In this paper, 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 compatible constitutive relations and boundary conditions. To be specific, the compatible hydrodynamic equations are solved in each iteration to get 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. With cell-by-cell sweeping strategy, the resulting alternating iteration can be further accelerated for steady-state computation. It is also worth mentioning 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, and all results show wonderful efficiency and robustness.

翻译：本文针对由Boltzmann-BGK方程导出的高阶矩系统所模拟的近连续流稳态问题，发展了一种新型快速迭代矩方法。该方法主要通过交替求解矩系统与具有相容本构关系及边界条件的流体动力学方程来实现快速收敛。具体而言，每次迭代中先求解相容流体动力学方程以获得宏观量的改进预测，进而利用这些预测加速矩系统的演化进程。此外，针对矩系统引入了碰撞项隐式处理的半隐格式。结合逐单元扫描策略，所构建的交替迭代过程可进一步加速稳态计算。值得指出的是，该交替迭代方法与非线性多重网格方法具有良好兼容性。通过平面Couette流、激波结构及顶盖驱动方腔流等数值算例，验证了本文所提快速迭代矩方法的性能，所有结果均展现出优异的计算效率与鲁棒性。