Numerical Simulation of High Mach Number Flow using the Finite Difference Lattice Boltzmann Method (FDLBM)

The Lattice Boltzmann Method (LBM) is known as a powerful numerical tool to simulate fluid flow problems. Particularly, it has shown a unified strength for solving incompressible fluid flows in complicated geometries. Many researchers have used Lattice Boltzmann (LB) concept to simulate compressible flows, but the common defect of most of previous models is the stability problem at high Mach number fluid flows. In this paper we introduce a FLDBM-model, which is capable to simulate fluid flows with any specific heat ratios and higher Mach numbers, from 0 to 30 or higher. Compressibility is applied using multiple particle speeds in a thermal fluid. Based on the discrete-velocity-model, a new finite difference method and an artificial viscosity are implemented, which must find a balance between numerical stability and accuracy of simulation. The introduced model is checked and validated again well-known benchmark tests such as one dimensional shock tubes, supersonic bump and ramp (two dimensional). Both sets of results have a reasonable agreement regarding to exact solutions.