An Explicit Multi-Time Stepping Algorithm for Multi-Time Scale Coupling Problems in SPH (Communications in Computational Physics, 2024)
Simulating physical problems with multi-time scale coupling presents a considerable challenge due to the concurrent solution of processes with different timescales. This complexity arises from the necessity to evolve large time scale processesover long physical time, while simultaneously small time step sizes are required tounveil the underlying physics in shorter time scale processes. To address this inherentconflict in the multi-time scale coupling problems, we propose an explicit multi-timestep algorithm within the framework of smoothed particle hydrodynamics (SPH), coupled with a solid dynamic relaxation scheme, to quickly achieve equilibrium state inthe comparatively fast solid response process. To assess the accuracy and efficiencyof the proposed algorithm, a manuscript torsional example, two distinct scenarios,i.e., a nonlinear hardening bar stretching and a fluid diffusion coupled with Nafionmembrane flexure, are simulated. The obtained results exhibit good agreement withanalytical solution, outcomes from other numerical methods and experimental data.With this explicitly multi-time step algorithm, the simulation time is reduced firstlyby independently addressing different processes being solved under distinct time stepsizes, which stands in contrast to the implicit counterpart, and secondly decreasingthe simulation time required to achieve a steady state for the solid by incorporatingthe dynamic relaxation scheme.