Lattice Boltzmann Method For Compressible Fluids And Its Application

Based on the Single-Relaxation-Time (SRT) Bhatnagar-Gross-Krook (BGK) ap-proximation, we construct highly efficient two-dimensional (2D) and three-dimensional (3D) lattice Boltzmann models for high speed compressible flows. In order to improve the stability we introduce additional viscosity into the LB equation. The additional viscosity term makes new models more easily meet with the von Neumann stability con-dition. The second way of constructing LB models for high speed compressible flows is the Multiple-Relaxation-Time (MRT) LB scheme. Based on the16-discrete-velocity model, we construct the moment space and corresponding transformation matrix ac-cording to the group representation theory; equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapnian-Enskog expansion. This model is the first multiple-relaxation-time finite difference LB model for high speed compressible flows, but the model is restricted to a nonphysical value of the specific-heat ratio. Subsequently, we construct a new MRT LB model for compressible flows with arbitrary specific-heat ratio. Nu-merical experiments showed that all the models based on the two different ways have obtained satisfactory results.