Thermal lattice Boltzmann model for compressible fluid

We formulate it new thermal lattice Boltzmann model to simulate compressibl e flows with a high Mach number. The main difference from the standard latt ice Boltzmann models is that the particle velocities are no longer a consta nt, varying with the mean velocity and internal energy. The proper heat con duction term in the energy equation is recovered by modification of the flu ctuating kinetic energy transported by particles. The simulation of Couette flow is in good agreement with the analytical solutions.