A coupled lattice Boltzmann model for thermal flows

We present a coupled lattice Boltzmann method (LBM) for thermal viscous flows based on a two relaxation times kinetic model. The method is directly derived by projecting the coupled kinetic model equations for the distribution functions onto the tensor Hermite polynomials following Grad’s moment expansion method. By choosing a proper reference velocity, the coupling of lattice velocities and the local temperature is avoided and the resultant method is consistent with the original kinetic model. The intrinsic discrete nodes of the Gauss–Hermite quadrature provide the natural lattice velocities for the thermal LBM. Simulations of 2D natural convection flows are shown. The numerical results agree well with the previous benchmark data.