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A conservative threedimensional Eulerian method for coupled solidfluid shock capturing
 Copyright © by SIAM. Unauthorized reproduction of this article is prohibited
"... A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions ..."
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Cited by 39 (9 self)
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A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions artificially extended representations of the individual phases. For fluids we use a new 3D spatially unsplit implementation of the piecewise parabolic (PPM) method of Colella and Woodward. For solids we use the 3D spatially unsplit Eulerian solid mechanics method of Miller and Colella. Vacuum and perfectly incompressible obstacles may also be employed as phases. A separate problem is the time evolution of material interfaces, which are represented by planar segments constructed with a volumeoffluid method. The volume fractions are advanced in time using a secondorder 3D spatially unsplit advection routine with a velocity field determined by solution of interfacenormal twophase Riemann problems. From the Riemann problem solutions we also determine crossinterface momentum and energy fluxes.
An unsplit, cellcentered Godunov method for ideal MHD
 JOURNAL OF COMPUTATIONAL PHYSICS 203 (2005) 422–448
, 2005
"... We present a secondorder Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. 87, 1990), with all of the primary dependent variables centered at the same location. To properly represent the divergencefree condition of the ..."
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Cited by 22 (3 self)
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We present a secondorder Godunov algorithm for multidimensional, ideal MHD. Our algorithm is based on the unsplit formulation of Colella (J. Comput. Phys. 87, 1990), with all of the primary dependent variables centered at the same location. To properly represent the divergencefree condition of the magnetic fields, we apply a discrete projection to the intermediate values of the field at cell faces, and apply a filter to the primary dependent variables at the end of each time step. We test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions. The test suite includes rotated planar linear waves, MHD shock tube problems, lowbeta flux tubes, and a magnetized rotor problem. For all of these cases, we observe that the algorithm is secondorder accurate for smooth solutions, converges to the correct weak solution for problems involving shocks, and exhibits no evidence of instability or loss of accuracy due to the possible presence of nonsolenoidal fields.
MINIMAL ROTATIONALLY INVARIANT BASES FOR HYPERELASTICITY
, 2004
"... Rotationally invariant polynomial bases of the hyperelastic strain energy function are rederived using methods of group theory, invariant theory, and computational algebra. A set of minimal basis functions is given for each of the 11 Laue groups, with a complete set of rewriting syzygies. The ideal ..."
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Cited by 1 (0 self)
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Rotationally invariant polynomial bases of the hyperelastic strain energy function are rederived using methods of group theory, invariant theory, and computational algebra. A set of minimal basis functions is given for each of the 11 Laue groups, with a complete set of rewriting syzygies. The ideal generated from this minimal basis agrees with the classic work of Smith and Rivlin [Trans. Amer. Math. Soc., 88 (1958), pp. 175–193]. However, the structure of the invariant algebra described here calls for fewer terms, beginning with the fourth degree in strain, for most groups.
Fully Eulerian finite element approximation of a fluidstructure interaction problem in cardiac cells
 Int. J. Numer. Methods Engrg
"... We propose in this paper an Eulerian finite element approximation of a coupled chemical fluidstructure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an anisotropic, hyperelastic, and incompressib ..."
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We propose in this paper an Eulerian finite element approximation of a coupled chemical fluidstructure interaction problem arising in the study of mesoscopic cardiac biomechanics. We simulate the active response of a myocardial cell (here considered as an anisotropic, hyperelastic, and incompressible material), the propagation of calcium concentrations inside it, and the presence of a surrounding Newtonian fluid. An active strain approach is employed to account for the mechanical activation, and the deformation of the cell membrane is captured using a level set strategy. We address in detail the main features of the proposed method, and we report several numerical experiments aimed at model validation. Copyright © 2013 John
Computational Fluid Dynamics (ICCFD7),
"... is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an authordeposited version published in: ..."
