An enhanced lattice Bhatnagar–Gross–Krook method for Boussinesq flow

We derive by the established method of Chapman–Enskog expansion a simple thermal lattice Bhatnagar–Gross–Krook fluid algorithm with adjustable Prandtl number, specifically adapted to the simulation of flows in the Boussinesq approximation, where there is negligible coupling between internal and translational kinetic energy. We consider implementation aspects of the model and apply it to the solution of flow in a uniformly heated duct and find the results of our simulations to be in good agreement with theory.