New absorbing layers conditions for short water waves

Authors:
H. Barucq;J. Diaz;M. Tlemcani
Affiliations:
INRIA, Bordeaux Sud-Ouest Research Center, Team-Project Magique3D, France and Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA- ...;INRIA, Bordeaux Sud-Ouest Research Center, Team-Project Magique3D, France and Laboratoire de Mathématiques Appliquées, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, IPRA- ...;Département de Physique, Faculté des Sciences, BP 1505, El M'Naouer (USTOMB), Oran 1300, Algeria
Venue:
Journal of Computational Physics
Year:
2010

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Abstract

We develop a new PML formulation for the linearized shallow-water equations including the Coriolis force. The construction process is based on the uncoupling of the velocity components with the depth of water. Then the damping effect is only applied to the propagative modes just as was formerly done by Nataf [1] to the linearized Euler equations to enforce the long-time stability. We assess numerically the performance of the new absorbing condition and we illustrate in particular that it is stable for long-time simulations.