High order accurate finite difference methods for hyperbolic and parabolic initial boundary value problems (IBVPs) are considered. Particular focus is on time dependent wave propagating problems in complex domains. Typical applications are acoustic and electromagnetic wave propagation and fluid dynamics. To solve such problems efficiently a strictly stable, high order accurate method is required. Our recipe to obtain such schemes is to: i) Approximate the (first and second) derivatives of the IBVPs with central finite difference operators, that satisfy a summation by parts (SBP) formula. ii) Use specific procedures for implementation of boundary conditions, that preserve the SBP property. iii) Add artificial dissipation. iv) Employ a multi block structure. Stable schemes for weakly nonlinear IBVPs require artificial dissipation to absorb the energy of the unresolved modes. This led to the construction of accurate and efficient artificial dissipation operators of SBP type, that preserve the energy and error estimate of the original problem. To solve problems on complex geometries, the computational domain is broken up into a number of smooth and structured meshes, in a multi block fashion. A stable and high order accurate approximation is obtained by discretizing each subdomain using SBP operators and using the Simultaneous Approximation Term (SAT) procedure for both the (external) boundary and the (internal) interface conditions. Steady and transient aerodynamic calculations around an airfoil were performed, where the first derivative SBP operators and the new artificial dissipation operators were combined to construct high order accurate upwind schemes. The computations showed that for time dependent problems and fine structures, high order methods are necessary to accurately compute the solution, on reasonably fine grids. The construction of high order accurate SBP operators for the second derivative is one of the considerations in this thesis. It was shown that the second derivative operators could be closed with two order less accuracy at the boundaries and still yield design order of accuracy, if an energy estimate could be obtained.

Thesis (MEng) -- University of South Australia, 1992

Copies of author's previously published works inserted. / Includes bibliographies. / 1 v. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / Thesis (Ph.D.)--University of Adelaide, Dept. of Microbiology and Immunology and Div. of Human Immunology, Hanson Centre for Cancer Research, Institute of Medical and Veterinary Science, 1996

