Lattice Bhatnagar-Gross-Krook studies of hydrodynamic and thermohydrodynamic internal pressure-driven flows.

In this thesis we develop applications of Lattice-Bhatnagar-Krook (LBGK) models to incompressible flow problems.We show that in geometries where flow is forced via application of a pressure difference, a modified Exactly Incompressible LBGK (EILBGK) scheme must be applied if significant pressure variations occur. We analyse the model's representation of the no-slip wall boundary condition for flow in a straight duct and recover a friction factor in excellent agreement with theory. Simulation of flow over a backward-facing step produces good agreement with other numerical techniques.We propose two new LBGK schemes, one directed towards the calculation of depth-averaged flow quantities and the other which focusses on thermal flows in the Boussinesq-Oberbeck limit. Depth-averaged flow facilitates the two-dimensional simulation of three-dimensional ducts of constant depth. The effect of the unmodelled dimension is accounted for by including momentum sinks in the momentum equations. We apply the scheme to flow in a bifurcating duct and results are again in good agreement with other numerical methods. We develop a thermal model in which energy is treated efficiently as a passively advected scalar quantity. This approach results in a model which is more simpleand robust than other previously reported LBGK thermal models. Our scheme is then validated by application to flow in a straight duct with constant heat flux applied at the walls. Excellent agreement with theoretical predictions is obtained for the calculated Nusselt number.