Dual-criteria time stepping for weakly compressible smoothed particle hydrodynamics

Abstract

Implementing particle-interaction configuration, which consists of determining particle-neighbor lists and computing corresponding kernel weights and gradients, and time integration are performance intensive essentials of smoothed particle hydrodynamic (SPH) method. In this paper, a dual-criteria time-stepping method is proposed to improve the computational efficiency of the weakly-compressible SPH (WCSPH) method for modeling incompressible flows. The key idea is to introduce an advection time-step criterion, which is based on flow speed, for recreating the particle-interaction configuration. Within an advection time-step, several steps of pressure relaxation, i.e. the time integration of the particle density, position and velocity due to the action of pressure gradient, according to the acoustic time-step criterion based on the artificial speed of sound, can be carried out without updating the particle-interaction configuration and with much larger time steps compared with the conventional counterpart. The method has shown optimized computational performance through CPU cost analysis. Good accuracy is also obtained for the presented benchmarks implying promising potential of the proposed method for simulating incompressible flows and fluid-structure interactions.