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Paul-Emile Bernard's PhD Thesis
Discontinuous Galerkin Methods for Geophysical Flow Modeling
by Paul-Emile BERNARD (Public defense : November 14th, 2008, 16h00, BARB94)
The first ocean general circulation models developed in the late sixties were based on finite differences schemes on structured grids. Many improvements in the fields of engineering have been achieved since three decades with the developments of new numerical methods based on unstructured meshes. New second generation models are now under study, with the aim of taking advantage of the potential of modern numerical techniques such as finite elements on unstructured grids. Besides the classical continuous finite element or finite volume methods, another popular new trend in engineering applications is the high-order Discontinuous Galerkin method, presenting many interesting numerical properties in terms of dispersion and dissipation, errors convergence rates, advection schemes, mesh adaptation, etc.
The motivation for this PhD research is therefore to investigate the use of the high-order DG method for geophysical flow modeling. A first part of the thesis is devoted to the mesh adaptation using the DG method and the jumps as error estimator. We then investigate the use of the high order DG method with high-order representation of geometrical features. On one hand, a high-order mapping approach is studied to deal with complex representations of coastlines. Realistic computations are performed around the Rattray island, located in the Great Barrier Reef, and the results are compared to in-situ measurements. On the other hand, an alternative technique is proposed to deal with curved manifolds in order to represent oceanic or atmospheric flows on the sphere, using a local high-order non-orthogonal tangent basis. A last part is devoted the analysis of the dispersion and dissipation properties. The method proposed deals with any numerical scheme on any kind of grid, possibly unstructured. The DG method is then compared to other techniques as the mixed conforming/non-conforming linear elements pair, and the impact of unstructured meshes is analyzed.
Pdf-file of thesis (local server)
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