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Pré-Publication, Document De Travail Année : 2009

BOUSSINESQ SYSTEMS OF BONA-SMITH TYPE ON PLANE DOMAINS: THEORY AND NUMERICAL ANALYSIS

Vassilios Dougalis
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Dimitrios Mitsotakis
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Jean-Claude Saut
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Résumé

We consider a class of Boussinesq systems of Bona-Smith type in two space dimensions approximating surface wave flows modelled by the three-dimensional Euler equations. We show that various initial-boundary-value problems for these systems, posed on a bounded plane domain are well posed locally in time. In the case of reflective boundary conditions, the systems are discretized by a modified Galerkin method which is proved to converge in $L^2$ at an optimal rate. Numerical experiments are presented with the aim of simulating two-dimensional surface waves in complex plane domains with a variety of initial and boundary conditions, and comparing numerical solutions of Bona-Smith systems with analogous solutions of the BBM-BBM system.
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Dates et versions

hal-00407927 , version 1 (27-07-2009)

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Vassilios Dougalis, Dimitrios Mitsotakis, Jean-Claude Saut. BOUSSINESQ SYSTEMS OF BONA-SMITH TYPE ON PLANE DOMAINS: THEORY AND NUMERICAL ANALYSIS. 2009. ⟨hal-00407927⟩
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