A nonlinear multigrid steady-state solver for 1D microflow

• Moment system is global hyperbolic.
• Implementation is unified for the system with moments up to arbitrary order.
• Nonlinear multigrid is developed with a nested iteration as its smoother.
• Robustness and efficiency of the solver are demonstrated by numerical examples.

We develop a nonlinear multigrid method to solve the steady state of 1D 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.