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

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 $\mathrm{\Delta }{t}_i$ is a sufficient condition for the time-averaged flux balance. This condition has not been stated in prior particle-based LTS work, where $\mathrm{\Delta }{t}_i$ 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-$\mathrm{\Delta }{t}_i$ 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.