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A semi-implicit, semi-Lagrangian, p-adaptive Discontinuous Galerkin method for the shallow water equations

le 28 mars 2012

14H - Groupe de travail "Applications des Mathématiques"

ENS Rennes Bâtiment Sauvy, Salle 5 (rdc)

Séminaire de Luca Bonaventura (MOX Milan) au groupe de travail "Applications des mathématiques"

Lien vers la page Web de l'orateur Résumé : A semi-implicit and semi-Lagrangian Discontinuous Galerkin method for the shallow water equations is proposed, for applications to geophysical scale flows. A non conservative formulation of the advection equation is employed, in order to achieve a more treatable form of the linear system to be solved at each time step. The method is equipped with a simple $p-$adaptivity criterion, that allows to adjust dynamically the number of local degrees of freedom employed to the local structure of the solution. Numerical results show that the method captures well the main features of gravity and inertial gravity waves, as well as reproducing correct solutions in nonlinear test cases with analytic solutions. The accuracy and effectiveness of the method are also demonstrated by numerical results obtained at high Courant numbers and with automatic choice of the local approximation degree. This is joint work with M.Restelli (MOX - Politecnico di Milano, Milano) and G. Tumolo (Abdus Salam International Center for Theoretical Physics, Trieste).

Recherche - Valorisation
Erwan Faou et Yannick Privat

Mise à jour le 26 mars 2012