Thermal lattice-Boltzmann models (TLBM) for compressible flows

The progress and challenges in thermal lattice-Boltzmann modeling are discussed. In particular, momentum and energy closures schemes are contrasted. Higher order symmetric (but no longer space filling) velocity lattices are constructed for both 2D and 3D flows and shown to have superior stability properties to the standard (but lower) symmetry lattices. While this decouples the velocity lattice from the spatial grid, the interpolation required following free-streaming is just 1D. The connection between fixed lattice vectors and temperature-dependent lattice vectors (obtained in the Gauss-Hermite quadrature approach) is discussed. Some (compressible) Rayleigh-Benard simulations on the 2D octagonal lattice are presented for extended BGK collision operators that allow for arbitrary Prandtl numbers.