Thermal lattice-Boltzmann models (TLBM) for compressible flows

The progress and challenges in thermal lattice-Boltzmann modeling are discu ssed. In particular, momentum and energy closures schemes are contrasted. H igher order symmetric (but no longer space filling) velocity lattices are c onstructed for both 2D and 3D flows and shown to have superior stability pr operties to the standard (but lower) symmetry lattices. While this decouple s the velocity lattice from the spatial grid, the interpolation required fo llowing free-streaming is just 1D. The connection between fixed lattice vec tors and temperature-dependent lattice vectors (obtained in the Gauss-Hermi te quadrature approach) is discussed. Some (compressible) Rayleigh-Benard s imulations on the 2D octagonal lattice are presented for extended BGK colli sion operators that allow for arbitrary Prandtl numbers.