effects, unlike existing Eshelby tensors. It reduces to the classical Eshelby tensor for the spherical inclusion in an infinite matrix if both the strain gradient and boundary effects are suppressed. Numerical results quantitatively show that the inclusion size effect can be quite large when the inclusion is very small and that the boundary effect can dominate when the inclusion volume fraction is very high. However, the inclusion size effect is diminishing as the inclusion becomes large enough, and the boundary effect is vanishing as the inclusion volume fraction gets sufficiently low.

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Berdnarcyk, Brett A.; Arnold, Steven M.; Collier, Craig S.

2009-01-01

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

Phase Transitions in Finite Systems

NASA Astrophysics Data System (ADS)

Chomaz, Philippe; Gulminelli, Francesca

In this series of lectures we will first review the general theory of phase transition in the framework of information theory and briefly address some of the well known mean field solutions of three dimensional problems. The theory of phase transitions in finite systems will then be discussed, with a special emphasis to the conceptual problems linked to a thermodynamical description for small, short-lived, open systems as metal clusters and data samples coming from nuclear collisions. The concept of negative heat capacity developed in the early seventies in the context of self-gravitating systems will be reinterpreted in the general framework of convexity anomalies of thermostatistical potentials. The connection with the distribution of the order parameter will lead us to a definition of first order phase transitions in finite systems based on topology anomalies of the event distribution in the space of observations. Finally a careful study of the thermodynamical limit will provide a bridge with the standard theory of phase transitions and show that in a wide class of physical situations the different statistical ensembles are irreducibly inequivalent.

Formulation and Validation of an Efficient Computational Model for a Dilute, Settling Suspension Undergoing Rotational Mixing

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

Sprague, Michael A.; Stickel, Jonathan J.; Sitaraman, Hariswaran

Designing processing equipment for the mixing of settling suspensions is a challenging problem. Achieving low-cost mixing is especially difficult for the application of slowly reacting suspended solids because the cost of impeller power consumption becomes quite high due to the long reaction times (batch mode) or due to large-volume reactors (continuous mode). Further, the usual scale-up metrics for mixing, e.g., constant tip speed and constant power per volume, do not apply well for mixing of suspensions. As an alternative, computational fluid dynamics (CFD) can be useful for analyzing mixing at multiple scales and determining appropriate mixer designs and operating parameters.more » We developed a mixture model to describe the hydrodynamics of a settling cellulose suspension. The suspension motion is represented as a single velocity field in a computationally efficient Eulerian framework. The solids are represented by a scalar volume-fraction field that undergoes transport due to particle diffusion, settling, fluid advection, and shear stress. A settling model and a viscosity model, both functions of volume fraction, were selected to fit experimental settling and viscosity data, respectively. Simulations were performed with the open-source Nek5000 CFD program, which is based on the high-order spectral-finite-element method. Simulations were performed for the cellulose suspension undergoing mixing in a laboratory-scale vane mixer. The settled-bed heights predicted by the simulations were in semi-quantitative agreement with experimental observations. Further, the simulation results were in quantitative agreement with experimentally obtained torque and mixing-rate data, including a characteristic torque bifurcation. In future work, we plan to couple this CFD model with a reaction-kinetics model for the enzymatic digestion of cellulose, allowing us to predict enzymatic digestion performance for various mixing intensities and novel reactor designs.« less

The effects of load history and design variables on performance limit states of circular bridge columns - volume 3 : analysis methods.

DOT National Transportation Integrated Search

2015-01-01

This report is the third of three volumes and presents the numerical portion of the research project on the impacts of loading history on : the behavior of reinforced concrete bridge columns. Two independent finite element methods were utilized to ac...

LaRC design analysis report for National Transonic Facility for 304 stainless steel tunnel shell. Volume 1S: Finite difference analysis of cone/cylinder junction

NASA Technical Reports Server (NTRS)

Ramsey, J. W., Jr.; Taylor, J. T.; Wilson, J. F.; Gray, C. E., Jr.; Leatherman, A. D.; Rooker, J. R.; Allred, J. W.

1976-01-01

The results of extensive computer (finite element, finite difference and numerical integration), thermal, fatigue, and special analyses of critical portions of a large pressurized, cryogenic wind tunnel (National Transonic Facility) are presented. The computer models, loading and boundary conditions are described. Graphic capability was used to display model geometry, section properties, and stress results. A stress criteria is presented for evaluation of the results of the analyses. Thermal analyses were performed for major critical and typical areas. Fatigue analyses of the entire tunnel circuit are presented.

High-Order Entropy Stable Formulations for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Carpenter, Mark H.; Fisher, Travis C.

2013-01-01

A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.

A new family of stable elements for the Stokes problem based on a mixed Galerkin/least-squares finite element formulation

NASA Technical Reports Server (NTRS)

Franca, Leopoldo P.; Loula, Abimael F. D.; Hughes, Thomas J. R.; Miranda, Isidoro

1989-01-01

Adding to the classical Hellinger-Reissner formulation, a residual form of the equilibrium equation, a new Galerkin/least-squares finite element method is derived. It fits within the framework of a mixed finite element method and is stable for rather general combinations of stress and velocity interpolations, including equal-order discontinuous stress and continuous velocity interpolations which are unstable within the Galerkin approach. Error estimates are presented based on a generalization of the Babuska-Brezzi theory. Numerical results (not presented herein) have confirmed these estimates as well as the good accuracy and stability of the method.

Some effects of finite spatial resolution on skin friction measurements in turbulent boundary layers

NASA Technical Reports Server (NTRS)

Westphal, Russell V.

1988-01-01

The effects of finite spatial resolution often cause serious errors in measurements in turbulent boundary layers, with particularly large effects for measurements of fluctuating skin friction and velocities within the sublayer. However, classical analyses of finite spatial resolution effects have generally not accounted for the substantial inhomogeneity and anisotropy of near-wall turbulence. The present study has made use of results from recent computational simulations of wall-bounded turbulent flows to examine spatial resolution effects for measurements made at a wall using both single-sensor probes and those employing two sensing volumes in a V shape. Results are presented to show the effects of finite spatial resolution on a variety of quantitites deduced from the skin friction field.

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

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

Assessment of chemistry models for compressible reacting flows

NASA Astrophysics Data System (ADS)

Lapointe, Simon; Blanquart, Guillaume

2014-11-01

Recent technological advances in propulsion and power devices and renewed interest in the development of next generation supersonic and hypersonic vehicles have increased the need for detailed understanding of turbulence-combustion interactions in compressible reacting flows. In numerical simulations of such flows, accurate modeling of the fuel chemistry is a critical component of capturing the relevant physics. Various chemical models are currently being used in reacting flow simulations. However, the differences between these models and their impacts on the fluid dynamics in the context of compressible flows are not well understood. In the present work, a numerical code is developed to solve the fully coupled compressible conservation equations for reacting flows. The finite volume code is based on the theoretical and numerical framework developed by Oefelein (Prog. Aero. Sci. 42 (2006) 2-37) and employs an all-Mach-number formulation with dual time-stepping and preconditioning. The numerical approach is tested on turbulent premixed flames at high Karlovitz numbers. Different chemical models of varying complexity and computational cost are used and their effects are compared.

Large eddy simulation modeling of particle-laden flows in complex terrain

NASA Astrophysics Data System (ADS)

Salesky, S.; Giometto, M. G.; Chamecki, M.; Lehning, M.; Parlange, M. B.

2017-12-01

The transport, deposition, and erosion of heavy particles over complex terrain in the atmospheric boundary layer is an important process for hydrology, air quality forecasting, biology, and geomorphology. However, in situ observations can be challenging in complex terrain due to spatial heterogeneity. Furthermore, there is a need to develop numerical tools that can accurately represent the physics of these multiphase flows over complex surfaces. We present a new numerical approach to accurately model the transport and deposition of heavy particles in complex terrain using large eddy simulation (LES). Particle transport is represented through solution of the advection-diffusion equation including terms that represent gravitational settling and inertia. The particle conservation equation is discretized in a cut-cell finite volume framework in order to accurately enforce mass conservation. Simulation results will be validated with experimental data, and numerical considerations required to enforce boundary conditions at the surface will be discussed. Applications will be presented in the context of snow deposition and transport, as well as urban dispersion.

A Gas Dynamics Method Based on The Spectral Deferred Corrections (SDC) Time Integration Technique and The Piecewise Parabolic Method (PPM)

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

Samet Y. Kadioglu

2011-12-01

We present a computational gas dynamics method based on the Spectral Deferred Corrections (SDC) time integration technique and the Piecewise Parabolic Method (PPM) finite volume method. The PPM framework is used to define edge averaged quantities which are then used to evaluate numerical flux functions. The SDC technique is used to integrate solution in time. This kind of approach was first taken by Anita et al in [17]. However, [17] is problematic when it is implemented to certain shock problems. Here we propose significant improvements to [17]. The method is fourth order (both in space and time) for smooth flows,more » and provides highly resolved discontinuous solutions. We tested the method by solving variety of problems. Results indicate that the fourth order of accuracy in both space and time has been achieved when the flow is smooth. Results also demonstrate the shock capturing ability of the method.« less

The Bethe ansatz

NASA Astrophysics Data System (ADS)

Levkovich-Maslyuk, Fedor

2016-08-01

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based on the exact S-matrix. Then we illustrate this method in several concrete theories. The first case we study is the SU(2) chiral Gross-Neveu model. We derive the Bethe equations via algebraic Bethe ansatz, solving in the process the Heisenberg XXX spin chain. We discuss this famous spin chain model in some detail, covering in particular the coordinate Bethe ansatz, some properties of Bethe states, and the classical scaling limit leading to finite-gap equations. Then we proceed to the more involved SU(3) chiral Gross-Neveu model and derive the Bethe equations using nested algebraic Bethe ansatz to solve the arising SU(3) spin chain. Finally we show how a method similar to the Bethe ansatz works in a completely different setting, namely for the 1D oscillator in quantum mechanics.

