A discontinuous finite element baroclinic marine model on unstructured prismatic meshes
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We describe the time discretization of a three-dimensional baroclinic finite element model for the hydrostatic Boussinesq equations based upon a discontinuous Galerkin finite element method. On one hand, the time marching algorithm is based on an efficient mode splitting. To ensure compatibility between the barotropic and baroclinic modes in the splitting algorithm, we introduce Lagrange multipliers in the discrete formulation. On the other hand, the use of implicit–explicit Runge–Kutta methods enables us to treat stiff linear operators implicitly, while the rest of the nonlinear dynamics is treated explicitly. By way of illustration, the time evolution of the flow over a tall isolated seamount on the sphere is simulated. The seamount height is 90% of the mean sea depth. Vortex shedding and Taylor caps are observed. The simulation compares well with results published by other authors.
KeywordsBaroclinic marine model Discontinuous Galerkin methods Time discretization
Sébastien Blaise and Jonathan Lambrechts are research fellows with the Belgian Fund for Research in Industry and Agriculture (FRIA). Richard Comblen is a research fellow with the Belgian National Fund for Scientific Research (FNRS). Eric Deleersnijder is a research associate with the Belgian National Fund for Scientific Research (FNRS). The research was conducted within the framework of the Interuniversity Attraction Pole TIMOTHY (IAP 6.13), funded by the Belgian Science Policy (BELSPO), and the programme ARC 04/09-316, funded by the Communauté Française de Belgique.
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