TY - JOUR
T1 - 1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application
AU - Gao , Si
AU - Liu , Tiegang
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 621
EP - 650
PY - 2018
DA - 2018/05
SN - 9
DO - http://doi.org/10.4208/aamm.2015.m1340
UR - https://global-sci.org/intro/article_detail/aamm/12167.html
KW - Riemann problem, elastic-plastic solid, ghost fluid method, multi-material flows.
AB - <p style="text-align: justify;">The equation of state (EOS) plays a crucial role in hyperbolic conservation
laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic
phase transition makes the analysis of the solid Riemann problem more difficult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem is
investigated and its exact Riemann solver is proposed. Different from previous works
treating the elastic and plastic phases integrally, we resolve the elastic wave and plastic
wave separately to understand the complicate nonlinear waves within the solid
and then assemble them together to construct the exact Riemann solver for the elastic-perfectly
plastic solid. After that, the exact solid Riemann solver is associated with the
fluid Riemann solver to decouple the fluid-solid multi-material interaction. Numerical
tests, including gas-solid, water-solid high-speed impact problems are simulated
by utilizing the modified ghost fluid method (MGFM).</p>