A Nonlinear Multigrid Steady-State Solver for Microflow

TL;DR

This paper introduces a nonlinear multigrid solver tailored for steady-state microflow problems modeled by high order moment systems, demonstrating robustness and efficiency improvements over traditional methods.

Contribution

A novel nonlinear multigrid method with a symmetric Gauss-Seidel and local Newton smoother for steady microflow equations is proposed, enhancing robustness and efficiency.

Findings

Solver is insensitive to implementation parameters

Achieves significant efficiency improvements

Demonstrates robustness through numerical examples

Abstract

We develop a nonlinear multigrid method to solve the steady state of microflow, which is modeled by the high order moment system derived recently for the steady-state Boltzmann equation with ES-BGK collision term. The solver adopts a symmetric Gauss-Seidel iterative scheme nested by a local Newton iteration on grid cell level as its smoother. Numerical examples show that the solver is insensitive to the parameters in the implementation thus is quite robust. It is demonstrated that expected efficiency improvement is achieved by the proposed method in comparison with the direct time-stepping scheme.