A novel fast iterative moment method for near-continuum flows

Abstract

We develop a novel fast iterative moment method for the steady-state simulation of near-continuum flows, which are modeled by the high-order moment system derived from the Boltzmann-BGK equation. The fast convergence of the present method is mainly achieved by alternately solving the moment system and the hydrodynamic equations with consistent constitutive relations and boundary conditions. To be specific, the consistent hydrodynamic equations are solved in each alternating iteration to obtain improved predictions of macroscopic quantities, which are subsequently utilized to expedite the evolution of the moment system. Additionally, a semi-implicit scheme treating the collision term implicitly is introduced for the moment system. The resulting alternating iteration can be further accelerated by employing the Gauss-Seidel method with a cell-by-cell sweeping strategy. It is also noteworthy that such an alternating iteration works well with the nonlinear multigrid method. Numerical experiments for planar Couette flow, shock structure, and lid-driven cavity flow are carried out to investigate the performance of the proposed fast iterative moment method. All results show impressive efficiency and robustness.