Simulations of Compressible Flows with Strong Shocks by an Adaptive Lattice Boltzmann Model

An adaptive lattice Boltzmann model for compressible flows is presented. The particle-velocity set is so large that the mean flow may have a high velocity. The support set of the equilibrium-distribution function is quite small and varies with the mean velocity and internal energy. The adaptive nature of this support set permits the mean flows to have high Mach number, meanwhile, it makes the model simple and practicable. The model is suitable for perfect gases with an arbitrary specific heat ratio. Navier–Stokes equations are derived by the Chapman–Enskog method from the BGK Boltzmann equation. When the viscous terms and the diffusion terms are considered as a discretion error this system becomes an inviscid Euler system. Several simulations of flows with strong shocks, including the forward-facing step test, double Mach reflection test, and a strong shock of Mach number 5.09 diffracting around a corner, were carried out on hexagonal lattices, showing the modelʹs capability of simulating the propagation of strong shock waves.