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 - <p style="text-align: justify;">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.</p>