SPH and Riemann solvers

Smooth particle hydrodynamics (SPH) is usually based on equations derived from the momentum and thermal energy equations of fluid dynamics. Artificial viscosity is added to these equations to handle shocks. In this paper we show how the equations may be formulated using the specific energy equation instead of the thermal energy equation. The resulting equations are very similar to the equations constructed for Riemann solutions of compressible gas dynamics. In particular the artificial viscosity is analogous to terms constructed from signal velocities and jumps in variables across characteristics. When applied to shock tubes, blast waves, wall shocks, and the Roberts and Sjogreen problems the new equations give very good results. They also provide the basis for the generalization of SPH to relativistic flows. (C) 1997 Academic Press.