Thesis (M. Sc.)--University of the Western Cape, 2007. / Includes bibliographical references (leaves 61-77).

Thesis (Ph. D.)--University of Texas at Austin, 1998. / Vita. Includes bibliographical references (leaves 238-250). Available also in a digital version from Dissertation Abstracts.

Thesis (MSc)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: Various numerical modelling software packages are available for predicting moored ship motions and forces. The focus of this study was to validate the numerical models QUAYSIM and WAVESCAT and how these models together form a procedure for predicting moored ship motions and forces under the impact of high and low frequency waves. The validation procedure applied in the study involved numerical modelling of a given physical model situation in which moored ship motions and forces were measured under both high and low frequency wave conditions. A physical model with built-in bathymetry was provided by the Council for Scientific and Industrial Research (CSIR) Hydraulics Laboratory in Stellenbosch. The model consisted of a moored container vessel at a jetty, with various mooring lines and fenders. A JONSWAP spectrum, which combines high and low frequency wave components, was used to simulate wave conditions for the modelling of ship motions. The wave periods and wave heights were measured at observation stations located at specific points in the basin. Other measurements such as those of the forces in the fenders and mooring lines were also determined. A multi-step approach was used to numerically predict the ship motions and forces. Firstly, the coastal processes occurring within the basin, which was set up to simulate the physical model wave behaviour, were measured to calibrate the SWAN Delft3D-WAVE model. The wave heights and periods for the respective observation stations were obtained and compared to the physical model measurements. The Delft3D-FLOW SURFBEAT model was used to calculate the low frequency waves in the coastal area. Low frequency waves are the main cause of larger ship motions and forces, therefore it is important to investigate them as part of the ship motion prediction procedure. After the waves had been computed, wave forces acting on the vessel needed to be determined for both high and low frequency waves. These wave forces were modelled with the combinations SURFBEAT/LF-STRIP (low frequency waves) and SWAN/WAVESCAT (high frequency waves). LF-STRIP provided the link between low frequency wave models and ship motion models, converting the low frequency waves into long wave forces acting on the vessel. WAVESCAT converted the high frequency waves to short wave forces. The calculated long wave forces and short wave forces served as the input required to run the ship motion model QUAYSIM to determine the movements of the moored ship as well as the restraining forces in the lines and fenders. The ship motions and forces were compared to the physical model, with the intention of possibly validating the QUAYSIM/WAVESCAT approach for predicting moored ship motions. The study provides an overview of both the setup and results of the physical and numerical model. A description of each of the numerical models SWAN, SURFBEAT, LF-STRIP, WAVESCAT and QUAYSIM is provided, along with a comparison between the physical and numerical models for each procedure. The validation procedure provided useful documentation of the quality of these numerical modelling approaches, already in use in some design projects. The numerical models WAVESCAT and QUAYSIM models of ship motion have shown to provide a good correlation between the physical model and the numerical approach. However, improvements are still required. Good comparisons were obtained for the long wave motions (horizontal movements - surge, sway and yaw). The surge and sway motions were slightly overestimated by QUAYSIM. The magnitude of the yaw was comparable but the not well represented in spectral plots. / AFRIKAANSE OPSOMMING: Daar is verskeie numeriese modellering-sagtewareprogramme beskikbaar waarmee skipbewegings en -kragte voorspel kan word. Die fokus van hierdie studie was om die numeriese modelle QUAYSIM en WAVESCAT te valideer. Saam vorm hierdie twee modelle ’n prosedure om vasgemeerde skipbewegings en -kragte veroorsaak deur lang- en kortgolfaksie te bepaal. Die validasieprosedure wat in hierdie studie gebruik is, behels ’n numeriese modelering van ’n fisiese situasie waar ’n vasgemeerde skip se bewegings en kragte onder kort- en langgolfkondisies gemeet is. ’n Fisiese model met ingeboude batimetrie is voorsien deur die Council for Scientific and Industrial Research (CSIR) se hidroliese laboratorium in Stellenbosch. Die model bestaan uit ’n vasgemeerde houerskip by ’n pier met verskeie ankerlyne en bootbuffers. ’n JONSWAPspektrum, wat kort- en langgolfkomponente kombineer, is gebruik om golfomstandighede vir die modellering van skipbewegings te simuleer. Golfperiodes en golfhoogtes is by spesifieke waarnemingstasies in die gesimuleerde hawe-area gemeet. Verdere opmetings, soos dié van die kragte in die bootbuffers en ankerlyne, is ook gedoen. ’n Stap-vir-stap benadering is gevolg om die skipbewegings numeries te voorspel. Eerstens is die kusprosesse wat in die gesimuleerde hawe plaasvind, gekalibreer met die numeriese paket SWAN Delft3D-WAVE. Die golfhoogtes en golfperiodes vir elke waarnemingstasie is bereken en vergelyk met die fisiese model se opmetings. Die SURFBEAT-module van Delft3D-FLOW is gebruik om die lae-frekwensie golwe in die kusarea te bereken. Lae-frekwensie golwe is die hoofoorsaak van skipbewegings en daarom is dit belangrik om dit te ondersoek gedurende die voorspellingsprosedure van skipbewegings. Na die golwe bereken is, moes die kragte wat beide kort en lang golwe op die skip uitoefen ook bereken word. Hierdie golfkragte is gemodelleer deur middel van die kombinasies SURFBEAT/LFSTRIP (langgolwe) en SWAN/WAVESCAT (kortgolwe). LF-STRIP het die skakel tussen golfmodelle en skipbewegingsmodelle verskaf en die lae-frekwensie golwe omgeskakel in langgolfkragte wat op die skip uitgeoefen is. WAVESCAT het die hoë-frekwensiegolwe omgeskakel in kortgolfkragte wat op die skip uitgeoefen is. Die berekende langgolf- en kortgolfkragte is ingevoer op die skipbewegingsmodel QUAYSIM om die skipbewegings en inperkingskragte in die bootbuffers en ankerlyne te bepaal sodat dit vergelyk kon word met die fisiese model, met die doel om moontlik die QUAYSIM/WAVESCAT-prosedure om gemeerde skipbewegings te voorspel te valideer. Die studie verskaf ’n oorsig van die opstel en resultate van die fisiese en numeriese modelle. Elk van die numeriese modelle SWAN, SURFBEAT, LF-STRIP, WAVESCAT en QUAYSIM word beskryf en vergelykings word getref tussen die numeriese en fisiese modelle vir elke prosedure. Die validasieprosedure verskaf nuttige dokumentasie van die kwaliteit van hierdie numeriese modeleringsprosedures wat reeds in sekere ontwerpprojekte gebruik word. Die numeriese WAVESCAT en QUAYSIM modelle van skipbewegings het ’n goeie korrelasie tussen die fisiese model en die numeriese benadering gelewer. Verbeteringe is wel steeds nodig. Goeie vergelykings is verkry vir langgolfbewegings (horisontale bewegings – stuwing (“surge”), swaai (“sway”) en gier (“yaw”)). Die stu- en swaaibewegings was effens oorskat met QUAYSIM. Die grootte van die gier was wel vergelykbaar maar is nie grafies goed uitgebeeld nie.

