Second Order Godunov SPH for High Velocity Impact Dynamics

Abstract

Abstract. In this work the Godunov Smoothed Particle Hydrodynamics (SPH) method for material with strength is extended to second order in space. This is achieved by separating the continuum equations of motion into their constituent hydrodynamic and deviatoric parts and using a MUSCL-type reconstruction and limiting procedure for the left and right Riemann states. The split equations are then advanced in time sequentially using a first-order operator splitting procedure. The resulting equations require no user defined artificial damping parameters as sufficient numerical dissipation is introduced through the use of a Riemann solver. One and two dimensional elastic-plastic flows are chosen to demonstrate the efficacy of the proposed formulation and the results are compared with exact solutions, the original first order scheme and the standard artificial viscosity SPH scheme. The new method is then applied to the simulation of a representative ballistic impact on a ceramic armour material.