A discontinuous finite element baroclinic marine model on unstructured prismatic meshes |
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Authors: | Sébastien Blaise Richard Comblen Vincent Legat Jean-François Remacle Eric Deleersnijder Jonathan Lambrechts |
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Institution: | 1. Institute of Mechanics, Materials and Civil Engineering (IMMC), Université catholique de Louvain, Euler, 4 Avenue G. Lema?tre, 1348, Louvain-la-Neuve, Belgium 2. Georges Lema?tre Centre for Earth and Climate Research (TECLIM), Université catholique de Louvain, Euler, 4 Avenue G. Lema?tre, 1348, Louvain-la-Neuve, Belgium 3. Centre for Systems Engineering and Applied Mechanics (CESAME), Université catholique de Louvain, Euler, 4 Avenue G. Lema?tre, 1348, Louvain-la-Neuve, Belgium 5. Institute for Mathematics Applied to Geosciences, National Center for Atmospheric Research, 1850 Table Mesa Drive, Boulder, CO, 80305, USA 4. Earth and Life Institute (ELI), Université catholique de Louvain, Euler, 4 Avenue G. Lema?tre, 1348, Louvain-la-Neuve, Belgium
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Abstract: | We describe the space discretization of a three-dimensional baroclinic finite element model, based upon a discontinuous Galerkin
method, while the companion paper (Comblen et al. 2010a) describes the discretization in time. We solve the hydrostatic Boussinesq equations governing marine flows on a mesh made
up of triangles extruded from the surface toward the seabed to obtain prismatic three-dimensional elements. Diffusion is implemented
using the symmetric interior penalty method. The tracer equation is consistent with the continuity equation. A Lax–Friedrichs
flux is used to take into account internal wave propagation. By way of illustration, a flow exhibiting internal waves in the
lee of an isolated seamount on the sphere is simulated. This enables us to show the advantages of using an unstructured mesh,
where the resolution is higher in areas where the flow varies rapidly in space, the mesh being coarser far from the region
of interest. The solution exhibits the expected wave structure. Linear and quadratic shape functions are used, and the extension
to higher-order discretization is straightforward. |
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