In this thesis, a theoretical investigation is undertaken into fluid and mixing flows generated by various geometries for Newtonian and non-Newtonian fluids, on both sequential and parallel computer systems. The thesis begins by giving the necessary background to the mixing process and a summary of the fundamental characteristics of parallel architecture machines. This is followed by a literature review which covers accomplished work in mixing flows, numerical methods employed to simulate fluid mechanics problems and also a review of relevant parallel algorithms. Next, an overview is given of the numerical methods that have been reviewed, discussing the advantages and disadvantages of the different methods. In the first section of the work the implementation of the primitive variable finite element method to solve a simple two dimensional fluid flow problem is studied. For the same geometry colour band mixing is also investigated. Further investigational work is undertaken into the flows generated by various rotors for both Newtonian and non-Newtonian fluids. An extended version of the primitive variable formulation is employed, colour band mixing is also carried out on two of these geometries. The latter work is carried out on a parallel architecture machine. The design specifications of a parallel algorithm for a MIMD system are discussed, with particular emphasis placed on frontal and multifrontal methods. This is followed by an explanation of the implementation of the proposed parallel algorithm, applied to the same fluid flow problems as considered earlier and a discussion of the efficiency of the system is given. Finally, a discussion of the conclusions of the entire accomplished work is presented. A number of suggestions for future work are also given. Three published papers relating to the work carried out on the transputer networks are included in the appendices.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / When considering flow through porous media, different flow regimes may be identified. At very small Reynolds numbers the relation between the pressure gradient and the velocity of the fluid is linear. This flow regime ...