A parallel multi-resolution Smoothed Particle Hydrodynamics model with local time stepping

Abstract

Smoothed Particle Hydrodynamics (SPH) model has exhibited remarkable efficacy in addressing strongly nonlinear large deformation problems. However, the expensive computational cost could limit its application. To address this, we propose a novel parallel multi-resolution SPH model with a local time step strategy. This model integrates the multi-resolution model with a Message Passing Interface-based parallelization framework, wherein subdomains discretize the computational domain at varying resolutions. Meanwhile, a local fourth-order Runge-Kutta time integration scheme is introduced, enabling different subdomains to use different time steps. Subdomains of varying resolutions are devoid of overlapping regions, and changes in particle resolution at interfaces are achieved through a dynamic strategy involving particle merging and splitting. Besides that, we conducted a comparative analysis of different SPH discretization formats concerning their impact on the accuracy of multi-resolution particle discretization. Finally, several numerical tests were conducted to validate the accuracy and efficiency of the present multi-resolution SPH model.