BISON Theory Manual The Equations behind Nuclear Fuel Analysis

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

Hales, J. D.; Williamson, R. L.; Novascone, S. R.

2016-09-01

BISON is a finite element-based nuclear fuel performance code applicable to a variety of fuel forms including light water reactor fuel rods, TRISO particle fuel, and metallic rod and plate fuel. It solves the fully-coupled equations of thermomechanics and species diffusion, for either 2D axisymmetric or 3D geometries. Fuel models are included to describe temperature and burnup dependent thermal properties, fission product swelling, densification, thermal and irradiation creep, fracture, and fission gas production and release. Plasticity, irradiation growth, and thermal and irradiation creep models are implemented for clad materials. Models are also available to simulate gap heat transfer, mechanical contact,more » and the evolution of the gap/plenum pressure with plenum volume, gas temperature, and fission gas addition. BISON is based on the MOOSE framework and can therefore efficiently solve problems using standard workstations or very large high-performance computers. This document describes the theoretical and numerical foundations of BISON.« less

Swimming in a two-dimensional Brinkman fluid: Computational modeling and regularized solutions

NASA Astrophysics Data System (ADS)

Leiderman, Karin; Olson, Sarah D.

2016-02-01

The incompressible Brinkman equation represents the homogenized fluid flow past obstacles that comprise a small volume fraction. In nondimensional form, the Brinkman equation can be characterized by a single parameter that represents the friction or resistance due to the obstacles. In this work, we derive an exact fundamental solution for 2D Brinkman flow driven by a regularized point force and describe the numerical method to use it in practice. To test our solution and method, we compare numerical results with an analytic solution of a stationary cylinder in a uniform Brinkman flow. Our method is also compared to asymptotic theory; for an infinite-length, undulating sheet of small amplitude, we recover an increasing swimming speed as the resistance is increased. With this computational framework, we study a model swimmer of finite length and observe an enhancement in propulsion and efficiency for small to moderate resistance. Finally, we study the interaction of two swimmers where attraction does not occur when the initial separation distance is larger than the screening length.

PRISM: An open source framework for the interactive design of GPU volume rendering shaders.

PubMed

Drouin, Simon; Collins, D Louis

2018-01-01

Direct volume rendering has become an essential tool to explore and analyse 3D medical images. Despite several advances in the field, it remains a challenge to produce an image that highlights the anatomy of interest, avoids occlusion of important structures, provides an intuitive perception of shape and depth while retaining sufficient contextual information. Although the computer graphics community has proposed several solutions to address specific visualization problems, the medical imaging community still lacks a general volume rendering implementation that can address a wide variety of visualization use cases while avoiding complexity. In this paper, we propose a new open source framework called the Programmable Ray Integration Shading Model, or PRISM, that implements a complete GPU ray-casting solution where critical parts of the ray integration algorithm can be replaced to produce new volume rendering effects. A graphical user interface allows clinical users to easily experiment with pre-existing rendering effect building blocks drawn from an open database. For programmers, the interface enables real-time editing of the code inside the blocks. We show that in its default mode, the PRISM framework produces images very similar to those produced by a widely-adopted direct volume rendering implementation in VTK at comparable frame rates. More importantly, we demonstrate the flexibility of the framework by showing how several volume rendering techniques can be implemented in PRISM with no more than a few lines of code. Finally, we demonstrate the simplicity of our system in a usability study with 5 medical imaging expert subjects who have none or little experience with volume rendering. The PRISM framework has the potential to greatly accelerate development of volume rendering for medical applications by promoting sharing and enabling faster development iterations and easier collaboration between engineers and clinical personnel.

PRISM: An open source framework for the interactive design of GPU volume rendering shaders

PubMed Central

Collins, D. Louis

2018-01-01

Direct volume rendering has become an essential tool to explore and analyse 3D medical images. Despite several advances in the field, it remains a challenge to produce an image that highlights the anatomy of interest, avoids occlusion of important structures, provides an intuitive perception of shape and depth while retaining sufficient contextual information. Although the computer graphics community has proposed several solutions to address specific visualization problems, the medical imaging community still lacks a general volume rendering implementation that can address a wide variety of visualization use cases while avoiding complexity. In this paper, we propose a new open source framework called the Programmable Ray Integration Shading Model, or PRISM, that implements a complete GPU ray-casting solution where critical parts of the ray integration algorithm can be replaced to produce new volume rendering effects. A graphical user interface allows clinical users to easily experiment with pre-existing rendering effect building blocks drawn from an open database. For programmers, the interface enables real-time editing of the code inside the blocks. We show that in its default mode, the PRISM framework produces images very similar to those produced by a widely-adopted direct volume rendering implementation in VTK at comparable frame rates. More importantly, we demonstrate the flexibility of the framework by showing how several volume rendering techniques can be implemented in PRISM with no more than a few lines of code. Finally, we demonstrate the simplicity of our system in a usability study with 5 medical imaging expert subjects who have none or little experience with volume rendering. The PRISM framework has the potential to greatly accelerate development of volume rendering for medical applications by promoting sharing and enabling faster development iterations and easier collaboration between engineers and clinical personnel. PMID:29534069

jInv: A Modular and Scalable Framework for Electromagnetic Inverse Problems

NASA Astrophysics Data System (ADS)

Belliveau, P. T.; Haber, E.

2016-12-01

Inversion is a key tool in the interpretation of geophysical electromagnetic (EM) data. Three-dimensional (3D) EM inversion is very computationally expensive and practical software for inverting large 3D EM surveys must be able to take advantage of high performance computing (HPC) resources. It has traditionally been difficult to achieve those goals in a high level dynamic programming environment that allows rapid development and testing of new algorithms, which is important in a research setting. With those goals in mind, we have developed jInv, a framework for PDE constrained parameter estimation problems. jInv provides optimization and regularization routines, a framework for user defined forward problems, and interfaces to several direct and iterative solvers for sparse linear systems. The forward modeling framework provides finite volume discretizations of differential operators on rectangular tensor product meshes and tetrahedral unstructured meshes that can be used to easily construct forward modeling and sensitivity routines for forward problems described by partial differential equations. jInv is written in the emerging programming language Julia. Julia is a dynamic language targeted at the computational science community with a focus on high performance and native support for parallel programming. We have developed frequency and time-domain EM forward modeling and sensitivity routines for jInv. We will illustrate its capabilities and performance with two synthetic time-domain EM inversion examples. First, in airborne surveys, which use many sources, we achieve distributed memory parallelism by decoupling the forward and inverse meshes and performing forward modeling for each source on small, locally refined meshes. Secondly, we invert grounded source time-domain data from a gradient array style induced polarization survey using a novel time-stepping technique that allows us to compute data from different time-steps in parallel. These examples both show that it is possible to invert large scale 3D time-domain EM datasets within a modular, extensible framework written in a high-level, easy to use programming language.

On the Behavior of Eisenstein Series Through Elliptic Degeneration

NASA Astrophysics Data System (ADS)

Garbin, D.; Pippich, A.-M. V.

2009-12-01

Let Γ be a Fuchsian group of the first kind acting on the hyperbolic upper half plane {mathbb{H}}, and let {M = Γbackslash mathbb{H}} be the associated finite volume hyperbolic Riemann surface. If γ is a primitive parabolic, hyperbolic, resp. elliptic element of Γ, there is an associated parabolic, hyperbolic, resp. elliptic Eisenstein series. In this article, we study the limiting behavior of these Eisenstein series on an elliptically degenerating family of finite volume hyperbolic Riemann surfaces. In particular, we prove the following result. The elliptic Eisenstein series associated to a degenerating elliptic element converges up to a factor to the parabolic Eisenstein series associated to the parabolic element which fixes the newly developed cusp on the limit surface.

Finite-volume Atmospheric Model of the IAP/LASG (FAMIL)

NASA Astrophysics Data System (ADS)

Bao, Q.

2015-12-01

The Finite-volume Atmospheric Model of the IAP/LASG (FAMIL) is introduced in this work. FAMIL have the flexible horizontal and vertical resolutions up to 25km and 1Pa respectively, which currently running on the "Tianhe 1A&2" supercomputers. FAMIL is the atmospheric component of the third-generation Flexible Global Ocean-Atmosphere-Land climate System model (FGOALS3) which will participate in the Coupled Model Intercomparison Project Phase 6 (CMIP6). In addition to describing the dynamical core and physical parameterizations of FAMIL, this talk describes the simulated characteristics of energy and water balances, precipitation, Asian Summer Monsoon and stratospheric circulation, and compares them with observational/reanalysis data. Finally, the model biases as well as possible solutions are discussed.

