An improved SPH method for compressible flows with high density ratios

Abstract

An improved Smoothed Particle Hydrodynamics (SPH) method is proposed for supersonic compressible flows with high density ratios. Based on the Reproducing Kernel Particle Method (RKPM), the interaction forces are adjusted by incorporating a pressure correction factor that accounts for the sound speed in the momentum and thermal energy equations. The modification enhances the accuracy and stability of the SPH method when calculating supersonic compressible flows with high density ratios while ensuring conservation. Numerical results demonstrate the capability of the improved SPH method to accurately capture shock waves and rarefaction waves in benchmark problems. Furthermore, compared with the RKPM, the improved SPH method exhibits reduced uncertainty at contact discontinuities in one dimensional strong shock problems with high density ratios. The method also mitigates unphysical oscillations in physical quantities and imposes lower requirements on the time step. Additionally, when simulating two dimensional compressible flow problems with high density ratios, it can effectively suppress tensile and compressive instabilities.