A conservative Eulerian formulation of the equations for elastic flow
Advances in Applied Mathematics
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Computational methods in Lagrangian and Eulerian hydrocodes
Computer Methods in Applied Mechanics and Engineering
A conservative formulation for plasticity
Advances in Applied Mathematics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
A free-Lagrange augmented Godunov method for the simulation of elastic-plastic solids
Journal of Computational Physics
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
Ghost fluid method for strong shock impacting on material interface
Journal of Computational Physics
On the computation of multi-material flows using ALE formulation
Journal of Computational Physics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
A conservative level set method for two phase flow
Journal of Computational Physics
Modelling wave dynamics of compressible elastic materials
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Short Note: On reinitializing level set functions
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
Discrete multi-material interface reconstruction for volume fraction data
EuroVis'08 Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
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An Eulerian, multi-material numerical method is described for computing dynamic problems involving large deformations in elastic-plastic solids. This approach addresses algorithm failures associated with reconnection and change in topology observed in previously proposed formulations. Among the information contained in the deformation gradients commonly employed for defining constitutive laws suitable for solids, only the symmetric matrix tensor obtained from a polar decomposition of the elastic component of the deformation is required to determine the stress state. The numerical utilization of this symmetric tensor, associated with material stretch, eliminates undesirable, discontinuous deformation states produced by local rigid-body rotations at same-material reconnecting interfaces. Such states appear even where stress states in impacting regions are similar. The temporal evolution of the stretches neither modifies the eigenstructure of the system of equations nor changes its size. We also present a new multi-material approximate Riemann solver based on the HLLD approach, previously applied to other hyperbolic systems, in which waves of distinct velocity exist, for example, as in magnetohydrodynamics. This solver is employed in combination with the modified ghost fluid method (M-GFM) in the description of multi-material interfaces. These composite algorithms enable numerical simulations of the Richtmyer-Meshkov instability (i.e., the instability produced by the interaction of an interface separating materials of different density with a shock wave at an angle) in converging geometries for solid materials that would have previously led to the failure of the method.