Discontinuous finite-element methods for two- and three-dimensional marine flows
(2010)
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- Authors
- Supervisors
- Legat, Vincent
- Abstract
- (en) Numerical modeling is now, along with experiment and theory, part of the scientific method. Numerical models for marine flows exist for more than forty years. These models have evolved dramatically, with improved numerical methods, and much more accurate modeling of unresolved phenomena. However, most of the mainstream marine models still rely on the old numerical paradigm, based on finite difference methods and structured grids. The development of new numerical models, based on state-of-the art numerical methods on unstructured grids, is now an area of active research. Those unstructured meshes allow a faithful representation of the coastlines and the choice of the resolution following guidelines from the physics and not from the numerics. This thesis fits within this research. It is part of the development of SLIM (http://www.climate.be/SLIM), the Second-generation Louvain-la-neuve Ice-ocean Model. This model uses finite element methods on unstructured meshes made up of triangles for two-dimensional modeling, and triangular prisms for three-dimensional modeling. Numerical aspects are considered in this work. First, a comparison of several finite-element discretizations of the two-dimensional shallow water equations is performed. Second, to handle flows on the sphere, a novel algorithm is described, based on local coordinate systems, that allows a discretization free from singularities. Finally, a prototype three-dimensional baroclinic model is presented. The model features a spatial discretization built upon discontinuous finite elements and a time integration performed with an implicit mode splitting.
- Affiliations
Citations
Comblen, R. (2010). Discontinuous finite-element methods for two- and three-dimensional marine flows. https://hdl.handle.net/2078.5/131089