Thesis (MEng) -- University of South Australia, 1992

Master of Science (Dentistry) / Dimensional stability was defined by Nicholls (1977) as “the ability (of a material) to maintain accuracy over time”, and the result of loss of accuracy, “distortion”, as “the relative movement of a single point, or group of points, away from some originally specified reference position such that permanent deformation is apparent”. Maintaining dimensional stability of dental impression materials is vital if the impression cannot be cast (in stone) soon after removal from the mouth. Dental irreversible hydrocolloid (alginate) is a major dental impression material used worldwide in many clinical procedures. However, alginate is dimensionally unstable and changes its dimensions (suffers “distortion”) after removal from the mouth. With storage times of more than ten minutes, alginate begins to distort, and after one to three hours (depending on the product and storage conditions) cannot be used for many clinical purposes, especially fixed prosthodontics such as crowns and bridges (Hampson 1955, Skinner & Hoblit 1956, Wilson & Smith 1963, Rudd et al. 1969, Miller 1975, Inohara 1977, Schoen et al. 1978, Coleman et al. 1979, Linke et al. 1985, Habu et al. 1986, Peutfeldt & Asmussen 1989, Mathilde & Peters 1992, Khan & Aziz Sahu 1995, Eriksson et al. 1998, Schleier et al. 2001, and Donovan & Chee 2004). This loss of accuracy, due to dimensional instability, manifests as a time-dependent distortion of the poured stone cast, and thus any prosthesis fabricated will not fit in the mouth. With the introduction of the more stable elastomers in the 1950s (Stackhouse 1970, Glenner 1997, Brown 2003) that could be stored for days if necessary, without loss of accuracy, the alginates fell out of favour for fixed prosthodontics. Recently, there has been a resurgence of interest in alginate for use in dental procedures where dimensional stability is critical (Peutzfeldt and Asmussen 1989, Eriksson et al. 1998). This in part is due to the favourable properties of alginate not found in the elastomers. Of greatest significance is that alginate hydrocolloid is hydrophilic, whereas elastomers are hydrophobic (Phillips & Ito 1958, Glenner 2004). Thus, alginate materials are able to reproduce wet oral areas with greater precision and to produce a superior "fit" of, say, a gold casting produced by the Lost Wax technique (Skinner and Phillips 1982). A number of reports have been published which investigate newer alginate materials that are claimed to be more dimensionally stable than older formulations. Puetzfeldt and Asmussen (1989) found that a newer alginate , if stored at 100% relative humidity, retained accuracy over 24 hours that was equivalent to that of the elastomers. More recently, the manufacturer of another alginate has claimed equivalent dimensional stability to the elastomers for up to 100 hours, and, whilst this claim has not been reported on in the literature, the present thesis will show that, under favourable conditions of storage, the material maintained clinically useful accuracy for up to 100 hours. Another approach to improving the accuracy of alginate impressions has been to combine reversible hydrocolloid with alginate (the “Bilaminar” technique). Frederick and Caputo (1997) confirmed that the new agar reversible hydrocolloids are just as accurate (at the time of removal from the mouth) as the new elastomers. Mathilde et al. (1992) and Eriksson et al. (1998) have shown that several of the “bilaminar” impression techniques for fixed prosthodontics, where alginate is used as a tray material supporting a reversible hydrocolloid (agar) wash, are as accurate and dimensionally stable as elastomers for up to three hours. However, these studies are difficult to interpret due to lack of uniformity in the testing methods, and the fact that there is no regulatory standard available to measure dimensional stability for dental alginates. The International Standard (IS) for alginate impression materials (ISO 1563:1990E) contains no specification for dimensional stability, and thus places no requirement for manufacturers to state dimensional stability properties on their labels. In contrast, ISO 4823:1992(E) specifies the IS for elastomeric dental impression materials, and it does specify a requirement for dimensional stability (less than 1.5% distortion after 24 hours). Further, the IS sets a method for determination of dimensional stability. Briefly, this method (the Optical Method) uses a travelling optical microscope to measure the accuracy of the distance between score lines on an impression of a test grid, at various time periods. The American Dental Association Specification No. 19 for dental elastomeric impression materials is identical to the IS. There is currently no specific Australian Standard (AS) for the dimensional stability of any dental impression material. Overview of Experimental Methods A. The Optical Method The aim of Part A of this investigation was to: 1. Adapt the Optical Method of the IS for elastomers to be reproducible for dental alginates. This was achieved by using a perforated test tray (to simulate clinical conditions), and measuring the grid pattern on a dental stone button after casting the test impression, rather than direct measurement of the impression, as for the IS. 2. To measure and rank the dimensional stability of a number of locally available dental alginates. Measurements of the test stone buttons proved reproducible, and the results were different for each sample, allowing them to be ranked according to dimensional stability after 50 and 100 hours of storage. The results show that the traditional optical method for measuring dimensional stability, as specified in the IS for dental elastomers, can be adapted to measure the dimensional stability of dental alginates However, the Optical Method of measuring dimensional stability of dental alginates is cumbersome and time-consuming. It was hypothesised that dimensional stability of dental alginates could be measured more conveniently by finding a thermal property that is directly proportional to dimensional stability. This method could be useful for the rapid determination of relative performance, and allow comparison with a determined benchmark. B. The Thermal Method Recently, modern methods of Thermal Analysis, Thermal Gravimetric Analysis (TGA) and Differential Scanning Calorimetry (DSC) have been used to rapidly age various polymers, including food alginates (Chinachoti 1996), in order to measure thermal stability. This thesis shows that thermal stability is an indicator of dimensional stability. The aim of Part B of this investigation was therefore to adapt thermal analysis techniques to dental alginates, and develop a method to measure their thermal stability. These results were then compared with those for dimensional stability measured by the Optical Method to determine the relationship between thermal and dimensional stability for dental alginates. The results show that current thermal analysis methods of TGA and DSC can be adapted to measure relative dental alginate dimensional stability, and are both rapid and convenient. This study also provides evidence that commercial products differ as regards the property of dimensional stability, and can be ranked accordingly. C. Practical Application of the Methods The aim of part C of this thesis was to validate the methods (both optical and thermal) developed in this study by using them to investigate the effect of varying the water/powder ratio on the dimensional stability of dental alginates. It was shown that dimensional stability is affected by changes to the recommended water/powder ratio, that both the methods detected and measured the changes, and that the results were proportional, in that any percentage change detected by the optical method, was mirrored by the thermal method, confirming that the more convenient thermal methods can be used to measure dimensional stability.

Thesis (MEng) -- University of South Australia, 1992

Thesis (M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 49)

Thesis (M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references (ℓ. 50-51)

Thesis (Ph.D.)--Tennessee Technological University, 2007. / Bibliography: leaves 108-114.

Thesis (Ph.D.) -- University of Newcastle, 2003. / School of Engineering. Includes bibliographical references (leaves 248-256). Also available online.