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Numerical methods for solving initial value problems in ordinary differential equations are studied. A notation is introduced to represent cyclic methods in terms of two matrices, A_h, and B_h, and this is developed to cover the very extensive class of m-block methods. Some stability results are obtained and convergence is analysed by means of a new consistency concept, namely optimal consistency. It is shown that optimal consistency allows one to give two-sided bounds on the global error, and examples are given to illustrate this. The form of the inverse of A_h is studied closely to give a criterion for the order of convergence to exceed that of consistency by one. Further convergence results are obtained , the first of which gives the orders of convergence for cases in which A_h, and B_h, have a special form, and the second of which gives rise to the possibility of the order of convergence exceeding that of consistency by two or more at some stages. In addition an alternative proof is given of the superconvergence result for collocation methods. In conclusion the work covered is set in the context of that done in recent years by various authors.

published_or_final_version / Computer Science / Doctoral / Doctor of Philosophy

This dissertation presents a duality theorem of the Aubin-Nitsche type for discontinuous Petrov Galerkin (DPG) methods. This explains the numerically observed higher convergence rates in weaker norms. Considering the specific example of the mild-weak (or primal) DPG method for the Laplace equation, two further results are obtained. First, for triangular meshes, the DPG method continues to be solvable even when the test space degree is reduced, provided it is odd. Second, a non-conforming method of analysis is developed to explain the numerically observed convergence rates for a test space of reduced degree. Finally, for rectangular meshes, the test space is reduced, yet the convergence is recovered regardless of parity.

No description available.

American meteorology was synonymous with subjective weather forecasting in the early twentieth century. Controlled by the Weather Bureau and with no academic programs of its own, the few hundred extant meteorologists had no standing in the scientific community. Until the American Meteorological Society was founded in 1919, meteorologists had no professional society. The post-World War I rise of aeronautics spurred demands for increased meteorological education and training. The Navy arranged the first graduate program in meteorology in 1928 at MIT. It was followed by four additional programs in the interwar years. When the U.S. military found itself short of meteorological support for World War II, a massive training program created thousands of new mathematics- and physics-savvy meteorologists. Those remaining in the field after the war had three goals: to create a mathematics-based theory for meteorology, to create a method for objectively forecasting the weather, and to professionalize the field. Contemporaneously, mathematician John von Neumann was preparing to create a new electronic digital computer which could solve, via numerical analysis, the equations that defined the atmosphere. Weather Bureau Chief Francis W. Reichelderfer encouraged von Neumann, with Office of Naval Research funding, to attack the weather forecasting problem. Assisting with the proposal was eminent Swedish-born meteorologist Carl-Gustav Rossby. Although Rossby returned to Stockholm to establish his own research school, he was the de facto head of the Meteorology Project providing personnel, ideas, and a publication venue. On-site leader Jule Charney provided the equations and theoretical underpinnings. Scandinavian meteorologists supplied by Rossby provided atmospheric reality. Six years after the Project began, meteorologists were ready to move their models from a research to an operational venue. Attempts by Air Force meteorologist Philip D. Thompson to co-opt numerical weather prediction (NWP) prompted the academics, Navy, and Weather Bureau members involved to join forces and guarantee that operational NWP would remain a joint activity not under the control of any weather service. This is the story of the professionalization of a scientific community, of significant differences in national styles in meteorology, and of the fascination (especially by non-meteorologists) in exploiting NWP for the control of weather. / Graduation date: 2003