** A coupled lattice BGK model for the Boussinesq equations, **
*Int. J. Num. Meth. Fluids 39, 325-342*

The Boltzmann equation describes the full statistical properties of a fluid, including temperature effects. But BGK and related models can only simulate isothermal fluids, because the lattice (D2Q9 or D3Q13-D3Q27) lacks sufficient symmetries to include thermal effects. This deficiency can be circumvented by using higher-order discretizations of Boltzmann equation, using a grid with higher connectivity. Yet another solution is to solve the temperature equation separately, as it is common in computational fluid dynamics, and to couple fluid and temperature appropriately. Such an approach is described in the paper by Guo, Shi, and Zheng. They simulate the fluid with a BGK model and the temperature field with a LB model for the advection-diffusion equation. A Boussinesq approximation is used to represent the action of temperature on the fluid by a linear buoyancy term.