Rigorously justified local time stepping in UGKWP method for steady multiscale flow simulation

Wenzhi Guo; Junzhe Cao; Wenpei Long; Kun Xu

Rigorously justified local time stepping in UGKWP method for steady multiscale flow simulation

Fluid Dynamics 2026-07-10 v1 Computational Physics

Authors: Wenzhi Guo , Junzhe Cao , Wenpei Long , Kun Xu

Abstract

In this Letter, local time stepping (LTS) is incorporated into the unified gas-kinetic wave-particle (UGKWP) method for steady multiscale flow simulation. It accelerates convergence step by a factor of $3.8\times$ -- $20\times$ and reduces wall-clock time by up to $21\times$ relative to global time stepping (GTS). A rigorous analysis of the particle flux under LTS identifies that fixed per-cell as $\Delta t_i$ is a sufficient condition for the time-averaged flux balance. This condition has not been stated in prior particle-based LTS work, where $\Delta t_i$ varies in time and the flux balance is therefore not guaranteed. Together with proportional rescaling of particle mass and free transport time at cell interfaces, the fixed- $\Delta t_i$ condition yields a conservative framework with no free parameters. The UGKWP-LTS method is validated on cylinder and flat-plate benchmarks that possess multiscale flow features.

Cite

@article{arxiv.2607.09552,
  title  = {Rigorously justified local time stepping in UGKWP method for steady multiscale flow simulation},
  author = {Wenzhi Guo and Junzhe Cao and Wenpei Long and Kun Xu},
  journal= {arXiv preprint arXiv:2607.09552},
  year   = {2026}
}