A denoising multiscale particle method for nonequilibrium flow simulations

The direct simulation Monte Carlo (DSMC) method is promising for simulating rarefied nonequilibrium flows, but its inherent limitations on spatiotemporal resolution and statistical noise hinder applications in near-continuum and low-signal regimes. This work proposes a denoising multiscale particle (DMP) method for efficient particle-based simulations. The DMP method employs a Bhatnagar–Gross–Krook (BGK) relaxation process to simplify binary collisions. Its denoising strategy, inspired by the information preservation method, incorporates low-noise collective information into each simulation particle. This collective information evolves anchored on the information-augmented Shakhov BGK equation, which provides a theoretical foundation for analyzing transport and denoising properties. Macroscopic flow quantities are obtained by statistically averaging this collective information, resulting in a signal-to-noise ratio independent of signal magnitude in low- to moderate-signal regimes, while proportional to the local rarefaction level. An operator splitting scheme is utilized to decouple particle movement and relaxation, enabling a simple and efficient implementation but introducing numerical dissipation in the Navier–Stokes limit. In DMP, this numerical dissipation error is quantified and mitigated through incorporating anti-dissipation target distribution and information compensation terms, endowing the method with multiscale simulation capability. Consequently, the DMP method allows for coarser spatiotemporal resolutions and requires fewer sampling particles than DSMC. Various numerical experiments validate the accuracy and demonstrate the efficiency of the DMP method in low- to moderate-rarefaction and signal regimes.