Department of Applied Mathematics

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Browsing Department of Applied Mathematics by browse.metadata.advisor "Diedericks, G. P. J."

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    Developing a methodology for the assessment of wave energy along the South African Coast
    (Stellenbosch : Stellenbosch University, 2018-03-19) Gweba, Bafana; Diedericks, G. P. J.; Wilms, Josefine M.; Rautenbach, C.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
    ENGLISH ABSTRACT : Ocean wave energy can become one of the alternative energy resources for fossil-fuelled power generation in South Africa. Due to global warming, several studies about the generation of wave energy have been done to find cleaner and sustainable renewable energy resources. An array of Wave Energy Converters (WECs) in a form of a wave farm may be used to harness the energy resource to generate electricity. Nearshore wave field effects due to the presence of a wave farm must be investigated particularly at the coastline as it will be affected. The principal objective of this thesis is to investigate the impacts induced by a wave farm on the nearshore wave field region through numerical modelling. Another objective is to give guidance about some of the parameters and input conditions for numerical modelling of wave transformations. In the present study, wave conditions have been assessed at selected locations of the South African coast. The JONSWAP model, which is the most frequently used spectral model to describe wind-generated waves, was used to represent wave energy spectrum along chosen locations. The JONSWAP model was fitted into the measured data along the coast to obtain the peak enhancement factor (gamma) values for chosen locations. The measured data was found to consist of bimodal spectra, local winds and distant storms and also multiple peaks in the spectra were observed. The spectral decomposition method was then applied to split the data into wind sea and swell to assess a more realistic description of the wave system. It was found that the method is effective in splitting bimodal spectra but is not successful in multi-peaked spectra. Saldanha Bay was chosen as the case study for installation of a wave farm due to its abundance of wave energy. A nested numerical wave model, referred to as SWAN (SimulatingWAves Nearshore), was used to simulate the nearshore wave field conditions in Saldanha Bay. The obtained gamma value for Saldanha Bay was used to set the wave model. Two model simulations in the study were considered, model simulations in the presence of a wave farm and model simulations in the absence of a wave farm. The difference in significant wave height and wave energy spectrum with and without the wave farm was assessed. The results show a reduction in significant wave height and a change in wave energy spectrum at the selected output locations. A gradual redirection of waves induced by the presence of wave farm has been observed for all selected boundary wave direction conditions. The overall results of the study indicate the change in the nearshore wave field during the presence of wave farm. A sensitivity assessment was conducted to investigate the change in wave energy due to the orientation of the original wave farm layout and the addition of two devices in the original wave farm layout. A proposed methodology for the assessment of wave energy was presented to evaluate the wave energy resource along the South African coast. The proposed methodology is based on analysis that was conducted in the study.
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    Incompressible flow with variations in density
    (Stellenbosch : Stellenbosch University, 2018-12) Rakotoarisoa, Avotra Elie; Diedericks, G. P. J.; Maritz, M. F.; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.
    ENGLISH ABSTRACT : This study involves the investigation of incompressible flow with variable density. The fact that variable density does not necessarily imply that the flow is compressible, may require some clarification. An attempt is made in this thesis to clarify this ambiguity by investigating examples of incompressible flow with density that varies with pressure, temperature and salinity. In order to investigate incompressible flow with variations in density, the conditions of incompressibility that will simplify the continuity equation are determined by using scaling analysis. The Boussinesq approximation as well as the hydrostatic approximation is then applied to simplify the momentum equations of incompressible fluid flow with variations in density. Depth-averaging is also used to re-derive the shallow water equations, also with variable density. A numerical method for solving the one-dimensional shallow water equations (suggested by Benkaldoun and Saiëd) is then reviewed. It is also implemented and applied to solve some typical examples in order to illustrate the behaviour of the flow under the assumptions of incompressible flow with density that varies with temperature and salinity. The main results of this study can be summarized as follows: The scaling analysis serves to explain in a systematic way some conditions of incompressible flow, such as that the speed of sound must be large compared to the flow velocity, and that the diffusion of heat and salt should be negligible. Next, the solution of the one-dimensional shallow water equations, using the stated numerical method, yields qualitatively expected results.
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    Investigation of a simplified open boundary condition for coastal and shelf sea hydrodynamic models
    (Stellenbosch : Stellenbosch University, 2015-03) Shabangu, Patrick Eminet; Smit, G. J. F.; Diedericks, G. P. J.; Van Ballegooyen, R. C.; Stellenbosch University. Faculty of Science. Department of Applied Mathematics.
    ENGLISH ABSTRACT : In general, coastal and shelf hydrodynamic modelling is undertaken with limited area numerical models such as Delft3D or Mike 21. To conduct successful numerical simulations these programmes require appropriate boundary conditions. Various options exist to obtain boundary conditions such as Neumann conditions, specifying water levels, specifying velocities and combination of these, amongst others. In this study one specific method is investigated, namely the specification of water levels on all the open boundaries using a "reduced physics" approach. This method may be more appropriate than Neumann conditions when the domain is fairly large and is also of particular interest as it allows measured data to be incorporated in the boundary conditions, although the latter was not considered in this study. The boundary conditions of interest are determined by separating the crossshore and alongshore components of the momentum equations. To justify the separation, the equations of motion are firstly non-dimensionalised to determine the relative importance of various terms and then scaled to determine under which conditions the cross-shore and alongshore components can be solved independently. The efficacy of a computer program, Tilt, to calculate the open boundary conditions have been investigated for a number of idealised cases. Based on an understanding of the underlying physics and scaling assumptions, situations where these open boundary conditions underperformed have been analysed and reasons given for their underperformance. When applied to "real-life" situations it is likely that one or more of the scaling assumptions will be violated. Comment is provided on the likely errors in model simulations should this occur. The main conclusions are that the "reduced physics" approach used in Tilt restricts fairly significantly the range of flow that can be simulated. Should the scaling assumptions underlying Tilt be satisfied, Tilt performs adequately for limited area model simulations of coastal and shelf regions, however there remain some concerns: • The no flux condition at the coast and clamped water level offshore