A hybrid approach to couple the discrete velocity method and Method of Moments for rarefied gas flows

It is known that the Method of Moments is less accurate close to the wall where non-equilibrium effects are strong. We therefore propose a hybrid algorithm that combines the discrete velocity method with the Method of Moments to accurately simulate rarefied gas flows in the transition regime. A discrete velocity approach, combined with Maxwell's wall boundary condition, is employed in the near-wall region and the moment equations are used to describe the bulk flow field. Numerical simulations demonstrate that the proposed hybrid scheme not only extends the applicability of the regularized 26 moment equations to a wider range of Knudsen numbers, but also reduces the computational cost (i.e. memory and time) in comparison with the discrete velocity method. For Poiseuille and cavity flows, good agreement is observed between the hybrid method and discrete velocity results, especially in the near-wall region. The thicker the computational kinetic layer used in the hybrid method, the more accurate the solution can be obtained. The hybrid scheme can also be used to simulate thermally induced non-equilibrium flows, where both the velocity magnitude and the stress tensor predicted by the hybrid method are in good agreement with results from the discrete velocity method. Our proposed approach is particularly suitable for flows where the number of wall boundary cells, relative to the total computational cells, is small, as demonstrated by a square cylinder case. The proposed hybrid method can readily be extended to simulate practical rarefied gas flows in the transition regime.