Shock Simulation by the Particle Method SPH

The particle method SPH is applied to one-dimensional shock tube problems by incorporating an artificial viscosity into the equations of motion. When the artificial viscosity is either a bulk viscosity or the Von Neumann-Richtmyer viscosity, in a form analogous to that for finite differences, the results show either excessive oscillation or excessive smearing of the shock front. The reason for the excessive particle oscillation is that, in the standard form, the artificial viscosity cannot dampen irregular motion on the scale of the particle separation since that scale is usually less than the resolution of the interpolating kernel. We propose a new form of artificial viscosity which eliminates this problem. The resulting shock simulation has negligible oscillation and satisfactorily sharp discontinuities. Results with a gaussian interpolating kernel (with second-order errors) are shown to be greatly inferior to those with a super gaussian kernel (with fourth-order errors).