Lattice-Boltzmann models for high speed flows

We formulate a lattice Boltzmann model to solve supersonic flows. The particle velocities are determined by the mean velocity and internal energy. The adaptive nature of particle velocities permits the mean flow to have a high Mach number. The introduction of a particle potential energy causes the model to be suitable for a perfect gas with an arbitrary specific heat ratio. The macroscopic conservation equations are derived by the Chapman-Enskog method. The simulations were carried out on the hexagonal lattice. However, the extension to both two- and three-dimensional square lattices is straightforward. As preliminary tests, we present the Sod shock-tube simulation and the two-dimensional shock reflection simulation.