  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.
