An Approximate Riemann Solver for Fluid-Solid Interaction Problems with Mie-Grüneisen Equations of State (Communications in Computational Physics, 2020)
We propose an approximate solver for compressible fluid-elastoplastic solid Riemann problems. The fluid and hydrostatic components of the solid are described by a family of general Mie-Grüneisen equations of state, and the hypo-elastoplastic constitutive law we studied includes the perfect plasticity and linearly hardened plasticity. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are verified 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, underground explosion and high speed impact applications, are presented to validate the approximate solver.