TY - JOUR
T1 - An Explicit Multi-Time Stepping Algorithm for Multi-Time Scale Coupling Problems in SPH
AU - Tang , Xiaojing
AU - Wu , Dong
AU - Wang , Zhentong
AU - Haidn , Oskar
AU - Hu , Xiangyu
JO - Communications in Computational Physics
VL - 5
SP - 1219
EP - 1261
PY - 2024
DA - 2024/12
SN - 36
DO - http://doi.org/10.4208/cicp.OA-2024-0037
UR - https://global-sci.org/intro/article_detail/cicp/23608.html
KW - SPH, multi-time scale coupling, multi-time step algorithm, dynamic relaxation, multi-physics problem.
AB - <p style="text-align: justify;">Simulating physical problems with multi-time scale coupling presents a considerable challenge due to the concurrent solution of processes with different time
scales. This complexity arises from the necessity to evolve large time scale processes
over long physical time, while simultaneously small time step sizes are required to
unveil the underlying physics in shorter time scale processes. To address this inherent
conflict in the multi-time scale coupling problems, we propose an explicit multi-time
step algorithm within the framework of smoothed particle hydrodynamics (SPH), coupled with a solid dynamic relaxation scheme, to quickly achieve equilibrium state in
the comparatively fast solid response process. To assess the accuracy and efficiency
of the proposed algorithm, a manuscript torsional example, two distinct scenarios,
i.e., a nonlinear hardening bar stretching and a fluid diffusion coupled with Nafion
membrane flexure, are simulated. The obtained results exhibit good agreement with
analytical solution, outcomes from other numerical methods and experimental data.
With this explicitly multi-time step algorithm, the simulation time is reduced firstly
by independently addressing different processes being solved under distinct time step
sizes, which stands in contrast to the implicit counterpart, and secondly decreasing
the simulation time required to achieve a steady state for the solid by incorporating
the dynamic relaxation scheme.</p>