A Two-Dimensional Lattice Boltzmann Method For Compressible Flows

In this paper we present an improved lattice Boltzmann model for compressible Navier–Stokes system with high Mach number.The model is composed of three components: (i) the discrete-velocity-model by M. Watari and M. Tsutahara [Phys. Rev. E 67(2003) 036306], (ii) a modified Lax–Wendroff finite difference scheme where reasonable dissipation and dispersion are naturallyincluded, (iii) artificial viscosity. The improved model is convenient to compromise thehigh accuracy and stability. The includeddispersion term can effectively reduce the numerical oscillation at discontinuity. The added artificial viscosity helps the schemeto satisfy the von Neumann stability condition. Shock tubes and shock reflections are used to validate the new scheme. In ournumerical tests the Mach numbers are successfully increased up to 20 or higher. The flexibility of the new model makes it suitablefor tracking shock waveswith high accuracy and for investigating nonlinear nonequilibrium complex systems