The applicability of lattice BGK modelling for turbulent hydrodynamics in internal geometrics.

Traditional approaches to simulating fluid dynamics have focused on spatially and temporally discretised versions of the underlying Navier-Stokes partial differential equations. These approaches form a huge body of work that has evolved over the last century; the modern technique of simulating these systems by numerical approximation is collectively referred to as computational fluid dynamics or CFD. Recently however, new schemes have evolved out of cellular automata and lattice gas approaches which can, under the right circumstances, form efficient and fast alternatives to CFD and which lend themselves to various computational streamlining procedures. These are well represented by the so called lattice Boltzmann and LBGK formalisms --- those employed in this work.In this work the LBGK mono-phase scheme for internal flows is extended, primarily to incorporate models of turbulent flow characteristics, in order to generalise the validity of the schemes for more complex flow geometries and to higher Reynolds numbers. Turbulent flow in infinite aspect ratio ducts is examined in detail. Results sets derived using the extended model are compared quantitatively against theory and experiment. Features of the model are analysed to deduce potential improvements to the scheme and alternatives. Propositions for continued work are discussed in detail.Before this is done, investigations are carried out on issues of closure for the general LBGK scheme and an improved, adaptable and high order accuracy boundary scheme is developed. For various benchmark geometries, this is qualitatively and quantitatively compared against accepted alternatives. In addition, a central geometric problem of simulating cylindrically symmetric systems on two dimensional Cartesian lattices is addressed. Work is presented on transforming the governing lattice Boltzmann BGK equation, to enable the use of a regular Cartesian grid for performing simulations of flow in pipes. Results for pipe flow are compared to the analytic solution.