An efficient correction method in Riemann SPH for the simulation of general free surface flows

Abstract

In this paper, a new efficient weighted correction method for weakly-compressible smoothed particle hydrodynamics is proposed and successfully implemented in the simulation of violent free-surface flow exhibiting breaking and impact events for the first time. It is well known that the original kernel gradient correction (KGC) encounters numerical instability resulting from matrix inversion. The present method remedies this issue by introducing a weighted average of the KGC matrix and the identity matrix, other than directly applying the KGC matrix, to achieve numerical stability meanwhile decrease numerical dissipation. To ensure momentum conservation, the correction is implemented in a particle-average pattern by rewriting the pressure term of the Riemann solution. Furthermore, the proposed weighted KGC scheme is incorporated into the dual-criteria time-stepping framework developed by Zhang et al. (2020) to achieve optimized computational efficiency. A set of numerical examples in both two- and three-dimensions are investigated to demonstrate that the present method can significantly reduce numerical dissipation meanwhile exhibit a smooth pressure field for general free-surface flows.