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The present research focuses on the development and computer implementation of a novel threedimensional, anisotropic turbulence model not only capable of handling complex geometries but also the turbulence driven secondary currents. The model equations comprise advanced algebraic Reynolds stress models in conjunction with Reynolds Averaged Navier-Stokes equations. In order to tackle the complex geometry of compound meandering channels, the body-fitted orthogonal coordinate system is used. The finite volume method with collocated arrangement of variables is used for discretization of the governing equations. Pressurevelocity coupling is achieved by the standard iterative SIMPLE algorithm. A central differencing scheme and upwind differencing scheme are implemented for approximation of diffusive and convective fluxes on the control volume faces respectively. A set of algebraic equations, derived after discretization, are solved with help of Stones implicit matrix solver. The model is validated against standard benchmarks on simple and compound straight channels. For the case of compound meandering channels with varying sinuosity and floodplain height, the model results are compared with the published experimental data. It is found that the present method is able to predict the mean velocity distribution, pressure and secondary flow circulations with reasonably good accuracy. In terms of engineering applications, the model is also tested to understand the importance of turbulence driven secondary currents in slightly curved channel. The development of this unique model has opened many avenues of future research such as flood risk management, the effects of trees near the bank on the flow mechanisms and prediction of pollutant transport.

To develop a complete numerical model for predicting fluid flow and mass transfer in domains with porous walls such as those found in cross flow filtration is not an easy task to undertake. Many gaps in theory exist that undermine any attempt to build a reliable representation of this process and a sensible effort to solving this problem must be built on sound and logical assumptions. The difficulties with modelling interacting particles, with simulating multiphase flow and with prescribing accurate boundary conditions are very much the essence of the problem. From a comprehensive literature search into areas of combined free and porous flow, mass transfer in porous domains and into the fields of rheology, and mathematical modelling of crossflow filtration it was discovered that present research although great in quantity, is overall limited by the difficulties described above. As well, the present research found in the literature is also limited for use in industrial applications as it generally considers dilute suspensions, it is often found to look at simple flow profiles for Newtonian fluids, the research scarcely looks into the dependency of flow profiles and mass transfer profiles on each other via rheology and many researchers who study crossflow filtration concentrate solely on the porous wall to solve the flux paradox situation and do not generally consider the whole domain. The purpose of the present thesis is to describe the concept, procedure and results behind the integration of a solids transport model into a previously developed flow algorithm and the explanation of ideas for solving the problem of prescribing appropriate concentration boundary conditions at the porous wall. The aim of the research is to develop a fast and cost effective tool for solving the given problem based on rational assumptions.