Ndivhuwo Mphephu | University of Stellenbosch (original) (raw)
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Papers by Ndivhuwo Mphephu
The flow of viscoelastic fluids in industries poses a number of challenges, not least from a mode... more The flow of viscoelastic fluids in industries poses a number of challenges, not least from a modelling point of view. Research is needed to further understand and be able to predict the flow behaviour of such fluids and to investigate ways of improving their processing. The properties of viscoelastic fluids cannot be captured by the momentum and continuity equations alone. As results, additional constitutive equation is needed for the characterisation of these fluids. Here, the study focuses on the momentum and continuity equation together with additional constitutive equation. These equations collectively form the model called the Oldroyd-B Model. We have derived a forward finite difference scheme for a creeping Oldroyd fluid flow. The derived scheme is then tested for convergence and error stability and thereafter, the scheme is used to simulate the flow in a circular curved pipe. In this simulation, we need to determine the pressure loss of the fluid when flowing in a curved pipe...
Convection-diffusion reactions are used in many applications in science and engineering. In many ... more Convection-diffusion reactions are used in many applications in science and engineering. In many of the applications, the governing equations are non-linear and this leads to difficulties in obtaining exact or analytical solutions. Under the circumstances where solutions are needed, the need for numerical methods become apparent. In this dissertation, we use the upwind forward Euler finite difference scheme, the nonstandard finite difference scheme and the unconditionally positive finite difference scheme to solve a linear convection-diffusion-reaction equation and a non-linear diffusion-reaction equation, both with constant coefficients. The unconditionally positive finite difference method has been proposed by (Chen-Charpentier and Kojouharov, 2013). We use the Von-Neumann stability analysis to study the stability of each scheme for the linear convection-diffusion-reaction equation directly, and for the non-linear diffusion-reaction, we first freeze the coefficients and then apply the Von-Neumann stability analysis. The consistency and spectral analysis for all the numerical schemes is also studied. We then compare the efficiency of each finite difference scheme by performing some numerical experiments. Declaration I, the undersigned, hereby declare that the work contained in this research project is my original work, and that any work done by others or by myself previously has been acknowledged and referenced accordingly. Ndivhuwo Mphephu,
The flow of viscoelastic fluids in industries poses a number of challenges, not least from a mode... more The flow of viscoelastic fluids in industries poses a number of challenges, not least from a modelling point of view. Research is needed to further understand and be able to predict the flow behaviour of such fluids and to investigate ways of improving their processing. The properties of viscoelastic fluids cannot be captured by the momentum and continuity equations alone. As results, additional constitutive equation is needed for the characterisation of these fluids. Here, the study focuses on the momentum and continuity equation together with additional constitutive equation. These equations collectively form the model called the Oldroyd-B Model. We have derived a forward finite difference scheme for a creeping Oldroyd fluid flow. The derived scheme is then tested for convergence and error stability and thereafter, the scheme is used to simulate the flow in a circular curved pipe. In this simulation, we need to determine the pressure loss of the fluid when flowing in a curved pipe...
Convection-diffusion reactions are used in many applications in science and engineering. In many ... more Convection-diffusion reactions are used in many applications in science and engineering. In many of the applications, the governing equations are non-linear and this leads to difficulties in obtaining exact or analytical solutions. Under the circumstances where solutions are needed, the need for numerical methods become apparent. In this dissertation, we use the upwind forward Euler finite difference scheme, the nonstandard finite difference scheme and the unconditionally positive finite difference scheme to solve a linear convection-diffusion-reaction equation and a non-linear diffusion-reaction equation, both with constant coefficients. The unconditionally positive finite difference method has been proposed by (Chen-Charpentier and Kojouharov, 2013). We use the Von-Neumann stability analysis to study the stability of each scheme for the linear convection-diffusion-reaction equation directly, and for the non-linear diffusion-reaction, we first freeze the coefficients and then apply the Von-Neumann stability analysis. The consistency and spectral analysis for all the numerical schemes is also studied. We then compare the efficiency of each finite difference scheme by performing some numerical experiments. Declaration I, the undersigned, hereby declare that the work contained in this research project is my original work, and that any work done by others or by myself previously has been acknowledged and referenced accordingly. Ndivhuwo Mphephu,