Finite element methods for coastal flows : application to the Great Barrier Reef

• Main Author: Lambrechts, Jonathan
• Other Authors: UCL - SST/IMMC/MEMA - Applied mechanics and mathematics, Legat, Vincent, Deleersnijder, Eric, Remacle, Jean-François, Winckelmans, Grégoire, Hanert, Emmanuel, Dupret, François, Geuzaine, Christophe, Wolanski, Eric
• Format: Doctoral or Postdoctoral Thesis
• Language: English
• Published: 2011
• Subjects: Finite elements; Ocean; Great Barrier Reef; Unstructured meshes; Mesh generation; Hydrodynamics; Coastal flows; Multiscale; Ocean acidification
• Online Access: http://hdl.handle.net/2078.1/75973

Traditional ocean models are based on finite difference methods and solve the governing equations on structured grids. This PhD research is part of the SLIM (Second-generation Louvain-la-neuve Ice-ocean Model) project whose objective is to bring to oceanography the geometrical flexibility of unstructured grids. The SLIM model is based on the finite element method which is widely used in engineering analysis. This thesis presents the developement of SLIM for a coastal hydrodynamic application. The first step consists in generating unstructured meshes specifically adjusted to the needs of coastal or oceanic applications. We then compare five finite element pairs in term of both their stability and their accuracy for solving the shallow water equations. Finally, an optimized implementation is developed to reduce the time spent in the spatial integrals required by the finite element formulation. As the world's largest reef network, the Great Barrier Reef constitutes a unique ecosystem threatened by climate change, ocean acidification and agriculture. Finite elements are well designed for dealing with the Great Barrier intrinsic multi-scale features and complex topology. With a resolution up to 100 m near islands and reefs, our model is the first able to capture small scale features like tidal jet and eddies in the wake of islands in the same simulation as the global circulation on the continental shelf. Our model is used for several studies on the Great Barrier Reef with the objective to understand complex ecosystems and predict the human influence on their evolution. (FSA 3) -- UCL, 2011