Numerical investigation of finite-volume effects for the HVP

NASA Astrophysics Data System (ADS)

Boyle, Peter; Gülpers, Vera; Harrison, James; Jüttner, Andreas; Portelli, Antonin; Sachrajda, Christopher

2018-03-01

It is important to correct for finite-volume (FV) effects in the presence of QED, since these effects are typically large due to the long range of the electromagnetic interaction. We recently made the first lattice calculation of electromagnetic corrections to the hadronic vacuum polarisation (HVP). For the HVP, an analytical derivation of FV corrections involves a two-loop calculation which has not yet been carried out. We instead calculate the universal FV corrections numerically, using lattice scalar QED as an effective theory. We show that this method gives agreement with known analytical results for scalar mass FV effects, before applying it to calculate FV corrections for the HVP. This method for numerical calculation of FV effects is also widely applicable to quantities beyond the HVP.

Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

NASA Astrophysics Data System (ADS)

Huang, Juntao; Shu, Chi-Wang

2018-05-01

In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu [43]. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.

On 3-D inelastic analysis methods for hot section components. Volume 1: Special finite element models

NASA Technical Reports Server (NTRS)

Nakazawa, S.

1988-01-01

This annual status report presents the results of work performed during the fourth year of the 3-D Inelastic Analysis Methods for Hot Section Components program (NASA Contract NAS3-23697). The objective of the program is to produce a series of new computer codes permitting more accurate and efficient 3-D analysis of selected hot section components, i.e., combustor liners, turbine blades and turbine vanes. The computer codes embody a progression of math models and are streamlined to take advantage of geometrical features, loading conditions, and forms of material response that distinguish each group of selected components. Volume 1 of this report discusses the special finite element models developed during the fourth year of the contract.

Ceramic component reliability with the restructured NASA/CARES computer program

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Starlinger, Alois; Gyekenyesi, John P.

1992-01-01

The Ceramics Analysis and Reliability Evaluation of Structures (CARES) integrated design program on statistical fast fracture reliability and monolithic ceramic components is enhanced to include the use of a neutral data base, two-dimensional modeling, and variable problem size. The data base allows for the efficient transfer of element stresses, temperatures, and volumes/areas from the finite element output to the reliability analysis program. Elements are divided to insure a direct correspondence between the subelements and the Gaussian integration points. Two-dimensional modeling is accomplished by assessing the volume flaw reliability with shell elements. To demonstrate the improvements in the algorithm, example problems are selected from a round-robin conducted by WELFEP (WEakest Link failure probability prediction by Finite Element Postprocessors).

Bound-preserving Legendre-WENO finite volume schemes using nonlinear mapping

NASA Astrophysics Data System (ADS)

Smith, Timothy; Pantano, Carlos

2017-11-01

We present a new method to enforce field bounds in high-order Legendre-WENO finite volume schemes. The strategy consists of reconstructing each field through an intermediate mapping, which by design satisfies realizability constraints. Determination of the coefficients of the polynomial reconstruction involves nonlinear equations that are solved using Newton's method. The selection between the original or mapped reconstruction is implemented dynamically to minimize computational cost. The method has also been generalized to fields that exhibit interdependencies, requiring multi-dimensional mappings. Further, the method does not depend on the existence of a numerical flux function. We will discuss details of the proposed scheme and show results for systems in conservation and non-conservation form. This work was funded by the NSF under Grant DMS 1318161.

Unstructured Finite Volume Computational Thermo-Fluid Dynamic Method for Multi-Disciplinary Analysis and Design Optimization

NASA Technical Reports Server (NTRS)

Majumdar, Alok; Schallhorn, Paul

1998-01-01

This paper describes a finite volume computational thermo-fluid dynamics method to solve for Navier-Stokes equations in conjunction with energy equation and thermodynamic equation of state in an unstructured coordinate system. The system of equations have been solved by a simultaneous Newton-Raphson method and compared with several benchmark solutions. Excellent agreements have been obtained in each case and the method has been found to be significantly faster than conventional Computational Fluid Dynamic(CFD) methods and therefore has the potential for implementation in Multi-Disciplinary analysis and design optimization in fluid and thermal systems. The paper also describes an algorithm of design optimization based on Newton-Raphson method which has been recently tested in a turbomachinery application.

An unstaggered central scheme on nonuniform grids for the simulation of a compressible two-phase flow model

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

Touma, Rony; Zeidan, Dia

In this paper we extend a central finite volume method on nonuniform grids to the case of drift-flux two-phase flow problems. The numerical base scheme is an unstaggered, non oscillatory, second-order accurate finite volume scheme that evolves a piecewise linear numerical solution on a single grid and uses dual cells intermediately while updating the numerical solution to avoid the resolution of the Riemann problems arising at the cell interfaces. We then apply the numerical scheme and solve a classical drift-flux problem. The obtained results are in good agreement with corresponding ones appearing in the recent literature, thus confirming the potentialmore » of the proposed scheme.« less

A QR accelerated volume-to-surface boundary condition for finite element solution of eddy current problems

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

White, D; Fasenfest, B; Rieben, R

2006-09-08

We are concerned with the solution of time-dependent electromagnetic eddy current problems using a finite element formulation on three-dimensional unstructured meshes. We allow for multiple conducting regions, and our goal is to develop an efficient computational method that does not require a computational mesh of the air/vacuum regions. This requires a sophisticated global boundary condition specifying the total fields on the conductor boundaries. We propose a Biot-Savart law based volume-to-surface boundary condition to meet this requirement. This Biot-Savart approach is demonstrated to be very accurate. In addition, this approach can be accelerated via a low-rank QR approximation of the discretizedmore » Biot-Savart law.« less

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.

Model Uncertainty and Test of a Segmented Mirror Telescope

DTIC Science & Technology

2014-03-01

Optical Telescope project EOM: equation of motion FCA: fine control actuator FCD: Face-Centered Cubic Design FEA: finite element analysis FEM: finite...housed in a dark tent to isolate the telescope from stray light, air currents, or dust and other debris. However, the closed volume is prone to...is composed of six hexagonal segments that each have six coarse control actuators (CCA) for segment phasing control, three fine control actuators

Finite element modelling of fibre Bragg grating strain sensors and experimental validation

NASA Astrophysics Data System (ADS)

Malik, Shoaib A.; Mahendran, Ramani S.; Harris, Dee; Paget, Mark; Pandita, Surya D.; Machavaram, Venkata R.; Collins, David; Burns, Jonathan M.; Wang, Liwei; Fernando, Gerard F.

2009-03-01

Fibre Bragg grating (FBG) sensors continue to be used extensively for monitoring strain and temperature in and on engineering materials and structures. Previous researchers have also developed analytical models to predict the loadtransfer characteristics of FBG sensors as a function of applied strain. The general properties of the coating or adhesive that is used to surface-bond the FBG sensor to the substrate has also been modelled using finite element analysis. In this current paper, a technique was developed to surface-mount FBG sensors with a known volume and thickness of adhesive. The substrates used were aluminium dog-bone tensile test specimens. The FBG sensors were tensile tested in a series of ramp-hold sequences until failure. The reflected FBG spectra were recorded using a commercial instrument. Finite element analysis was performed to model the response of the surface-mounted FBG sensors. In the first instance, the effect of the mechanical properties of the adhesive and substrate were modelled. This was followed by modelling the volume of adhesive used to bond the FBG sensor to the substrate. Finally, the predicted values obtained via finite element modelling were correlated to the experimental results. In addition to the FBG sensors, the tensile test specimens were instrumented with surface-mounted electrical resistance strain gauges.

Investigation of supersonic chemically reacting and radiating channel flow

NASA Technical Reports Server (NTRS)

Mani, Mortaza; Tiwari, Surendra N.

1988-01-01

The 2-D time-dependent Navier-Stokes equations are used to investigate supersonic flows undergoing finite rate chemical reaction and radiation interaction for a hydrogen-air system. The explicit multistage finite volume technique of Jameson is used to advance the governing equations in time until convergence is achieved. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The multidimensional radiative transfer equations for a nongray model are provided for a general configuration and then reduced for a planar geometry. Both pseudo-gray and nongray models are used to represent the absorption-emission characteristics of the participating species. The supersonic inviscid and viscous, nonreacting flows are solved by employing the finite volume technique of Jameson and the unsplit finite difference scheme of MacCormack. The specified problem considered is of the flow in a channel with a 10 deg compression-expansion ramp. The calculated results are compared with those of an upwind scheme. The problem of chemically reacting and radiating flows are solved for the flow of premixed hydrogen-air through a channel with parallel boundaries, and a channel with a compression corner. Results obtained for specific conditions indicate that the radiative interaction can have a significant influence on the entire flow field.

Electrodiffusion: a continuum modeling framework for biomolecular systems with realistic spatiotemporal resolution.

PubMed

Lu, Benzhuo; Zhou, Y C; Huber, Gary A; Bond, Stephen D; Holst, Michael J; McCammon, J Andrew

2007-10-07

A computational framework is presented for the continuum modeling of cellular biomolecular diffusion influenced by electrostatic driving forces. This framework is developed from a combination of state-of-the-art numerical methods, geometric meshing, and computer visualization tools. In particular, a hybrid of (adaptive) finite element and boundary element methods is adopted to solve the Smoluchowski equation (SE), the Poisson equation (PE), and the Poisson-Nernst-Planck equation (PNPE) in order to describe electrodiffusion processes. The finite element method is used because of its flexibility in modeling irregular geometries and complex boundary conditions. The boundary element method is used due to the convenience of treating the singularities in the source charge distribution and its accurate solution to electrostatic problems on molecular boundaries. Nonsteady-state diffusion can be studied using this framework, with the electric field computed using the densities of charged small molecules and mobile ions in the solvent. A solution for mesh generation for biomolecular systems is supplied, which is an essential component for the finite element and boundary element computations. The uncoupled Smoluchowski equation and Poisson-Boltzmann equation are considered as special cases of the PNPE in the numerical algorithm, and therefore can be solved in this framework as well. Two types of computations are reported in the results: stationary PNPE and time-dependent SE or Nernst-Planck equations solutions. A biological application of the first type is the ionic density distribution around a fragment of DNA determined by the equilibrium PNPE. The stationary PNPE with nonzero flux is also studied for a simple model system, and leads to an observation that the interference on electrostatic field of the substrate charges strongly affects the reaction rate coefficient. The second is a time-dependent diffusion process: the consumption of the neurotransmitter acetylcholine by acetylcholinesterase, determined by the SE and a single uncoupled solution of the Poisson-Boltzmann equation. The electrostatic effects, counterion compensation, spatiotemporal distribution, and diffusion-controlled reaction kinetics are analyzed and different methods are compared.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Effect of framework material and vertical misfit on stress distribution in implant-supported partial prosthesis under load application: 3-D finite element analysis.

