  In this paper, a coupling lattice Boltzmann (LB) model for simulating thermal
flows on the standard D2Q9 lattice is developed in the framework of the
double-distribution-function (DDF) approach in which the viscous heat
dissipation and compression work are considered. In the model, a density
distribution function is used to simulate the flow field, while a total energy
distribution function is employed to simulate the temperature field. The
discrete equilibrium density and total energy distribution functions are
obtained from the Hermite expansions of the corresponding continuous
equilibrium distribution functions. The pressure given by the equation of state
of perfect gases is recovered in the macroscopic momentum and energy equations.
The coupling between the momentum and energy transports makes the model
applicable for general thermal flows such as non-Boussinesq flows, while the
existing DDF LB models on standard lattices are usually limited to Boussinesq
flows in which the temperature variation is small. Meanwhile, the simple
structure and basic advantages of the DDF LB approach are retained. The model
is tested by numerical simulations of thermal Couette flow, attenuation-driven
acoustic streaming, and natural convection in a square cavity with small and
large temperature differences. The numerical results are found to be in good
agreement with the analytical solutions and/or other numerical results reported
in the literature.
