An efficient nonlinear multigrid solver for the simulation of rarefied gas cavity flow

TL;DR

This paper introduces a nonlinear multigrid solver for steady-state rarefied gas flow simulation, utilizing a regularized moment method, fast sweeping iteration, and parallelization to improve efficiency and robustness.

Contribution

A novel nonlinear multigrid solver combining regularized moment methods and fast sweeping iteration for efficient rarefied gas flow simulation.

Findings

Demonstrates significant convergence rate improvement.

Shows robustness for first- and second-order discretizations.

Achieves accelerated computation with OpenMP parallelization.

Abstract

We study efficient simulation of steady state for 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 efficiency and robustness of the solver for both first- and second-order spatial discretization.