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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. This is an authordeposited version published in:
SimBRS: A UNIVERSITY/INDUSTRY CONSORTIUM FOCUSED ON SIMULATION BASED SOLUTIONS FOR GROUND VEHICLES
"... The Simulation Based Reliability and Safety (SimBRS) research program focuses the efforts of a university and industry consortium in meeting the objectives of TARDEC to address the various aspects of design and simulation of vehicular systems to improve the safety and reliability related to the warf ..."
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The Simulation Based Reliability and Safety (SimBRS) research program focuses the efforts of a university and industry consortium in meeting the objectives of TARDEC to address the various aspects of design and simulation of vehicular systems to improve the safety and reliability related to the warfighter. The activities performed by the consortium are in support of any aspect of the TARDEC mission to create a broad range of multiscale modeling, simulation, and validation tools and methodologies addressing reliability and safety, soldierenvironment interface, biomechanics, and simulationbased design optimization. These methodologies include multiscale experiments to optimize the robustness and reliability of the ground vehicle systems (tactical and combat) with the consideration of the human interaction. This paper will describe the present research focus of the consortium and illustrate the advantages of the consortium approach to solving complex engineering problems for ground vehicles.
Reducing the shear
, 2005
"... As gravitational lensing measurements become increasingly precise, it becomes necessary to include ever higher order effects in the theoretical calculations. Here we show how the difference between the shear and the reduced shear manifest themselves in a number of commonly used measures of shear pow ..."
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As gravitational lensing measurements become increasingly precise, it becomes necessary to include ever higher order effects in the theoretical calculations. Here we show how the difference between the shear and the reduced shear manifest themselves in a number of commonly used measures of shear power. If we are to reap the science rewards of future, high precision measurements of cosmic shear we will need to include this effect in our theoretical predictions.
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"... Frontiers in the Constitutive Modeling of Anisotropic Shock Waves Studies of anisotropic materials and the discovery of various novel and unexpected phenomena under shock loading has contributed significantly to our understanding of the behavior of condensed matter. The variety of experimental stud ..."
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Frontiers in the Constitutive Modeling of Anisotropic Shock Waves Studies of anisotropic materials and the discovery of various novel and unexpected phenomena under shock loading has contributed significantly to our understanding of the behavior of condensed matter. The variety of experimental studies for isotropic materials displays systematic patterns, giving basic insights into the underlying physics of anisotropic shock wave modeling. There are many similarities and significant differences in the phenomena observed for isotropic and anisotropic materials under shockwave loading. Despite this, the anisotropic constitutive equations must represent mathematical and physical generalization of the conventional constitutive equations for isotropic material and reduce to the conventional constitutive equations in the limit of isotropy. This article presents the current state of the art in the constitutive modeling of this fascinating field.
A HIGHERORDER UPWIND METHOD FOR VISCOELASTIC FLOW
"... We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier–Stokes equations with an extra viscoelastic stress described by the OldroydB constitutive equations. The equations are cast in ..."
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We present a conservative finite difference method designed to capture elastic wave propagation in viscoelastic fluids in two dimensions. We model the incompressible Navier–Stokes equations with an extra viscoelastic stress described by the OldroydB constitutive equations. The equations are cast into a hybrid conservation form which is amenable to the use of a secondorder Godunov method for the hyperbolic part of the equations, including a new exact Riemann solver. A numerical stress splitting technique provides a wellposed discretization for the entire range of Newtonian and elastic fluids. Incompressibility is enforced through a projection method and a partitioning of variables that suppresses compressive waves. Irregular geometry is treated with an embedded boundary/volumeoffluid approach. The method is stable for time steps governed by the advective Courant– Friedrichs–Lewy (CFL) condition. We present secondorder convergence results in L 1 for a range of OldroydB fluids. 1.
unknown title
, 2003
"... www.elsevier.com/locate/jcp An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics q ..."
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www.elsevier.com/locate/jcp An iterative Riemann solver for systems of hyperbolic conservation laws, with application to hyperelastic solid mechanics q