Particle distribution and numerical stability in smoothed particle hydrodynamics method

Abstract

Smoothed particle hydrodynamics(SPH) is a Lagrangian meshfree particle method, and has been widely applied to different areas including incompressible or pseudo-incompressible flows with multiphase interfaces and moving boundaries. In this paper, an instability problem has been identified when the conventional SPH method is applied to modeling the Poiseuille flow problem at long-term simulations. It is found that this instability resulted from the particle inconsistency inherent to the SPH method, which originates from the discrete particle approximation and is a fundamental cause for poor approximation accuracy. A new particle approximation approach has been used to restore the particle consistency. We show that this particle consistency restoring approach can produce stable solutions for both regular and irregular particle distributions even at long-term simulations.