PubMed

Bacchi, Ataís; Consani, Rafael Leonardo Xediek; Mesquita, Marcelo Ferraz; Dos Santos, Mateus Bertolini Fernandes

2013-09-01

This study evaluated the influence of framework material and vertical misfit on stress created in an implant-supported partial prosthesis under load application. The posterior part of a severely reabsorbed jaw with a fixed partial prosthesis above two osseointegrated titanium implants at the place of the second premolar and second molar was modeled using SolidWorks 2010 software. Finite element models were obtained by importing the solid model into an ANSYS Workbench 11 simulation. The models were divided into 15 groups according to their prosthetic framework material (type IV gold alloy, silver-palladium alloy, commercially pure titanium, cobalt-chromium alloy or zirconia) and vertical misfit level (10 µm, 50 µm and 100 µm). After settlement of the prosthesis with the closure of the misfit, simultaneous loads of 110 N vertical and 15 N horizontal were applied on the occlusal and lingual faces of each tooth, respectively. The data was evaluated using Maximum Principal Stress (framework, porcelain veneer and bone tissue) and a von Mises Stress (retention screw) provided by the software. As a result, stiffer frameworks presented higher stress concentrations; however, these frameworks led to lower stresses in the porcelain veneer, the retention screw (faced to 10 µm and 50 µm of the misfit) and the peri-implant bone tissues. The increase in the vertical misfit resulted in stress values increasing in all of the prosthetic structures and peri-implant bone tissues. The framework material and vertical misfit level presented a relevant influence on the stresses for all of the structures evaluated.

Generation of deterministic tsunami hazard maps in the Bay of Cadiz, south-west Spain

NASA Astrophysics Data System (ADS)

Álvarez-Gómez, J. A.; Otero, L.; Olabarrieta, M.; González, M.; Carreño, E.; Baptista, M. A.; Miranda, J. M.; Medina, R.; Lima, V.

2009-04-01

The bay of Cádiz is a densely populated and industrialized area, and an important centre of tourism which multiplies its population in the summer months. This bay is situated in the Gulf of Cádiz, the south-west Atlantic margin of the Iberian Peninsula. From a tectonic point of view this area can be defined as a diffuse plate boundary, comprising the eastern edge of the Gloria and Tydeman transforms (where the deformation is mainly concentrated in these shear corridors), the Gorringe Bank, the Horseshoe Abyssal plain, the Portimao and Guadalquivir banks, and the western termination of the arcuated Gibraltar Arc. This deformation zone is the eastern edge of the Azores - Gibraltar seismic zone, being the present day boundary between the Eurasian and African plates. The motion between the plates is mainly convergent in the Gulf of Cádiz, but gradually changes to almost pure transcurrent along the Gloria Fault. The relative motion between the two plates is of the order of 4-5 mm/yr. In order to define the different tsunamigenic zones and to characterize its worst tsunamigenic source we have used seismic, structural and geological data. The numerical model used to simulate the wave propagation and coastal inundation is the C3 (Cantabria, COMCOT and Tsunami-Claw) model. C3 is a hybrid finite difference-finite volume method which balances between efficiency and accuracy. For offshore domain in deep waters the model applies an explicit finite difference scheme (FD), which is computationally fast and accurate in large grids. For near coast domains in coastal areas, it applies a finite volume scheme (VOF). It solves correctly the bore formation and the bore propagation. It is very effective solving the run-up and the run down. A set of five worst case tsunamigenic sources has been used with four different sea levels (minimum tide, most probable low tide, most probable high tide and maximum tide), in order to produce the following thematic maps with the C3 model: maximum free surface elevation, maximum water depth, maximum current speed, maximum Froude number and maximum impact forces (hydrostatic and dynamic forces). The fault rupture and sea bottom displacement has been computed by means of the Okada equations. As result, a set of more than 100 deterministic thematic maps have been created in a GIS environment incorporating geographical data and high resolution orthorectified satellite images. These thematic maps form an atlas of inundation maps that will be distributed to different government authorities and civil protection and emergency agencies. The authors gratefully acknowledge the financial support provided by the EU under the frame of the European Project TRANSFER (Tsunami Risk And Strategies For the European Region), 6th Framework Programme.

Modeling of Complex Coupled Fluid-Structure Interaction Systems in Arbitrary Water Depth

DTIC Science & Technology

2008-01-01

model in a particle finite element method ( PFEM ) based framework for the ALE-RANS solver and submitted a journal paper recently [1]. In the paper, we...developing a fluid-flexible structure interaction model without free surface using ALE-RANS and k-ε turbulence closure model implemented by PFEM . In...the ALE_RANS and k-ε turbulence closure model based on the particle finite element Method ( PFEM ) and obtained some satisfying results [1-2]. The

Optimization of Turbine Engine Cycle Analysis with Analytic Derivatives

NASA Technical Reports Server (NTRS)

Hearn, Tristan; Hendricks, Eric; Chin, Jeffrey; Gray, Justin; Moore, Kenneth T.

2016-01-01

A new engine cycle analysis tool, called Pycycle, was built using the OpenMDAO framework. Pycycle provides analytic derivatives allowing for an efficient use of gradient-based optimization methods on engine cycle models, without requiring the use of finite difference derivative approximation methods. To demonstrate this, a gradient-based design optimization was performed on a turbofan engine model. Results demonstrate very favorable performance compared to an optimization of an identical model using finite-difference approximated derivatives.

Functional Validation and Comparison Framework for EIT Lung Imaging

PubMed Central

Meybohm, Patrick; Weiler, Norbert; Frerichs, Inéz; Adler, Andy

2014-01-01

Introduction Electrical impedance tomography (EIT) is an emerging clinical tool for monitoring ventilation distribution in mechanically ventilated patients, for which many image reconstruction algorithms have been suggested. We propose an experimental framework to assess such algorithms with respect to their ability to correctly represent well-defined physiological changes. We defined a set of clinically relevant ventilation conditions and induced them experimentally in 8 pigs by controlling three ventilator settings (tidal volume, positive end-expiratory pressure and the fraction of inspired oxygen). In this way, large and discrete shifts in global and regional lung air content were elicited. Methods We use the framework to compare twelve 2D EIT reconstruction algorithms, including backprojection (the original and still most frequently used algorithm), GREIT (a more recent consensus algorithm for lung imaging), truncated singular value decomposition (TSVD), several variants of the one-step Gauss-Newton approach and two iterative algorithms. We consider the effects of using a 3D finite element model, assuming non-uniform background conductivity, noise modeling, reconstructing for electrode movement, total variation (TV) reconstruction, robust error norms, smoothing priors, and using difference vs. normalized difference data. Results and Conclusions Our results indicate that, while variation in appearance of images reconstructed from the same data is not negligible, clinically relevant parameters do not vary considerably among the advanced algorithms. Among the analysed algorithms, several advanced algorithms perform well, while some others are significantly worse. Given its vintage and ad-hoc formulation backprojection works surprisingly well, supporting the validity of previous studies in lung EIT. PMID:25110887

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

Bialas, A.; Czyz, W.; Zalewski, K.

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

Stress distribution of single-implant-retained overdenture reinforced with a framework: A finite element analysis study.

PubMed

Amaral, Camilla F; Gomes, Rafael S; Rodrigues Garcia, Renata C M; Del Bel Cury, Altair A

2018-05-01

Studies have demonstrated the effectiveness of a single-implant-retained mandibular overdenture for elderly patients with edentulism. However, due to the high concentration of stress around the housing portion of the single implant, this prosthesis tends to fracture at the anterior region more than the 2-implant-retained mandibular overdenture. The purpose of this finite-element analysis study was to evaluate the stress distribution in a single-implant-retained mandibular overdenture reinforced with a cobalt-chromium framework, to minimize the incidence of denture base fracture. Two 3-dimensional finite element models of mandibular overdentures supported by a single implant with a stud attachment were designed in SolidWorks 2013 software. The only difference between the models was the presence or absence of a cobalt-chromium framework at the denture base between canines. Subsequently, the models were imported into the mathematical analysis software ANSYS Workbench v15.0. A mesh was generated with an element size of 0.7 mm and submitted to convergence analysis before mechanical simulation. All materials were considered to be homogeneous, isotropic, and linearly elastic. A 100-N load was applied to the incisal edge of the central mandibular incisors at a 30-degree angle. Maximum principal stress was calculated for the overdenture, von Mises stress was calculated for the attachment and implant, and minimum principal stress was calculated for cortical and cancellous bone. In both models, peak stress on the overdenture was localized at the anterior intaglio surface region around the implant. However, the presence of the framework reduced the stress by almost 62% compared with the overdenture without a framework (8.7 MPa and 22.8 MPa, respectively). Both models exhibited similar stress values in the attachment, implant, and bone. A metal framework reinforcement for a single-implant-retained mandibular overdenture concentrates less stress through the anterior area of the prosthesis and could minimize the incidence of fracture. Copyright © 2017 Editorial Council for the Journal of Prosthetic Dentistry. Published by Elsevier Inc. All rights reserved.

