TY - JOUR T1 - An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow AU - Hu , Zhicheng AU - Li , Guanghan JO - Communications in Computational Physics VL - 2 SP - 357 EP - 391 PY - 2023 DA - 2023/09 SN - 34 DO - http://doi.org/10.4208/cicp.OA-2022-0271 UR - https://global-sci.org/intro/article_detail/cicp/21972.html KW - Boltzmann equation, moment method, multigrid, rarefied gas flow, steady state. AB -

We study efficient simulation of steady state for multi-dimensional rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following approaches. The unified framework of numerical regularized moment method is first adopted to derive the high-quality discretization of the underlying problem. A fast sweeping iteration is introduced to solve the derived discrete problem more efficiently than the usual time-integration scheme on a single level grid. Taking it as the smoother, the nonlinear multigrid solver is then established to significantly improve the convergence rate. The OpenMP-based parallelization is applied in the implementation to further accelerate the computation. Numerical experiments for two lid-driven cavity flows and a bottom-heated cavity flow are carried out to investigate the performance of the resulting nonlinear multigrid solver. All results show the wonderful efficiency and robustness of the solver for both first- and second-order spatial discretization.