Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: See full text for abstract / AFRIKAANSE OPSOMMING: Sien volteks vir opsomming

Uma família de esquemas upwind denominada FUS-RF (Family of Upwind Scheme via Rational Functions), que é derivada via funções racionais e dependentes de parâmetros, é proposta para o cálculo de soluções aproximadas de equações de conservação. A fim de ilustrar a capacidade dos novos esquemas, vários resultados computacionais para sistemas hiperbólicos de leis de conservação são apresentados. Esses testes mostram a inflluência dos parâmetros escolidos sobre a qualidade dos resultados numéricos. Fazendo o uso de alguns testes de padrões, comparação dos novos limitadores de fluxo correspondentes com o esquema bem estabelecido van Albada e esquema atual EPUS (Eight-degree Polynomial Upwind Scheme) é também realizada. Os testes numéricos realizados em transporte de escalares e problemas de dinâmica dos gases confirmam que alguns esquemas da família FUS-RF são não oscilatórios e fornecem resultados confiáveis quando perfis descontínuos são transportados. Um esquema particular dessa nova família de esquemas upwind é então selecionado e utilizado para resolver escoamentos complexos com superfícies livres móveis / A family of upwind schemes named as FUS-RF (Family of Upwind Scheme via Rational Functions), which is derived via rational functions and dependent of parameters, is proposed for computing approximated solutions of conservation equations. In order to illustrate the capability of the new schemes, several computational results for system of hyperbolic conservation laws are presented. These results clarify the influence of the chosen parameters on the quality of the numerical calculations. Using some standard test cases, comparison of the new corresponding limiters with the well established van Albada and the recently introduced EPUS (Eight-degree Polynomial Upwind Scheme) limiters is also done. Numerical tests on both scalar and gas dynamics problems confirm that some schemes of the FUS-RF family are non-oscillatory and yield sharp results when solving profiles with discontinuities. A particular upwind scheme of this new family is then slected and used for solving complex incompressible moving free surface flows

Uma família de esquemas upwind denominada FUS-RF (Family of Upwind Scheme via Rational Functions), que é derivada via funções racionais e dependentes de parâmetros, é proposta para o cálculo de soluções aproximadas de equações de conservação. A fim de ilustrar a capacidade dos novos esquemas, vários resultados computacionais para sistemas hiperbólicos de leis de conservação são apresentados. Esses testes mostram a inflluência dos parâmetros escolidos sobre a qualidade dos resultados numéricos. Fazendo o uso de alguns testes de padrões, comparação dos novos limitadores de fluxo correspondentes com o esquema bem estabelecido van Albada e esquema atual EPUS (Eight-degree Polynomial Upwind Scheme) é também realizada. Os testes numéricos realizados em transporte de escalares e problemas de dinâmica dos gases confirmam que alguns esquemas da família FUS-RF são não oscilatórios e fornecem resultados confiáveis quando perfis descontínuos são transportados. Um esquema particular dessa nova família de esquemas upwind é então selecionado e utilizado para resolver escoamentos complexos com superfícies livres móveis / A family of upwind schemes named as FUS-RF (Family of Upwind Scheme via Rational Functions), which is derived via rational functions and dependent of parameters, is proposed for computing approximated solutions of conservation equations. In order to illustrate the capability of the new schemes, several computational results for system of hyperbolic conservation laws are presented. These results clarify the influence of the chosen parameters on the quality of the numerical calculations. Using some standard test cases, comparison of the new corresponding limiters with the well established van Albada and the recently introduced EPUS (Eight-degree Polynomial Upwind Scheme) limiters is also done. Numerical tests on both scalar and gas dynamics problems confirm that some schemes of the FUS-RF family are non-oscillatory and yield sharp results when solving profiles with discontinuities. A particular upwind scheme of this new family is then slected and used for solving complex incompressible moving free surface flows

