An Efficient Nonlinear Multigrid Solver for the Simulation of Rarefied Gas Cavity Flow (Communications in Computational Physics, 2023)
We study efficient simulation of steady state for multi-dimensional rarefiedgas 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 isfirst adopted to derive the high-quality discretization of the underlying problem. Afast 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 asthe 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 twolid-driven cavity flows and a bottom-heated cavity flow are carried out to investigatethe performance of the resulting nonlinear multigrid solver. All results show the wonderful efficiency and robustness of the solver for both first- and second-order spatialdiscretization.