Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
A conservative Eulerian formulation of the equations for elastic flow
Advances in Applied Mathematics
A second-order Godunov method for conservation laws of nonlinear elastodynamics
IMPACT of Computing in Science and Engineering
IMPACT of Computing in Science and Engineering
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
On the implicit large eddy simulations of homogeneous decaying turbulence
Journal of Computational Physics
An Eulerian method for multi-component problems in non-linear elasticity with sliding interfaces
Journal of Computational Physics
An Eulerian hybrid WENO centered-difference solver for elastic-plastic solids
Journal of Computational Physics
A conservative level-set based method for compressible solid/fluid problems on fixed grids
Journal of Computational Physics
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Journal of Computational Physics
An Eulerian algorithm for coupled simulations of elastoplastic-solids and condensed-phase explosives
Journal of Computational Physics
Hi-index | 31.47 |
Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented.