Thermal Lattice Boltzmann Model for Compressible Fluid

We formulate a new thermal lattice Boltzmann model to simulate compressible flows with a high Mach number. The main difference from the standard lattice Boltzmann models is that the particle velocities are no longer a constant, varying with the mean velocity and internal energy. The proper heat conduction term in the energy equation is recovered by modification of the fluctuating kinetic energy transported by particles. The simulation of Couette flow is in good agreement with the analytical solutions.