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots.

PubMed

Busch, Martin H J; Vollmann, Wolfgang; Grönemeyer, Dietrich H W

2006-05-26

Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach (1/4) of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to. First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q V(ind) < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q V(ind) > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for.

Finite volume analysis of temperature effects induced by active MRI implants: 2. Defects on active MRI implants causing hot spots

PubMed Central

Busch, Martin HJ; Vollmann, Wolfgang; Grönemeyer, Dietrich HW

2006-01-01

Background Active magnetic resonance imaging implants, for example stents, stent grafts or vena cava filters, are constructed as wireless inductively coupled transmit and receive coils. They are built as a resonator tuned to the Larmor frequency of a magnetic resonance system. The resonator can be added to or incorporated within the implant. This technology can counteract the shielding caused by eddy currents inside the metallic implant structure. This may allow getting diagnostic information of the implant lumen (in stent stenosis or thrombosis for example). The electro magnetic rf-pulses during magnetic resonance imaging induce a current in the circuit path of the resonator. A by material fatigue provoked partial rupture of the circuit path or a broken wire with touching surfaces can set up a relatively high resistance on a very short distance, which may behave as a point-like power source, a hot spot, inside the body part the resonator is implanted to. This local power loss inside a small volume can reach ¼ of the total power loss of the intact resonating circuit, which itself is proportional to the product of the resonator volume and the quality factor and depends as well from the orientation of the resonator with respect to the main magnetic field and the imaging sequence the resonator is exposed to. Methods First an analytical solution of a hot spot for thermal equilibrium is described. This analytical solution with a definite hot spot power loss represents the worst case scenario for thermal equilibrium inside a homogeneous medium without cooling effects. Starting with this worst case assumptions additional conditions are considered in a numerical simulation, which are more realistic and may make the results less critical. The analytical solution as well as the numerical simulations use the experimental experience of the maximum hot spot power loss of implanted resonators with a definite volume during magnetic resonance imaging investigations. The finite volume analysis calculates the time developing temperature maps for the model of a broken linear metallic wire embedded in tissue. Half of the total hot spot power loss is assumed to diffuse into both wire parts at the location of a defect. The energy is distributed from there by heat conduction. Additionally the effect of blood perfusion and blood flow is respected in some simulations because the simultaneous appearance of all worst case conditions, especially the absence of blood perfusion and blood flow near the hot spot, is very unlikely for vessel implants. Results The analytical solution as worst case scenario as well as the finite volume analysis for near worst case situations show not negligible volumes with critical temperature increases for part of the modeled hot spot situations. MR investigations with a high rf-pulse density lasting below a minute can establish volumes of several cubic millimeters with temperature increases high enough to start cell destruction. Longer exposure times can involve volumes larger than 100 mm3. Even temperature increases in the range of thermal ablation are reached for substantial volumes. MR sequence exposure time and hot spot power loss are the primary factors influencing the volume with critical temperature increases. Wire radius, wire material as well as the physiological parameters blood perfusion and blood flow inside larger vessels reduce the volume with critical temperature increases, but do not exclude a volume with critical tissue heating for resonators with a large product of resonator volume and quality factor. Conclusion The worst case scenario assumes thermal equilibrium for a hot spot embedded in homogeneous tissue without any cooling due to blood perfusion or flow. The finite volume analysis can calculate the results for near and not close to worst case conditions. For both cases a substantial volume can reach a critical temperature increase in a short time. The analytical solution, as absolute worst case, points out that resonators with a small product of inductance volume and quality factor (Q Vind < 2 cm3) are definitely save. Stents for coronary vessels or resonators used as tracking devices for interventional procedures therefore have no risk of high temperature increases. The finite volume analysis shows for sure that also conditions not close to the worst case reach physiologically critical temperature increases for implants with a large product of inductance volume and quality factor (Q Vind > 10 cm3). Such resonators exclude patients from exactly the MRI investigation these devices are made for. PMID:16729878

Object-oriented philosophy in designing adaptive finite-element package for 3D elliptic deferential equations

NASA Astrophysics Data System (ADS)

Zhengyong, R.; Jingtian, T.; Changsheng, L.; Xiao, X.

2007-12-01

Although adaptive finite-element (AFE) analysis is becoming more and more focused in scientific and engineering fields, its efficient implementations are remain to be a discussed problem as its more complex procedures. In this paper, we propose a clear C++ framework implementation to show the powerful properties of Object-oriented philosophy (OOP) in designing such complex adaptive procedure. In terms of the modal functions of OOP language, the whole adaptive system is divided into several separate parts such as the mesh generation or refinement, a-posterior error estimator, adaptive strategy and the final post processing. After proper designs are locally performed on these separate modals, a connected framework of adaptive procedure is formed finally. Based on the general elliptic deferential equation, little efforts should be added in the adaptive framework to do practical simulations. To show the preferable properties of OOP adaptive designing, two numerical examples are tested. The first one is the 3D direct current resistivity problem in which the powerful framework is efficiently shown as only little divisions are added. And then, in the second induced polarization£¨IP£©exploration case, new adaptive procedure is easily added which adequately shows the strong extendibility and re-usage of OOP language. Finally we believe based on the modal framework adaptive implementation by OOP methodology, more advanced adaptive analysis system will be available in future.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

Topology optimization of finite strain viscoplastic systems under transient loads

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Self-weight effect in the measurement of the volume of silicon spheres

NASA Astrophysics Data System (ADS)

Mari, D.; Massa, E.; Kuramoto, N.; Mana, G.

2018-04-01

The volume of 28Si spheres about 94 mm in diameter is an input datum for the determination of the Avogadro constant. We report a finite element analysis of the self-weight effect on the volume determination via optical interferometric measurements of the sphere diameters. The self-weight expansion or shrinkage of the equatorial diameters, which ranges from  -31 pm to  +180 pm, depends on the southern latitude of the supports.

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).

Nonlocal birth-death competitive dynamics with volume exclusion

NASA Astrophysics Data System (ADS)

Khalil, Nagi; López, Cristóbal; Hernández-García, Emilio

2017-06-01

A stochastic birth-death competition model for particles with excluded volume is proposed. The particles move, reproduce, and die on a regular lattice. While the death rate is constant, the birth rate is spatially nonlocal and implements inter-particle competition by a dependence on the number of particles within a finite distance. The finite volume of particles is accounted for by fixing an upper value to the number of particles that can occupy a lattice node, compromising births and movements. We derive closed macroscopic equations for the density of particles and spatial correlation at two adjacent sites. Under different conditions, the description is further reduced to a single equation for the particle density that contains three terms: diffusion, a linear death, and a highly nonlinear and nonlocal birth term. Steady-state homogeneous solutions, their stability which reveals spatial pattern formation, and the dynamics of time-dependent homogeneous solutions are discussed and compared, in the one-dimensional case, with numerical simulations of the particle system.

Estimation of Effective Directional Strength of Single Walled Wavy CNT Reinforced Nanocomposite

NASA Astrophysics Data System (ADS)

Bhowmik, Krishnendu; Kumar, Pranav; Khutia, Niloy; Chowdhury, Amit Roy

2018-03-01

In this present work, single walled wavy carbon nanotube reinforced into composite has been studied to predict the effective directional strength of the nanocomposite. The effect of waviness on the overall Young’s modulus of the composite has been analysed using three dimensional finite element model. Waviness pattern of carbon nanotube is considered as periodic cosine function. Both long (continuous) and short (discontinuous) carbon nanotubes are being idealized as solid annular tube. Short carbon nanotube is modelled with hemispherical cap at its both ends. Representative Volume Element models have been developed with different waviness, height fractions, volume fractions and modulus ratios of carbon nanotubes. Consequently a micromechanics based analytical model has been formulated to derive the effective reinforcing modulus of wavy carbon nanotubes. In these models wavy single walled wavy carbon nanotubes are considered to be aligned along the longitudinal axis of the Representative Volume Element model. Results obtained from finite element analyses are compared with analytical model and they are found in good agreement.

Development of the Joint NASA/NCAR General Circulation Model

NASA Technical Reports Server (NTRS)

Lin, S.-J.; Rood, R. B.

1999-01-01

The Data Assimilation Office at NASA/Goddard Space Flight Center is collaborating with NCAR/CGD in an ambitious proposal for the development of a unified climate, numerical weather prediction, and chemistry transport model which is suitable for global data assimilation of the physical and chemical state of the Earth's atmosphere. A prototype model based on the NCAR CCM3 physics and the NASA finite-volume dynamical core has been built. A unique feature of the NASA finite-volume dynamical core is its advanced tracer transport algorithm on the floating Lagrangian control-volume coordinate. The model currently has a highly idealized ozone production/loss chemistry derived from the observed 2D (latitude-height) climatology of the recent decades. Nevertheless, the simulated horizontal wave structure of the total ozone is in good qualitative agreement with the observed (TOMS). Long term climate simulations and NWP experiments have been carried out. Current up to date status and futur! e plan will be discussed in the conference.

