TY - JOUR
T1 - A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid   Mediums
AU - Li , Ruo
AU - Wang , Yanli
AU - Yao , Chengbao
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 212
EP - 250
PY - 2019
DA - 2019/12
SN - 12
DO - http://doi.org/10.4208/aamm.OA-2019-0039
UR - https://global-sci.org/intro/article_detail/aamm/13425.html
KW - Riemann solver, Mie-Grüneisen, hydro-elastoplastic solid, multi-medium flow.
AB - <p style="text-align: justify;">We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Grüneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.</p>