Conservative smoothing with B-splines stabilizes SPH material dynamics in both tension and compression

摘要

Smooth particle hydrodynamics (SPH) is a grid free method for material dynamics which appears to have potential advantages over fixed grid methods with respect to grid tangling. Standard SPH (with stress σ and interpolation weight W) has instabilities of two types when σW″<0: compression (σ>0) and tension (σ<0). In theory, conservative smoothing can stabilize both types, but carefully controlling smoothing to prevent excessive loss of fine detail had been found to be difficult in some numerical experiments. Here we present an easy, natural way of using the SPH B-spline finite interpolation method to introduce sufficient conservative smoothing to stabilize SPH material dynamics in both tension and compression. We present numerical results for both tension and compression which provide evidence of the efficacy of this approach.