LANNES, David; RIGAL, Mathieu

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Licencia de uso del documento

http://creativecommons.org/licenses/by-sa/

LANNES, David
Institut de Mathématiques de Bordeaux [IMB]

RIGAL, Mathieu
Institut de Mathématiques de Bordeaux [IMB]

Idioma

Document de travail - Pré-publication

Este ítem está publicado en

2024-02-06

Resumen en inglés

This paper is devoted to the theoretical and numerical investigation of the initial boundary value problem for a system of equations used for the description of waves in coastal areas, namely, the Boussinesq-Abbott system in the presence of topography. We propose a procedure that allows one to handle very general linear or nonlinear boundary conditions. It consists in reducing the problem to a system of conservation laws with nonlocal fluxes and coupled to an ODE. This reformulation is used to propose two hybrid finite volumes/finite differences schemes of first and second order respectively. The possibility to use many kinds of boundary conditions is used to investigate numerically the asymptotic stability of the boundary conditions, which is an issue of practical relevance in coastal oceanography since asymptotically stable boundary conditions would allow one to reconstruct a wave field from the knowledge of the boundary data only, even if the initial data is not known.< Leer menos

Palabras clave en inglés

Boussinesq-Abbott model

Initial boundary value problem

Inhomogeneous boundary conditions

Dispersive boundary layer

Nonlocal flux

Finite volumes

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190242

Proyecto ANR

Parois, congestion et vorticité dans les fluides : des défis théoriques aux applications environnementales - ANR-23-CE40-0014

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251