Consistent two-population lattice Boltzmann model for thermal flows

Theory of two-population lattice Boltzmann equations for thermal flow simulations is revisited. The present approach makes use of a consistent division of the conservation laws between the two lattices, where mass and the momentum are conserved quantities on the first lattice, and the energy is conserved quantity of the second lattice. The theory of such a division is developed, and the advantage of energy conservation in the model construction is demonstrated in detail. The present fully local lattice Boltzmann theory is specified on the standard lattices for the simulation of thermal flows. Extension to the subgrid entropic lattice Boltzmann formulation is also given. The theory is validated with a set of standard two-dimensional simulations including planar Couette flow and natural convection in two dimensions.