Lattice Boltzmann simulation for high-speed compressible viscous flows with a boundary layer

Abstract

• A coupled DDF-LB model was used to simulate high-speed compressible viscous flows. • NND and second-order upwind difference schemes were compared in simulations. • The DDF-LB model could simulate a compressible boundary layer up to Ma = 6. • Local high pressure appeared with the shock wave due to LBM’s mesoscopic feature. • High potential of LBM was shown for the shock boundary layer interaction problem. In this study, the lattice Boltzmann method is employed for simulating high-speed compressible viscous flows with a boundary layer. The coupled double-distribution-function lattice Boltzmann method proposed by Li et al. (2007) is employed because of its good numerical stability and non-free-parameter feature. The non-uniform mesh construction near the wall boundary in fine grids is combined with an appropriate wall boundary treatment for the finite difference method in order to obtain accurate spatial resolution in the boundary layer problem. Three typical problems in high-speed viscous flows are solved in the lattice Boltzmann simulation, i.e., the compressible boundary layer problem, shock wave problem, and shock boundary layer interaction problem. In addition, in-depth comparisons are made with the non-oscillatory and non-free-parameter dissipation (NND) scheme and second order upwind scheme in the present lattice Boltzmann model. Our simulation results indicate the great potential of the lattice Boltzmann method for simulating high-speed compressible viscous flows with a boundary layer. Further research is needed (e.g., better numerical models and appropriate finite difference schemes) because the lattice Boltzmann method is still immature for high-speed compressible viscous flow applications.