An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow  

作　　者：Zhicheng Hu Guanghan Li 

机构地区：[1]School of Mathematics,Nanjing University of Aeronautics and Astronautics,Nanjing 211106,China [2]Key Laboratory of Mathematical Modelling and High Performance Computing of Air Vehicles(NUAA),MIIT,Nanjing 211106,China

出　　处：《Communications in Computational Physics》2023年第7期357-391,共35页计算物理通讯（英文）

基　　金：partially supported by the National Natural Science Foundation of China,No.12171240;the Fundamental Research Funds for the Central Universities,China,No.NS2021054.

摘　　要：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.

关 键 词：Boltzmann equation moment method MULTIGRID rarefied gas flow steady state 

分 类 号：O24[理学—计算数学]