Consistent two-population lattice Boltzmann model for thermal flows

摘要: Despite the vast number of suggestions, extending the Lattice Boltzmann method to the simulation of thermal and compressible flows remains an open issue. Three main approaches are reported in the literature for this type of problems: the multi-speed approach [1], the correction terms approach [2], and the two-populations approach [3]. In the present work a two-population approach is employed, making use of consistent conservation laws between the two lattices; the mass and the momentum are conserved quantities on the first lattice, while the total energy is conserved on the second lattice. The theory of such a division is presented in detail and is specified for standard lattices in two and three dimensions. The model is capable of variable Prandtl number, and, under the assumption of low Mach number, the extension to the sub-grid entropic lattice Boltzmann formulation enables the simulation of highly turbulent …