Godunov SPH with an operator-splitting procedure for materials with strength

This paper presents a modification of the Godunov Smoothed Particle Hydrody- namics (GSPH) method of Parshikov et al. for isotropic materials with strength. The motiva- tion behind this modification is that it facilitates a higher-order reconstruction of the left and right hand Riemann states, thus increasing the accuracy of the method. A consequence of this modification is that different smoothing kernel functions may be used within each timestep, which may be exploited to help alleviate the intrinsic instabilities of the SPH method. The paper begins with a description of the SPH method then reviews the different Godunov SPH formulations available. The modified GSPH procedure is then detailed and results are pre- sented for one and two-dimensional test cases and compared with predictions made with the standard Artificial Viscosity SPH (AVSPH) formulation.

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