Thesis (PhD (Mechanical and Mechatronic Engineering))-- University of Stellenbosch, 2007. / ENGLISH ABSTRACT: The dissertation builds on previous research (Pretorius, 2004) and investigates the optimization and control of a large-scale solar chimney power plant. Performance results are based on a reference location near Sishen in South Africa and a so-called reference solar chimney power plant, with a 5000 m collector diameter and a 1000 m high, 210 m diameter chimney. The numerical simulation model is refined and used to perform a sensitivity analysis on the most prominent operating and technical plant specifications. Thermo-economically optimal plant configurations are established from simulation results and calculations according to an approximate plant cost model. The effects of ambient wind, temperature lapse rates and nocturnal temperature inversions on plant performance are examined. Various new technologies are investigated for the purpose of controlling plant output according to specific demand patterns. The incorporation of vegetation under the collector roof of the plant and the influence thereof on plant performance is also explored. Results indicate that, through the modification of the collector roof reflectance, collector roof emissivity, ground surface absorptivity or ground surface emissivity, major improvements on plant performance are possible. Introducing thermal insulation or double glazing of the collector roof also facilitates substantial enhancements on plant yield. Simulations predict a notable sensitivity to the ground surface absorptivity value, while variable atmospheric temperature lapse rates and windy ambient conditions may impair plant performance significantly. Furthermore, sand is found to be unsuitable as plant ground type and thermoeconomically optimal solar chimney plant dimensions are determined to be generally larger than plant dimensions employed in previous studies. Good dynamic control of solar chimney power output is established, suggesting that a solar chimney power plant can be implemented as a base or peak load electricity generating facility. Lastly, results predict that vegetation, when provided with sufficient water, will be able to survive under the collector roof but the inclusion of vegetation will however cause major reductions in plant performance. / AFRIKAANSE OPSOMMING: Die proefskrif bou op vorige navorsing (Pretorius, 2004) en ondersoek die optimering en beheer van 'n grootskaalse sonskoorsteen-kragstasie. Uitsetresultate word baseer op 'n verwysingsligging naby Sishen in Suid-Afrika en 'n sogenaamde verwysingskragstasie, met 'n kollektor deursnee van 5000 m en 'n 1000 m hoë, 210 m deursnee skoorsteen. Die numeriese rekenaarmodel is verbeter en gebruik vir die uitvoering van 'n sensitiwiteits-analise op die belangrikste bedryfs- en tegniese kragstasie spesifikasies. Termo-ekonomiese optimale aanlegkonfigurasies is bepaal volgens die uitsetresultate van die rekenaarmodel en benaderde aanleg-kosteberekeninge volgens 'n eenvoudige kostemodel. Die invloed van wind, atmosferiese temperatuur gradiënte en nagtelike temperatuur inversies op kragstasie uitset word beskou. Verskeie nuwe tegnologië word ondersoek met die doel om aanleg uitset te kan beheer volgens spesifieke elektrisiteit aanvraagspatrone. Die inkorporasie van plantegroei onder die kollektordak, en die invloed daarvan op kragstasie uitset, word ook beskou. Bevindings dui aan dat, deur die wysiging van die kollektordak refleksie, kollektordak emissiwiteit, grondoppervlak absorptiwiteit of grondoppervlak emissiwiteit, groot verbeterings op aanleg uitset moontlik is. Die implementering van termiese isolasie of 'n dubbelglaslaag vir die kollektordak veroorsaak ook 'n beduidende verheffing in kragstasie uitset. Simulasies voorspel 'n merkbare sensitiwiteit teenoor die grondoppervlak absorptiwiteitswaarde, terwyl veranderlike atmosferiese temperatuur daaltempos en winderige omgewingstoestande aanleg uitset beduidend mag belemmer. Verder is bevind dat sand ongeskik is as aanleg grond tipe en dat termo-ekonomiese optimale sonskoorsteen-kragstasie dimensies in die algemeen groter is as die aanvaarde aanlegdimensies van vorige studies. Goeie dinamiese beheer van sonskoorsteen-kragstasie uitset is bevestig, wat suggereer dat die sonskoorsteenkragstasie as 'n basis of pieklas elektrisiteitopwekkings-aanleg ingespan kan word. Ten laaste voorspel resultate dat plantegroei, mits dit voorsien word van genoegsame water, sal kan oorleef onder die kollektordak maar dat die inkorporasie van plantegroei die aanleg uitset beduidend sal benadeel. / Sponsored by the Centre for Renewable and Sustainable Energy Studies