Simulations of Compressible Flows with Strong Shocks by an Adaptive Lattice Boltzmann Model

An adaptive lattice Boltzmann model for compressible flows is presented. The particle-velocity set is so large that the mean flow may have a high velocity. The support set of the equilibrium-distribution function is quite small and varies with the mean velocity and internal energy. The adaptive nature of this support set permits the mean flows to have high Mach number, meanwhile, it makes the model simple and practicable. The model is suitable for perfect gases with an arbitrary specific heat ratio. Navier?Stokes equations are derived by the Chapman?Enskog method from the BGK Boltzmann equation. When the viscous terms and the diffusion terms are considered as a discretion error this system becomes an inviscid Euler system. Several simulations of flows with strong shocks, including the forward-facing step test, double Mach reflection test, and a strong shock of Mach number 5.09 diffracting around a corner, were carried out on hexagonal lattices, showing the model's capability of simulating the propagation of strong shock waves.

[1]  P. Colella.  Multidimensional upwind methods for hyperbolic conservation laws , 1990 .

[2]  Thermal Lattice Boltzmann Model for Compressible Fluid , 2000 .

[3]  Y. Qian,et al.  Lattice BGK Models for Navier-Stokes Equation , 1992 .

[4]  Shiyi Chen,et al.  LATTICE BOLTZMANN METHOD FOR FLUID FLOWS , 2001 .

[5]  Pierre Lallemand,et al.  Lattice Gas Hydrodynamics in Two and Three Dimensions , 1987, Complex Syst..

[6]  Chen,et al.  Lattice Boltzmann model for compressible fluids , 1992 .

[7]  R. Gatignol.  Théorie cinétique des gaz à répartition discrète de vitesses , 1975 .

[8]  Chenghai Sun,et al.  Adaptive lattice Boltzmann model for compressible flows: Viscous and conductive properties , 2000 .

[9]  Matthaeus,et al.  Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[10]  Chenghai Sun,et al.  Lattice-Boltzmann models for high speed flows , 1998 .

[11]  B. Nadiga.  An Euler solver based on locally adaptive discrete velocities , 1995, comp-gas/9501010.

[12]  O. Séro-Guillaume,et al.  Multispecies 2D lattice gas with energy levels: diffusive properties , 1991 .

[13]  Antony Jameson,et al.  Gas-kinetic finite volume methods, flux-vector splitting, and artificial diffusion , 1995 .

[14]  Y. Pomeau,et al.  Lattice-gas automata for the Navier-Stokes equation. , 1986, Physical review letters.

[15]  Lattice-Boltzmann Models for heat transfer☆☆☆ , 1997 .

[16]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[17]  Kun Xu,et al.  A new class of gas-kinetic relaxation schemes for the compressible Euler equations , 1995 .

[18]  R. Benzi,et al.  The lattice Boltzmann equation: theory and applications , 1992 .

[19]  Yang Guangwu,et al.  A lattice boltzmann model for compressible perfect gas , 1997 .

[20]  Exact stability results in stochastic lattice gas cellular automata , 1995 .