Three-dimensional blade coating of complex fluid

NASA Astrophysics Data System (ADS)

Singh, Vachitar; Grimaldi, Emma; Sauret, Alban; Dressaire, Emilie

2015-11-01

The application of a layer of non-newtonian fluid on a solid substrate is an important industrial problem involved in polymer or paint coatings, and an everyday life challenge when it comes to spreading peanut butter on a toast. Most experimental and theoretical work has focused on the two-dimensional situation, i.e. the scraping of a fixed blade on a moving substrate to turn a thick layer of liquid into a thin coat. However the spreading of a finite volume of non-newtonian fluid using a blade has received less attention, despite significant practical and fundamental implications. In this study, we investigate experimentally the spreading of a finite volume of a model non-newtonian fluid, carbopol, initially deposited against the fixed blade. As the substrate is translated at constant speed, we characterize the dynamics of spreading and the final shape of the coated layer. We measure and rationalize the influence of the liquid volume, the height and orientation of the blade, and the speed of the substrate on the spreading.

Controlling sign problems in spin models using tensor renormalization

NASA Astrophysics Data System (ADS)

Denbleyker, Alan; Liu, Yuzhi; Meurice, Y.; Qin, M. P.; Xiang, T.; Xie, Z. Y.; Yu, J. F.; Zou, Haiyuan

2014-01-01

We consider the sign problem for classical spin models at complex β =1/g02 on L ×L lattices. We show that the tensor renormalization group method allows reliable calculations for larger Imβ than the reweighting Monte Carlo method. For the Ising model with complex β we compare our results with the exact Onsager-Kaufman solution at finite volume. The Fisher zeros can be determined precisely with the tensor renormalization group method. We check the convergence of the tensor renormalization group method for the O(2) model on L×L lattices when the number of states Ds increases. We show that the finite size scaling of the calculated Fisher zeros agrees very well with the Kosterlitz-Thouless transition assumption and predict the locations for larger volume. The location of these zeros agree with Monte Carlo reweighting calculation for small volume. The application of the method for the O(2) model with a chemical potential is briefly discussed.

Drekar v.2.0

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

Seefeldt, Ben; Sondak, David; Hensinger, David M.

Drekar is an application code that solves partial differential equations for fluids that can be optionally coupled to electromagnetics. Drekar solves low-mach compressible and incompressible computational fluid dynamics (CFD), compressible and incompressible resistive magnetohydrodynamics (MHD), and multiple species plasmas interacting with electromagnetic fields. Drekar discretization technology includes continuous and discontinuous finite element formulations, stabilized finite element formulations, mixed integration finite element bases (nodal, edge, face, volume) and an initial arbitrary Lagrangian Eulerian (ALE) capability. Drekar contains the implementation of the discretized physics and leverages the open source Trilinos project for both parallel solver capabilities and general finite element discretization tools.more » The code will be released open source under a BSD license. The code is used for fundamental research for simulation of fluids and plasmas on high performance computing environments.« less

Crashworthiness analysis on alternative square honeycomb structure under axial loading

NASA Astrophysics Data System (ADS)

Li, Meng; Deng, Zongquan; Guo, Hongwei; Liu, Rongqiang; Ding, Beichen

2013-07-01

Hexagonal metal honeycomb is widely used in energy absorption field for its special construction. However, many other metal honeycomb structures also show good energy absorption characteristics. Currently, most of the researches focus on hexagonal honeycomb, while few are performed into different honeycomb structures. Therefore, a new alternative square honeycomb is developed to expand the non-hexagonal metal honeycomb applications in the energy absorption fields with the aim of designing low mass and low volume energy absorbers. The finite element model of alternative square honeycomb is built to analyze its specific energy absorption property. As the diversity of honeycomb structure, the parameterized metal honeycomb finite element analysis program is conducted based on PCL language. That program can automatically create finite element model. Numerical results show that with the same foil thickness and cell length of metal honeycomb, the alternative square has better specific energy absorption than hexagonal honeycomb. Using response surface method, the mathematical formulas of honeycomb crashworthiness properties are obtained and optimization is done to get the maximum specific energy absorption property honeycomb. Optimal results demonstrate that to absorb same energy, alternative square honeycomb can save 10% volume of buffer structure than hexagonal honeycomb can do. This research is significant in providing technical support in the extended application of different honeycomb used as crashworthiness structures, and is absolutely essential in low volume and low mass energy absorber design.

A CLASS OF RECONSTRUCTED DISCONTINUOUS GALERKIN METHODS IN COMPUTATIONAL FLUID DYNAMICS

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

Hong Luo; Yidong Xia; Robert Nourgaliev

2011-05-01

A class of reconstructed discontinuous Galerkin (DG) methods is presented to solve compressible flow problems on arbitrary grids. The idea is to combine the efficiency of the reconstruction methods in finite volume methods and the accuracy of the DG methods to obtain a better numerical algorithm in computational fluid dynamics. The beauty of the resulting reconstructed discontinuous Galerkin (RDG) methods is that they provide a unified formulation for both finite volume and DG methods, and contain both classical finite volume and standard DG methods as two special cases of the RDG methods, and thus allow for a direct efficiency comparison.more » Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are presented to obtain a quadratic polynomial representation of the underlying linear discontinuous Galerkin solution on each cell via a so-called in-cell reconstruction process. The devised in-cell reconstruction is aimed to augment the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. These three reconstructed discontinuous Galerkin methods are used to compute a variety of compressible flow problems on arbitrary meshes to assess their accuracy. The numerical experiments demonstrate that all three reconstructed discontinuous Galerkin methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstructed DG method provides the best performance in terms of both accuracy, efficiency, and robustness.« less

Coupled numerical approach combining finite volume and lattice Boltzmann methods for multi-scale multi-physicochemical processes

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

Chen, Li; He, Ya-Ling; Kang, Qinjun

2013-12-15

A coupled (hybrid) simulation strategy spatially combining the finite volume method (FVM) and the lattice Boltzmann method (LBM), called CFVLBM, is developed to simulate coupled multi-scale multi-physicochemical processes. In the CFVLBM, computational domain of multi-scale problems is divided into two sub-domains, i.e., an open, free fluid region and a region filled with porous materials. The FVM and LBM are used for these two regions, respectively, with information exchanged at the interface between the two sub-domains. A general reconstruction operator (RO) is proposed to derive the distribution functions in the LBM from the corresponding macro scalar, the governing equation of whichmore » obeys the convection–diffusion equation. The CFVLBM and the RO are validated in several typical physicochemical problems and then are applied to simulate complex multi-scale coupled fluid flow, heat transfer, mass transport, and chemical reaction in a wall-coated micro reactor. The maximum ratio of the grid size between the FVM and LBM regions is explored and discussed. -- Highlights: •A coupled simulation strategy for simulating multi-scale phenomena is developed. •Finite volume method and lattice Boltzmann method are coupled. •A reconstruction operator is derived to transfer information at the sub-domains interface. •Coupled multi-scale multiple physicochemical processes in micro reactor are simulated. •Techniques to save computational resources and improve the efficiency are discussed.« less

Surface flaw reliability analysis of ceramic components with the SCARE finite element postprocessor program

NASA Technical Reports Server (NTRS)

Gyekenyesi, John P.; Nemeth, Noel N.

1987-01-01

The SCARE (Structural Ceramics Analysis and Reliability Evaluation) computer program on statistical fast fracture reliability analysis with quadratic elements for volume distributed imperfections is enhanced to include the use of linear finite elements and the capability of designing against concurrent surface flaw induced ceramic component failure. The SCARE code is presently coupled as a postprocessor to the MSC/NASTRAN general purpose, finite element analysis program. The improved version now includes the Weibull and Batdorf statistical failure theories for both surface and volume flaw based reliability analysis. The program uses the two-parameter Weibull fracture strength cumulative failure probability distribution model with the principle of independent action for poly-axial stress states, and Batdorf's shear-sensitive as well as shear-insensitive statistical theories. The shear-sensitive surface crack configurations include the Griffith crack and Griffith notch geometries, using the total critical coplanar strain energy release rate criterion to predict mixed-mode fracture. Weibull material parameters based on both surface and volume flaw induced fracture can also be calculated from modulus of rupture bar tests, using the least squares method with known specimen geometry and grouped fracture data. The statistical fast fracture theories for surface flaw induced failure, along with selected input and output formats and options, are summarized. An example problem to demonstrate various features of the program is included.

Experimental Non-Violation of the Bell Inequality

NASA Astrophysics Data System (ADS)

Palmer, Tim

2018-05-01

A finite non-classical framework for physical theory is described which challenges the conclusion that the Bell Inequality has been shown to have been violated experimentally, even approximately. This framework postulates the universe as a deterministic locally causal system evolving on a measure-zero fractal-like geometry $I_U$ in cosmological state space. Consistent with the assumed primacy of $I_U$, and $p$-adic number theory, a non-Euclidean (and hence non-classical) metric $g_p$ is defined on cosmological state space, where $p$ is a large but finite Pythagorean prime. Using number-theoretic properties of spherical triangles, the inequalities violated experimentally are shown to be $g_p$-distant from the CHSH inequality, whose violation would rule out local realism. This result fails in the singular limit $p=\\infty$, at which $g_p$ is Euclidean. Broader implications are discussed.

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.

Plasticity - Theory and finite element applications.

NASA Technical Reports Server (NTRS)

Armen, H., Jr.; Levine, H. S.

1972-01-01

A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.

