Simulations of compressible flows with strong shocks by an adaptive lattice Boltzmann model

An adaptive lattice Boltzmann model for compressible flows is presented. Th e particle-velocity set is so large that the mean flow may have a high velo city. The support set of the equilibrium-distribution function is quite sma ll and varies with the mean velocity and internal energy. The adaptive natu re of this support set permits the mean flows to have high Mach number, mea nwhile, it makes the model simple and practicable. The model is suitable fo r perfect gases with an arbitrary specific heat ratio. Navier-Stokes equati ons are derived by the Chapman-Enskog method from the BGK Boltzmann equatio n. When the viscous terms and the diffusion terms are considered as a discr etion error this system becomes an inviscid Euler system. Several simulatio ns of flows with strong shocks, including the forward-facing step test, dou ble Mach reflection test, and a strong shock of Mach number 5.09 diffractin g around a corner, were carried out on hexagonal lattices, showing the mode l's capability of simulating the propagation of strong shock waves. (C) 200 0 Academic Press.