The Lattice Boltzmann Equation Method for the Simulation of Compressible Fluid Flow

We systematically derived hydrodynamic equations and transport coe cients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical uid is recovered by a modi ed equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled uid. When the sound speed is tuned small enough, the compressible region of uid ow can be reached. An example 2-D model is presented, together with the numerical veri cation for its transport coe cients.