On the derivation of SPH schemes for shocks through inhomogeneous media

Smoothed Particle Hydrodynamics (SPH) is typically used for the simulation of shock propagation through solid media, commonly observed during hypervelocity impacts. Although schemes for impacts into monolithic structures have been studied using SPH, problems occur when multimaterial structures are considered. This study begins from a variational framework and builds schemes for multiphase compressible problems, coming from different density estimates. Algorithmic details are discussed and results are compared upon three one-dimensional Riemann problems of known behavior.