Journal of Statistical Physics, Vol. 81. Nos. 1/2, 1995, p. 395-408.
A three-dimensional thermal lattice-Boltzmann model with two relaxation times to separately control viscosity and thermal diffusion is developed. Numerical stability of the model is significantly improved using Lax-Wendroff advection to provide an adjustable time step. Good agreement with a conventional finite-difference Navier-Stokes solver is obtained in modeling compressible Rayleigh-Benard convection when boundary conditions are treated similarly.