A gas kinetic Lax–Wendroff scheme-based finite volume lattice Boltzmann method for high Mach compressible flows

This paper presents a gas kinetic Lax–Wendroff scheme (GKLWS)-based finite volume lattice Boltzmann method for high Mach compressible flows. The scheme is constructed based on the total energy kinetic model, which realizes the exact and efficient recovery of the full compressible Navier–Stokes equations through Hermite expansions. A characteristic temperature is introduced to non-dimensionalize the equilibrium states, such that the truncation errors can be reduced and the numerical stability can be enhanced in simulating high Mach compressible problems. Furthermore, the total energy kinetic model is performed on an unstructured second-order accurate finite volume discretization formulation, and the GKLWS is implemented to reconstruct the fluxes on the cell interfaces, enabling the present scheme to compute the compressible flows over complex geometries with lower numerical dissipations. Numerical tests are conducted to validate the present scheme, including compressible Couette flow, the Riemann problem, the double Mach reflection problem, the shock boundary layer interaction and the hypersonic flow over a cylinder. Comparisons with the benchmark results confirm that the proposed scheme is a reliable tool for high Mach compressible flow simulations.