Effective and robust high resolution schemes are of vital importance for simulation of viscous and inviscid flows. Since second-order high resolution schemes in practice are inadquate for many applications, large efforts have been put towards developing higher- order accurate schemes in the past. Although some progress has been made, the efforts were frustrated by the lack of effective and robust new schemes. Therefore this thesis is aimed at challenging this difficult but very important issue. Some new theories and methodologies were established during this research, which covers the linear stability analysis for high-order numerical schemes; the fully discrete techniques for model equations; the formulation of conservative high-order schemes and the high-order Total Variation Diminishing (TVD) schemes. According to these theories arbitrary-order high resolution schemes can be developed. To illustrate the methodologies second-, third-, fourth-, and 20th-order schemes are presented. These high resolution schemes were tested and validated by solving some popular test problems for one and two dimensional Euler and incompressible Navier-Stokes equations. The efficiency and robustness are the features of these high-order schemes.

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There have been countless research investigations taking place on Marion Island (MI), both ecological and geological, which have reached conclusions that must necessarily neglect the impacts of wind on the systems under study. Since only the dominant wind direction of the general atmospheric wind is known from weather and satellite data, not much can be said about local wind conditions at ground level. Therefore, a baseline Computational Fluid Dynamics (CFD) model has been developed for simulating wind patterns over Marion and Prince Edward Islands, a South African territory lying in the subantarctic Indian Ocean. A review of the current state of the art of Computational Wind Engineering (CWE) revealed that large-scale Atmospheric Boundary Layer (ABL) simulations have been successfully performed before with varying degrees of success. With ANSYS Fluent chosen as the numerical solver, the Reynolds-Averaged Navier-Stokes (RANS) equations were set up to simulate a total of 16 wind flow headings approaching MI from each of the cardinal compass directions. The standard k-epsilon turbulence closure scheme with modified constants was used to numerically approximate the atmospheric turbulence. A strategy was devised for generating a reusable mesh system to simulate multiple climatic conditions and wind directions around MI. In conjunction with the computational simulations, a wind measurement campaign was executed to install 17 wind data logging stations at key locations around MI. Raw data output from the stations were cleaned and converted into an easily accessible MySQL database format using the Python scripting language. The Marion Island Recorded Experimental Dataset (MIRED) database contains all wind measurements gathered over the span of two years. The decision was taken to focus on validating only three of the 16 cardinal wind directions against the measured wind data; North-Westerly, Westerly and South-Westerly winds. An initial interrogation of the simulation results showed that island-to-island wake interactions could not be ignored as the turbulent stream from MI could definitely be intercepted by its neighbour under the right conditions, and vice versa. An underestimation of the true strength of the Coriolis effect led to larger wind deflection in the simulations than originally expected, thus resulting in the wind flow at surface levels having an entirely different heading to what was intended. The westerly and south-westerly wind validation cases did not seem too badly affected by the lapse in judgement but the north-westerly case suffered strong losses in accuracy. Significant effort was put into quantifying the error present in the simulations. After a full validation exercise, it was finally resolved to apply a conservative uncertainty factor of 35 % when using these simulations to predict actual wind speed conditions. Similarly, the predicted wind direction can only be trusted within the bounds of a 35 degree prediction uncertainty. Under these circumstances, the baseline CFD model was successfully validated against the measured wind data and can thus be used in further research. In terms of post-processing, all the wind direction simulations have been combined into a single wind velocity map, generated by weighting each of the simulations by the frequency of wind prevalence measured in the corresponding wind sector. A second turbulence intensity combined map has been provided using similar techniques. These maps, as well as the individual wind maps showing all 16 cardinal wind directions, are believed to be helpful to many future biological studies on MI as well as any possible forays into wind energy generation on the island. Despite the encountered deficiencies, this project offers significant value to academia by providing a reliable method of predicting fine-scale wind patterns in a location previously devoid of any accurate data. Furthermore, it has highlighted where future CFD attempts can be improved in order to produce a compelling approximation of the realistic atmospheric phenomena occurring in the Marion Island territory. While error cannot be avoided when modelling such complex systems, it has been well quantified and discussed here so that any further research may make informed judgements in future studies. / Dissertation (MEng (Mechanical Engineering))--University of Pretoria, 2021. / South African National Antarctic Programme (SANAP) grant number 110726 / National Research Foundation (NRF) / Mechanical and Aeronautical Engineering / MEng (Mechanical Engineering) / Unrestricted

D.Ing. (Mechanical Engineering) / Most coal fired power stations in South Africa are equipped with Electrostatic Precipitators (ESP's). With the ongoing reduction of allowable emissions, as negotiated with the Chief Air . Pollution Control Officer (CAPCO) of the Department of Environmental Affairs and Tourism (DEAT), ways to reduce emissions are sought. In the case of emission levels exceeding the values set by the controlling authority load losses are required for compliance. This however has the effect of plant operating inefficiently and a loss of revenue will result. Specifically in times of growing demand, when more and more of the currently installed generation capacity is required to satisfy the demand, forced load reductions are not desirable. Performance enhancement of ESP's can be achieved by means of system optimisation. Research was initiated to achieve the capability of modelling important dynamic aspects of ESP performance using Computational Fluid Dynamics (CFD). This modelling capability would create the opportunity to investigate the different influencing factors which govern the dust collection efficiency. In the past ESP flow has been modelled by means of mathematical modelling with various degrees of success world-wide. It was found that the accuracy of flow modelling as presently carried outby researchers world wide, is not sufficient to represent the complex inlet flow. Commercially available performance simulation software is based on empirical modelling principles and do not include the complexity of flow fields and re-entrainment and thus results have been limited in accuracy. Computational fluid dynamics software is commercially available and widely used to simulate industrial flow for plant design and optimisation. This technology has been applied with increasing confidence and success in the past. However, often the physical phenomena relevant for the performance simulation of the plant is not integrated into the code and specialised user routines are created to achieve a valid performance model. This research study introduces a unique integrated simulation methodology based on a commercial CFD code. The work focuses on the accurate modelling of fluid flow and collection dynamics in an ESP. User subroutines have been created to simulate particle charging, collection and re-entrainment. The results of the simulations are compared to measurement at actual plant.

Hydraulic energy absorbers may be described as high-loss centrifugal turbomachines arranged to operate as stalled torque converters. The device absorbs the kinetic energy of a vehicle in motion and dissipates the energy into water. A steady, single-phase, Computational Fluid Dynamics (CFD) simulation has been performed to investigate the flow field in a hydraulic energy absorber. It was determined that to better predict the performance of the energy absorber, more sophisticated modeling approaches may be needed. In this research, a steady, two-phase calculation with basic turbulence modeling was used as a first assessment. The two-phase model was used to investigate cavitation effects. Unsteady and advanced turbulence modeling techniques were then incorporated into single-phase calculations. The Multiple Reference Frame (MRF) Technique was used to model the interaction between the rotor and the stator. The calculations provided clearer details of the flow field without dramatically increasing the computational cost. It was found that unsteady modeling was necessary to correctly capture the close coupling between the rotor and the stator. The predicted torque in the unsteady calculations was 70% of the experimental value and twice of the result in the steady-state calculations. It was found that the inaccuracy of torque prediction was due to (1) high pressures in the regions with complicated geometrical boundaries and, (2) dynamic interactions between the rotor and the stator were not captured fully. It was also determined that the unrealistically low pressure values were not caused by the physical cavitation, but by the lack of proper boundary conditions for the model. Further integration of the modeling techniques studied would improve the CFD results for use in the design of the energy absorber. / Master of Science