Browsing Department of Applied Mathematics by browse.metadata.advisor "Fidder-Woudberg, Sonia"
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- ItemAnalysis of Extreme Events in the Coastal Engineering Environment(Stellenbosch : Stellenbosch University, 2015-12) Stander, Cornel; Diedericks, Gerhardus Petrus Jacobus; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Department of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : Coastal zones are subject to storm events and extreme waves with certain return periods. The return period of such events is defined as the average time interceding two independent, consecutive events, similar in nature, i.e., with the same return level. Coastal structures have to be designed to provide sufficient protection against flooding or erosion to a desired return level associated with a particular return period, for example 100 years. Statistical analyses of measured wave data over a time series are used for these estimations. In this study, wave data, measured by a Datawell Waverider buoy, is analysed by means of extreme value analyses. This dataset covers only approximately 18 years. Extreme value theory provides a framework that enables extrapolation in order to estimate the probability of events that are more extreme than any that have already been observed. It can, for example, be used to estimate wave return levels over the next 100 years given only an 18 year history. Different methods for making these estimations are implemented and evaluated. Datasets containing periods where data values are absent (i.e., gaps in a dataset), as well as the effects these missing values have on the estimation of extreme values, are also investigated. Methods for the treatment of gaps are evaluated by using NCEP (National Centre for Environmental Prediction) hindcast data, containing no missing values, and creating incomplete datasets from this data. Estimations are then made based on these incomplete sets. The resulting estimations are compared to the estimations made based on the complete NCEP dataset. Finally, recommendations are made for conducting optimal extreme value analyses, based on this study.
- ItemPredicting the effect of biofilm growth on the pressure drop over a biofilter(Stellenbosch : Stellenbosch University, 2017-12) van Jaarsveld, Jacoline; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. Division Applied Mathematics.ENGLISH ABSTRACT : Hydrogen sulphide is a poisonous gas produced by several industries. It is therefore crucial to investigate and mathematically model the environmentally friendly biofiltration process, which has the ability to remove poisonous gasses, such as hydrogen sulphide, from an air stream. In this study two approaches are used for modelling biofilm growth in three different biofilters, i.e. an empirical and analytical approach. In the empirical modelling approach, the pressure drop prediction of the Modified-Macdonald equation, the existing granular rectangular Representative Unit Cell (RUC) model and the model of Comiti and Renaud are used to determine the changes in biofilm affected porosity, specific surface area, tortuosity and biofilm thickness. The results are obtained by using Excel R Solver, which is based on an optimization method. Thereafter a sensitivity analysis is performed in order to analyze the effect of the sphericity. The analytical modelling approach involves only the RUC model. The first step is to predict the biofilm thickness. Thereafter, two methods are suggested for predicting the biofilm affected specific surface area. The first method is based on an approach suggested in the literature. In the second method, the RUC model is used to express the pressure drop in terms of the biofilm affected specific surface area, which yields the adapted RUC model. The biofilm affected specific surface area values are then obtained by making use of experimental pressure drop data and superficial velocity values. After incorporating both the analytically and empirically determined sphericity values into the adapted RUC model, the pressure drop results show the significant effect that the sphericity value has on the model predictions. Finally, a sensitivity analysis is performed on the input parameters to the model.
- ItemTime series analysis of data measured in the nearshore area(Stellenbosch : Stellenbosch University, 2016-03) Mphasha, Rosa; Diedericks, Gerhardus Petrus Jacobus; Fidder-Woudberg, Sonia; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)ENGLISH ABSTRACT : Factors that lead to the generation of currents in the nearshore area within the Natal Bight were investigated. The investigation was carried out on data that spans from the 6th June 2012 to the 16th January 2013. The data comprised current measurements, wave measurements, water level measurements, as well as wind measurements. The measurements were decomposed into different direction components in order to study their impacts on corresponding current measurements. Current measurements were resolved into tidal currents and non-tidal currents through the use of harmonic analysis. Stokes drift was estimated using a monochromatic spectrum to obtain the wave induced current. The effect of the wind on the currents was analysed through the use of wind roses and duration analysis. The study was completed with an exploration of the contribution of the Agulhas current. It was found that the waters are characterized by a semi-diurnal, micro-tidal system and tides have a limited contribution to the generation of currents. The contribution of Stokes drift to the overall currents is less than that of tides. Wind is the most significant generator of the nearshore currents.