An explicit multi-time stepping algorithm for multi-time scale coupling problems in SPH

TL;DR

This paper introduces an explicit multi-time step algorithm with relaxation techniques for efficiently simulating multi-time scale coupling problems in SPH, demonstrating improved accuracy and reduced computational time.

Contribution

It presents a novel explicit multi-time step algorithm coupled with a relaxation scheme for SPH, enabling efficient simulation of multi-time scale problems with reduced computational effort.

Findings

Good agreement with experimental data

Reduced simulation time compared to traditional methods

Effective coupling of different physical processes

Abstract

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step algorithm coupled with a solid dynamic relaxation scheme. The explicit scheme simplifies the equation system in contrast to the implicit scheme, while the multi-time step algorithm allows the equations of different physical processes to be solved under different time step sizes. Furthermore, an implicit viscous damping relaxation technique is applied to significantly reduce computational iterations required to achieve equilibrium in the comparatively fast solid response process. To validate the accuracy and efficiency of the proposed algorithm, two distinct scenarios, i.e., a nonlinear hardening bar stretching and a fluid diffusion coupled with Nafion membrane flexure, are simulated. The results show good agreement with experimental data and results from other numerical methods, and the simulation time is reduced firstly by independently addressing different processes with the multi-time step algorithm and secondly decreasing solid dynamic relaxation time through the incorporation of damping techniques.