Combining the modified Skyrme-like model and the local density approximation to determine the symmetry energy of nuclear matter

NASA Astrophysics Data System (ADS)

Liu, Jian; Ren, Zhongzhou; Xu, Chang

2018-07-01

Combining the modified Skyrme-like model and the local density approximation model, the slope parameter L of symmetry energy is extracted from the properties of finite nuclei with an improved iterative method. The calculations of the iterative method are performed within the framework of the spherical symmetry. By choosing 200 neutron rich nuclei on 25 isotopic chains as candidates, the slope parameter is constrained to be 50 MeV < L < 62 MeV. The validity of this method is examined by the properties of finite nuclei. Results show that reasonable descriptions on the properties of finite nuclei and nuclear matter can be obtained together.

Models and finite element approximations for interacting nanosized piezoelectric bodies and acoustic medium

NASA Astrophysics Data System (ADS)

Nasedkin, A. V.

2017-01-01

This research presents the new size-dependent models of piezoelectric materials oriented to finite element applications. The proposed models include the facilities of taking into account different mechanisms of damping for mechanical and electric fields. The coupled models also incorporate the equations of the theory of acoustics for viscous fluids. In particular cases, these models permit to use the mode superposition method with full separation of the finite element systems into independent equations for the independent modes for transient and harmonic problems. The main boundary conditions were supplemented with the facilities of taking into account the coupled surface effects, allowing to explore the nanoscale piezoelectric materials in the framework of theories of continuous media with surface stresses and their generalizations. For the considered problems we have implemented the finite element technologies and various numerical algorithms to maintain a symmetrical structure of the finite element quasi-definite matrices (matrix structure for the problems with a saddle point).

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

[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.

Discontinuous finite volume element discretization for coupled flow-transport problems arising in models of sedimentation

NASA Astrophysics Data System (ADS)

Bürger, Raimund; Kumar, Sarvesh; Ruiz-Baier, Ricardo

2015-10-01

The sedimentation-consolidation and flow processes of a mixture of small particles dispersed in a viscous fluid at low Reynolds numbers can be described by a nonlinear transport equation for the solids concentration coupled with the Stokes problem written in terms of the mixture flow velocity and the pressure field. Here both the viscosity and the forcing term depend on the local solids concentration. A semi-discrete discontinuous finite volume element (DFVE) scheme is proposed for this model. The numerical method is constructed on a baseline finite element family of linear discontinuous elements for the approximation of velocity components and concentration field, whereas the pressure is approximated by piecewise constant elements. The unique solvability of both the nonlinear continuous problem and the semi-discrete DFVE scheme is discussed, and optimal convergence estimates in several spatial norms are derived. Properties of the model and the predicted space accuracy of the proposed formulation are illustrated by detailed numerical examples, including flows under gravity with changing direction, a secondary settling tank in an axisymmetric setting, and batch sedimentation in a tilted cylindrical vessel.

Dynamic growth of slip surfaces in catastrophic landslides.

PubMed

Germanovich, Leonid N; Kim, Sihyun; Puzrin, Alexander M

2016-01-01

This work considers a landslide caused by the shear band that emerges along the potential slip (rupture) surface. The material above the band slides downwards, causing the band to grow along the slope. This growth may first be stable (progressive), but eventually becomes dynamic (catastrophic). The landslide body acquires a finite velocity before it separates from the substrata. The corresponding initial-boundary value problem for a dynamic shear band is formulated within the framework of Palmer & Rice's ( Proc. R. Soc. Lond. A 332 , 527-548. (doi:10.1098/rspa.1973.0040)) approach, which is generalized to the dynamic case. We obtain the exact, closed-form solution for the band velocity and slip rate. This solution assesses when the slope fails owing to a limiting condition near the propagating tip of the shear band. Our results are applicable to both submarine and subaerial landslides of this type. It appears that neglecting dynamic (inertia) effects can lead to a significant underestimation of the slide size, and that the volumes of catastrophic slides can exceed the volumes of progressive slides by nearly a factor of 2. As examples, we consider the Gaviota and Humboldt slides offshore of California, and discuss landslides in normally consolidated sediments and sensitive clays. In particular, it is conceivable that Humboldt slide is unfinished and may still displace a large volume of sediments, which could generate a considerable tsunami. We show that in the case of submarine slides, the effect of water resistance on the shear band dynamics may frequently be limited during the slope failure stage. For a varying slope angle, we formulate a condition of slide cessation.

A mixed model framework for teratology studies.

PubMed

Braeken, Johan; Tuerlinckx, Francis

2009-10-01

A mixed model framework is presented to model the characteristic multivariate binary anomaly data as provided in some teratology studies. The key features of the model are the incorporation of covariate effects, a flexible random effects distribution by means of a finite mixture, and the application of copula functions to better account for the relation structure of the anomalies. The framework is motivated by data of the Boston Anticonvulsant Teratogenesis study and offers an integrated approach to investigate substantive questions, concerning general and anomaly-specific exposure effects of covariates, interrelations between anomalies, and objective diagnostic measurement.

The Effect of Framework Design on Stress Distribution in Implant-Supported FPDs: A 3-D FEM Study

PubMed Central

Eraslan, Oguz; Inan, Ozgur; Secilmis, Asli

2010-01-01

Objectives: The biomechanical behavior of the superstructure plays an important role in the functional longevity of dental implants. However, information about the influence of framework design on stresses transmitted to the implants and supporting tissues is limited. The purpose of this study was to evaluate the effects of framework designs on stress distribution at the supporting bone and supporting implants. Methods: In this study, the three-dimensional (3D) finite element stress analysis method was used. Three types of 3D mathematical models simulating three different framework designs for implant-supported 3-unit posterior fixed partial dentures were prepared with supporting structures. Convex (1), concave (2), and conventional (3) pontic framework designs were simulated. A 300-N static vertical occlusal load was applied on the node at the center of occlusal surface of the pontic to calculate the stress distributions. As a second condition, frameworks were directly loaded to evaluate the effect of the framework design clearly. The Solidworks/Cosmosworks structural analysis programs were used for finite element modeling/analysis. Results: The analysis of the von Mises stress values revealed that maximum stress concentrations were located at the loading areas for all models. The pontic side marginal edges of restorations and the necks of implants were other stress concentration regions. There was no clear difference among models when the restorations were loaded at occlusal surfaces. When the veneering porcelain was removed, and load was applied directly to the framework, there was a clear increase in stress concentration with a concave design on supporting implants and bone structure. Conclusions: The present study showed that the use of a concave design in the pontic frameworks of fixed partial dentures increases the von Mises stress levels on implant abutments and supporting bone structure. However, the veneering porcelain element reduces the effect of the framework and compensates for design weaknesses. PMID:20922156

Finite-temperature Gutzwiller approximation from the time-dependent variational principle

NASA Astrophysics Data System (ADS)

Lanatà, Nicola; Deng, Xiaoyu; Kotliar, Gabriel

2015-08-01

We develop an extension of the Gutzwiller approximation to finite temperatures based on the Dirac-Frenkel variational principle. Our method does not rely on any entropy inequality, and is substantially more accurate than the approaches proposed in previous works. We apply our theory to the single-band Hubbard model at different fillings, and show that our results compare quantitatively well with dynamical mean field theory in the metallic phase. We discuss potential applications of our technique within the framework of first-principle calculations.

Ramses-GPU: Second order MUSCL-Handcock finite volume fluid solver

NASA Astrophysics Data System (ADS)

Kestener, Pierre

2017-10-01

RamsesGPU is a reimplementation of RAMSES (ascl:1011.007) which drops the adaptive mesh refinement (AMR) features to optimize 3D uniform grid algorithms for modern graphics processor units (GPU) to provide an efficient software package for astrophysics applications that do not need AMR features but do require a very large number of integration time steps. RamsesGPU provides an very efficient C++/CUDA/MPI software implementation of a second order MUSCL-Handcock finite volume fluid solver for compressible hydrodynamics as a magnetohydrodynamics solver based on the constraint transport technique. Other useful modules includes static gravity, dissipative terms (viscosity, resistivity), and forcing source term for turbulence studies, and special care was taken to enhance parallel input/output performance by using state-of-the-art libraries such as HDF5 and parallel-netcdf.

Dust Emissions, Transport, and Deposition Simulated with the NASA Finite-Volume General Circulation Model

NASA Technical Reports Server (NTRS)

Colarco, Peter; daSilva, Arlindo; Ginoux, Paul; Chin, Mian; Lin, S.-J.

2003-01-01

Mineral dust aerosols have radiative impacts on Earth's atmosphere, have been implicated in local and regional air quality issues, and have been identified as vectors for transporting disease pathogens and bringing mineral nutrients to terrestrial and oceanic ecosystems. We present for the first time dust simulations using online transport and meteorological analysis in the NASA Finite-Volume General Circulation Model (FVGCM). Our dust formulation follows the formulation in the offline Georgia Institute of Technology-Goddard Global Ozone Chemistry Aerosol Radiation and Transport Model (GOCART) using a topographical source for dust emissions. We compare results of the FVGCM simulations with GOCART, as well as with in situ and remotely sensed observations. Additionally, we estimate budgets of dust emission and transport into various regions.

Probability density function approach for compressible turbulent reacting flows

NASA Technical Reports Server (NTRS)

Hsu, A. T.; Tsai, Y.-L. P.; Raju, M. S.

