Yuen, Man Chun. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 58-[60]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese.

Bibliography: leaves 169-178.

Waves and circulation processes interact in daily wind and tide driven flows as well as in more extreme events such as hurricanes. Currents and water levels affect wave propagation and the location of wave-breaking zones, while wave forces induce setup and currents. Despite this interaction, waves and circulation processes are modeled separately using different approaches. Circulation processes are represented by the shallow water equations, which conserve mass and momentum. This approach for wind-generated waves is impractical for large geographic scales due to the fine resolution that would be required. Therefore, wind-waves are instead represented in a spectral sense, governed by the action balance equation, which propagates action density through both geographic and spectral space. Even though wind-waves and circulation are modeled separately, it is important to account for their interactions by coupling their respective models. In this dissertation we use discontinuous-Galerkin (DG) methods to couple spectral wave and circulation models to model wave-current interactions. We first develop, implement, verify and validate a DG spectral wave model, which allows for the implementation of unstructured meshes in geographic space and the utility of adaptive, higher-order approximations in both geographic and spectral space. We then couple the DG spectral wave model to an existing DG circulation model, which is run on the same geographic mesh and allows for higher order information to be passed between the two models. We verify and validate coupled wave/circulation model as well as analyzing the error of the coupled wave/circulation model. / text

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The issue of local scale and smoothness presents a crucial and daunting challenge for numerical simulation methods in fluid dynamics. Yet in the interests of both accuracy and economy, how can one devise a general technique that efficiently resolves flow features of consequence and discriminates against others which are either ``negligible' or amenable to ``universal' modeling? This is particularly difficult because geometries of engineering interest are complex and multi-dimensional, precluding a priori knowledge of the flowfield. To address this challenge, the current work employs wavelet theory for the local scale decomposition of functions, which provides a natural mechanism for the adaptive compression of data. The resulting technique is known as the Multi-Resolution Discontinuous Galerkin (MRDG) method. This research successfully demonstrates that the multi-resolution framework and the discontinuous Galerkin method are well-suited for a new approach to accuracy and cost as demonstrated by the relative ease of their integration in spatial dimension greater than one. Some specific steps achieved include the implementation of suitable data encoding and compression algorithms, construction of multi-wavelet expansion bases in one and two dimensions, and derivation of the multi-resolution derivative operator that includes an upwind-type correction to the central scheme. Solutions with the MRDG method are observed to adapt to and track both smooth and discontinuous flow features in an entirely solution-driven manner without the need for a priori user knowledge of those flow features. Run-time efficiency and local adaptation characteristics are explored via a series of classic test problems.

Bibliography: leaves 169-178 / iv, 201 leaves : 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, 1989

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2008. / Title from title screen (site viewed Aug. 12, 2008). PDF text: ix, 150 p. : ill. (come col.) ; 913 K. UMI publication number: AAT 3297747. Includes bibliographical references. Also available in microfilm and microfiche formats.

Thesis (M. Phil.)--University of Hong Kong, 1995. / Includes bibliographical references (leaves 123-126).

Thesis (Ph.D.)--Mississippi State University. Department of Mechanical Engineering. / Title from title screen. Includes bibliographical references.

Thesis (Ph.D.)--Memorial University of Newfoundland, 2004. / Bibliography: leaves 170-183.