Aspects of shallow water modelling

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dc.contributor.advisor O’Sullivan, Mike en Trew, Mark Linton en 2020-07-08T05:01:06Z en 2020-07-08T05:01:06Z en 1999 en
dc.identifier.uri en
dc.description Full text is available to authenticated members of The University of Auckland only. en
dc.description.abstract This thesis investigates aspects of mathematical, numerical and computational modelling of shallow water flows. An understanding of the mathematical model of shallow water flow leads to new numerical models of the governing equations that are constructed with a particular emphasis on advective transport and the wetting and drying of the solution domain. Computational models of test problems and the Manukau Harbour validate the numerical models. A Lagrangian-Eulerian Galerkin finite element method is developed. This combines an efficient algorithm for performing auxiliary Lagrangian particle source calculations with a numerically effective moving boundary technique and the geometric flexibility of a mixed interpolation Galerkin finite element method. Test problems show the model to be numerically well behaved and converging to a solution with increasing spatial and temporal discretisation. The model simulates highly advective flows using a minimal amount of artificial momentum dissipation and produces stable solutions when wetting and drying of the solution domain occurs. An integrated finite difference method is also developed. This model combines the numerically sound staggered variable discretisation with an integral description of the Shallow Water Equations. The resulting method has the geometric flexibility of a finite element method but more attractive numerical properties. An Eulerian-Lagrangian method is also incorporated together with a robust moving boundary technique that smoothly tracks the wet to dry interface. Test problems show computational results converging with spatial and temporal refinement. Highly advective flows are simulated without the need for any form of momentum dissipation or numerical control. The model produces computational results for moving boundary problems that are smooth and convergent. Computational models of the Manukau Harbour produce solutions from the integrated finite difference method of equivalent accuracy to those of the Lagrangian-Eulerian Galerkin finite element method, and at a much lower computational cost. Results from both methods agree with previous studies and recorded values. A highly refined computational solution from the integrated finite difference method captures features of flow in the Manukau Harbour that are not usually resolved. The integrated finite difference method emerges as a powerful new modelling tool for shallow water flows. en
dc.publisher ResearchSpace@Auckland en
dc.relation.ispartof PhD Thesis - University of Auckland en
dc.relation.isreferencedby UoA9986806514002091 en
dc.rights Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. en
dc.rights Restricted Item. Full text is available to authenticated members of The University of Auckland only. en
dc.rights.uri en
dc.title Aspects of shallow water modelling en
dc.type Thesis en Engineering Science en The University of Auckland en Doctoral en PhD en
dc.rights.holder Copyright: The author en
dc.identifier.wikidata Q112850016

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