A gas kinetic Lax–Wendroff scheme for low-speed isothermal rarefied gas flows

Abstract

Previously, a gas kinetic Bhatnagar–Gross–Krook (BGK) scheme was proposed by us for incompressible flows in the continuum limits. [W. Li and W. Li, “A gas-kinetic BGK scheme for the finite volume lattice Boltzmann method for nearly incompressible flows,” Comput. Fluids 162, 126–138 (2018).] In the present work, we extend the gas kinetic BGK scheme to simulate low-speed isothermal rarefied nonequilibrium gas flows. This scheme is a gas kinetic Lax–Wendroff scheme (GKLWS) for the discrete velocity Boltzmann equation in the finite volume discretization framework with second-order accuracy in both time and space. As collision and transport of the molecular particles are coupled in the present GKLWS, the time step of the present method is not limited by the relaxation time, for which the present scheme is efficient for multiscale gas flows. Moreover, the present GKLWS holds the asymptotic preserving (AP) property, which ensures that both the Navier–Stokes solutions in the continuum limits and free-molecular flow solutions in the rarefied limits can be reliably obtained. To validate the accuracy and AP property of the GKLWS, several numerical benchmarks of isothermal low-speed rarefied gas flows are simulated by the present scheme. The numerical results show that the present scheme can be a reliable multiscale method for all Knudsen number low-speed isothermal gas flows.