1994-01-01

The objective of the present work is to extend the probability density function (PDF) tubulence model to compressible reacting flows. The proability density function of the species mass fractions and enthalpy are obtained by solving a PDF evolution equation using a Monte Carlo scheme. The PDF solution procedure is coupled with a compression finite-volume flow solver which provides the velocity and pressure fields. A modeled PDF equation for compressible flows, capable of treating flows with shock waves and suitable to the present coupling scheme, is proposed and tested. Convergence of the combined finite-volume Monte Carlo solution procedure is discussed. Two super sonic diffusion flames are studied using the proposed PDF model and the results are compared with experimental data; marked improvements over solutions without PDF are observed.

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

DOE PAGES

Guzik, Stephen M.; Gao, Xinfeng; Owen, Landon D.; ...

2015-12-20

We present a fourth-order accurate finite-volume method for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Some novel considerations for formulating the semi-discrete system of equations in computational space are combined with detailed mechanisms for accommodating the adapting grids. Furthermore, these considerations ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). The solution in time is advanced with a fourth-order Runge-Kutta method. A series of tests verifies that the expected accuracy is achieved in smooth flows and the solution ofmore » a Mach reflection problem demonstrates the effectiveness of the algorithm in resolving strong discontinuities.« 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.

Direct Numerical Simulation of Acoustic Waves Interacting with a Shock Wave in a Quasi-1D Convergent-Divergent Nozzle Using an Unstructured Finite Volume Algorithm

NASA Technical Reports Server (NTRS)

Bui, Trong T.; Mankbadi, Reda R.

1995-01-01

Numerical simulation of a very small amplitude acoustic wave interacting with a shock wave in a quasi-1D convergent-divergent nozzle is performed using an unstructured finite volume algorithm with a piece-wise linear, least square reconstruction, Roe flux difference splitting, and second-order MacCormack time marching. First, the spatial accuracy of the algorithm is evaluated for steady flows with and without the normal shock by running the simulation with a sequence of successively finer meshes. Then the accuracy of the Roe flux difference splitting near the sonic transition point is examined for different reconstruction schemes. Finally, the unsteady numerical solutions with the acoustic perturbation are presented and compared with linear theory results.

Resonance Extraction from the Finite Volume

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

Doring, Michael; Molina Peralta, Raquel

2016-06-01

The spectrum of excited hadrons becomes accessible in simulations of Quantum Chromodynamics on the lattice. Extensions of Lüscher's method allow to address multi-channel scattering problems using moving frames or modified boundary conditions to obtain more eigenvalues in finite volume. As these are at different energies, interpolations are needed to relate different eigenvalues and to help determine the amplitude. Expanding the T- or the K-matrix locally provides a controlled scheme by removing the known non-analyticities of thresholds. This can be stabilized by using Chiral Perturbation Theory. Different examples to determine resonance pole parameters and to disentangle resonances from thresholds are dis-more » cussed, like the scalar meson f0(980) and the excited baryons N(1535)1/2^- and Lambda(1405)1/2^-.« less

Finite element solution of low bond number sloshing

NASA Technical Reports Server (NTRS)

Wohlen, R. L.; Park, A. C.; Warner, D. M.

1975-01-01

The dynamics of liquid propellant in a low Bond number environment which are critical to the design of spacecraft systems with respect to orbital propellant transfer and attitude control system were investigated. Digital computer programs were developed for the determination of liquid free surface equilibrium shape, lateral slosh natural vibration mode shapes, and frequencies for a liquid in a container of arbitrary axisymmetric shape with surface tension forces the same order of magnitude as acceleration forces. A finite volume element representation of the liquid was used for the vibration analysis. The liquid free surface equilibrium shapes were computed for several tanks at various contact angles and ullage volumes. A configuration was selected for vibration analysis and lateral slosh mode shapes and natural frequencies were obtained. Results are documented.

Accuracy and convergence of coupled finite-volume/Monte Carlo codes for plasma edge simulations of nuclear fusion reactors

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

Ghoos, K., E-mail: kristel.ghoos@kuleuven.be; Dekeyser, W.; Samaey, G.

2016-10-01

The plasma and neutral transport in the plasma edge of a nuclear fusion reactor is usually simulated using coupled finite volume (FV)/Monte Carlo (MC) codes. However, under conditions of future reactors like ITER and DEMO, convergence issues become apparent. This paper examines the convergence behaviour and the numerical error contributions with a simplified FV/MC model for three coupling techniques: Correlated Sampling, Random Noise and Robbins Monro. Also, practical procedures to estimate the errors in complex codes are proposed. Moreover, first results with more complex models show that an order of magnitude speedup can be achieved without any loss in accuracymore » by making use of averaging in the Random Noise coupling technique.« less

On the divergence-free condition in Godunov-type schemes for ideal magnetohydrodynamics: the upwind constrained transport method

NASA Astrophysics Data System (ADS)

Londrillo, P.; del Zanna, L.

2004-03-01

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the constrained transport (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures [∇.B]num=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here upwind constrained transport (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second-order Roe-type positive scheme by Liu and Lax [J. Comput. Fluid Dyn. 5 (1996) 133], and both the second- and third-order versions of a central-type MHD scheme presented by Londrillo and Del Zanna [Astrophys. J. 530 (2000) 508], where the basic UCT strategies have been first outlined.

Stochastic filtering for damage identification through nonlinear structural finite element model updating

NASA Astrophysics Data System (ADS)

Astroza, Rodrigo; Ebrahimian, Hamed; Conte, Joel P.

2015-03-01

This paper describes a novel framework that combines advanced mechanics-based nonlinear (hysteretic) finite element (FE) models and stochastic filtering techniques to estimate unknown time-invariant parameters of nonlinear inelastic material models used in the FE model. Using input-output data recorded during earthquake events, the proposed framework updates the nonlinear FE model of the structure. The updated FE model can be directly used for damage identification and further used for damage prognosis. To update the unknown time-invariant parameters of the FE model, two alternative stochastic filtering methods are used: the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). A three-dimensional, 5-story, 2-by-1 bay reinforced concrete (RC) frame is used to verify the proposed framework. The RC frame is modeled using fiber-section displacement-based beam-column elements with distributed plasticity and is subjected to the ground motion recorded at the Sylmar station during the 1994 Northridge earthquake. The results indicate that the proposed framework accurately estimate the unknown material parameters of the nonlinear FE model. The UKF outperforms the EKF when the relative root-mean-square error of the recorded responses are compared. In addition, the results suggest that the convergence of the estimate of modeling parameters is smoother and faster when the UKF is utilized.

Molecular finite-size effects in stochastic models of equilibrium chemical systems.

PubMed

Cianci, Claudia; Smith, Stephen; Grima, Ramon

2016-02-28

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

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

Estimating finite-population reproductive numbers in heterogeneous populations.

PubMed

Keegan, Lindsay T; Dushoff, Jonathan

2016-05-21

The basic reproductive number, R0, is one of the most important epidemiological quantities. R0 provides a threshold for elimination and determines when a disease can spread or when a disease will die out. Classically, R0 is calculated assuming an infinite population of identical hosts. Previous work has shown that heterogeneity in the host mixing rate increases R0 in an infinite population. However, it has been suggested that in a finite population, heterogeneity in the mixing rate may actually decrease the finite-population reproductive numbers. Here, we outline a framework for discussing different types of heterogeneity in disease parameters, and how these affect disease spread and control. We calculate "finite-population reproductive numbers" with different types of heterogeneity, and show that in a finite population, heterogeneity has complicated effects on the reproductive number. We find that simple heterogeneity decreases the finite-population reproductive number, whereas heterogeneity in the intrinsic mixing rate (which affects both infectiousness and susceptibility) increases the finite-population reproductive number when R0 is small relative to the size of the population and decreases the finite-population reproductive number when R0 is large relative to the size of the population. Although heterogeneity has complicated effects on the finite-population reproductive numbers, its implications for control are straightforward: when R0 is large relative to the size of the population, heterogeneity decreases the finite-population reproductive numbers, making disease control or elimination easier than predicted by R0. Copyright © 2016 Elsevier Ltd. All rights reserved.

A comparison of error bounds for a nonlinear tracking system with detection probability Pd < 1.

PubMed

Tong, Huisi; Zhang, Hao; Meng, Huadong; Wang, Xiqin

2012-12-14

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds.

A Comparison of Error Bounds for a Nonlinear Tracking System with Detection Probability Pd < 1

PubMed Central

Tong, Huisi; Zhang, Hao; Meng, Huadong; Wang, Xiqin

2012-01-01

Error bounds for nonlinear filtering are very important for performance evaluation and sensor management. This paper presents a comparative study of three error bounds for tracking filtering, when the detection probability is less than unity. One of these bounds is the random finite set (RFS) bound, which is deduced within the framework of finite set statistics. The others, which are the information reduction factor (IRF) posterior Cramer-Rao lower bound (PCRLB) and enumeration method (ENUM) PCRLB are introduced within the framework of finite vector statistics. In this paper, we deduce two propositions and prove that the RFS bound is equal to the ENUM PCRLB, while it is tighter than the IRF PCRLB, when the target exists from the beginning to the end. Considering the disappearance of existing targets and the appearance of new targets, the RFS bound is tighter than both IRF PCRLB and ENUM PCRLB with time, by introducing the uncertainty of target existence. The theory is illustrated by two nonlinear tracking applications: ballistic object tracking and bearings-only tracking. The simulation studies confirm the theory and reveal the relationship among the three bounds. PMID:23242274

Higher order solution of the Euler equations on unstructured grids using quadratic reconstruction

NASA Technical Reports Server (NTRS)

Barth, Timothy J.; Frederickson, Paul O.

1990-01-01

High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.