A stable and accurate Davies-like relaxation procedure using multiple penalty terms for lateral boundary conditions |
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| Institution: | 1. Université de Lyon, IMP@UJM St-Étienne, CNRS UMR 5223, Faculté des Sciences et Techniques, Université Jean-Monnet, 23 rue du docteur Paul Michelon, 42023 St-Étienne cédex 2, France;2. Université de Lille I, Laboratoire de Mécanique de Lille, F59655 Villeneuve d’Ascq cédex, France;3. Ecole Centrale de Nantes, Institut de Calcul Intensif (ICI), 1 rue de la Noë BP 92101, 44321 Nantes cedex 3, France |
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| Abstract: | A lateral boundary treatment using summation-by-parts operators and simultaneous approximation terms is introduced. The method is similar to Davies relaxation technique used in the weather prediction community and have similar areas of application, but is also provably stable. In this paper, it is shown how this technique can be applied to the shallow water equations, and that it reduces the errors in the computational domain. |
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| Keywords: | Boundary conditions Boundary layers Summation-by-parts Energy method Convergence Shallow water equations |
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