A shock-capturing scheme with a novel limiter for compressible flows solved by smoothed particle hydrodynamics

Abstract

There are many compressible flows involving strong discontinuities in nature and engineering applications. Their behaviors are complicated by the existence of shock waves, rarefaction waves and contact discontinuities. To investigate these flows, a shock-capturing scheme based on smoothed particle hydrodynamics (SPH) is proposed. In this scheme, Roe’s approximate Riemann solver cooperated with a novel limiter is embedded into the SPH governing equations to capture shocks. This limiter is simple and effective to control numerical dissipations, and the use of this limiter eliminates the tunable artificial viscosity as required by the conventional SPH. Additionally, to restore the accuracy limited by heterogeneous particle distribution that is usually encountered in the simulation of strongly-compressible flows, the gradient operator in the continuity equation is corrected by a renormalization procedure. Last but not least, for initial particle distribution, unlike the equal mass particle distribution commonly used in compressible SPH simulations, the equal spacing particle distribution is adopted in this scheme, which makes it much easier to model multidimensional problems. The present scheme has been verified by a set of benchmark tests involving contact discontinuities, extreme shock waves and strong rarefaction waves, some of which are firstly simulated by the SPH method.