Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver for two-dimensional elastic-plastic flows with slip/no-slip interface boundary conditions

We present a multi-material Harten-Lax-van Leer-discontinuities with elastic waves (HLLD-e) approximate Riemann solver with a hypoelastic model for solving two-dimensional elastic-plastic flows under tangential slip/no-slip interface boundary conditions. Shear waves and their effects have not been fully explored in HLL-type (Harten, Lax, and van Leer) Riemann solvers. To this end, transformed equations corresponding to the deviatoric stress and their Rankine–Hugoniot (RH) relations are obtained. In addition, normal interface and slip/no-slip boundary conditions are imposed separately to close the solver system. Associated with the modified ghost fluid method (MGFM), the propagation and configurations of the shear waves are examined, and the results agree with those of previous studies. In addition, rarefaction waves and fluid-structure interactions can be computed owing to the wide applicability of this solver. In the future, to better describe the behavior of plastic waves, elastoplastic results can be considered for an approximate Riemann solver.