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Pré-Publication, Document De Travail Année : 2009

Numerical solution of Boussinesq systems of the Bona-Smith family

Dimitrios Antonopoulos
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Vassilios Dougalis
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Dimitrios Mitsotakis
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  • PersonId : 858982

Résumé

In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study numerically three initial-boundary-value problems for these systems, corresponding, respectively, to homogeneous Dirichlet, reflection, and periodic boundary conditions posed at the endpoints of a finite spatial interval.We approximate these problems using the standard Galerkin-finite element method for the spatial discretization and a fourth-order, explicit Runge-Kutta scheme for the time stepping, and analyze the convergence of the fully discrete schemes. We use these numerical methods as exploratory tools in a series of numerical experiments aimed at illuminating interactions of solitary-wave solutions of the Bona-Smith systems, such as head-on and overtaking collisions, and interactions of solitary waves with the boundaries.
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Dates et versions

hal-00371943 , version 1 (30-03-2009)
hal-00371943 , version 2 (31-03-2009)

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  • HAL Id : hal-00371943 , version 2

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Dimitrios Antonopoulos, Vassilios Dougalis, Dimitrios Mitsotakis. Numerical solution of Boussinesq systems of the Bona-Smith family. 2009. ⟨hal-00371943v2⟩
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