2022/09/16 by Liyan Luo, Qi Li, Luo, Liyan +3
Engineering · Mathematics · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Particle Dynamics in Fluid Flows
paper · pdf · doi:10.48550/arxiv.2209.07733
openalex publication_date 2022/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The low-variance direct simulation Monte Carlo (LVDSMC) is a powerful method to simulate low-speed rarefied gas flows. However, in the near-continuum flow regime, due to limitations on the time step and spatial cell size, it takes plenty of time to find the steady-state solution. Here we remove these deficiencies by coupling the LVDSMC with the general synthetic iterative scheme (GSIS) which permits the simulation at the hydrodynamic scale rather than the much smaller kinetic scale. As a proof of concept, we propose the stochastic-deterministic coupling method based on the Bhatnagar-Gross-Krook kinetic model. First, macroscopic synthetic equations are derived exactly from the kinetic equation, which not only contain the Navier-Stokes-Fourier constitutive relation, but also encompass the higher-order terms describing the rarefaction effects. Then, the high-order terms are extracted from LVDSMC and fed into synthetic equations to predict macroscopic properties which are closer to the steady-state solution than LVDSMC. Finally, the state of simulation particles in LVDSMC is updated to reflect the change of macroscopic properties. As a result, the convergence to steady state is greatly accelerated, and the restriction on cell size and the time step are removed: after simulating several canonical rarefied gas flows, we demonstrate that the LVDSMC-GSIS reduces the computational cost by two orders of magnitude in the near-continuum flow regime.