Work

General boundary conditions for a Boussinesq model with varying bathymetry

Year: 2024

Type: article

Abstract: 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 ordinary differential equation. 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 are not known.

Source: Studies in Applied Mathematics

DOI: 10.1111/sapm.12751

Authors: David Lannes, Mathieu Rigal

Institutions: Centre National de la Recherche Scientifique, Université de Bordeaux, Institut de Mathématiques de Bordeaux

Language: English

Topic: Coastal and Marine Dynamics

Subfield: Earth-Surface Processes

Field: Earth and Planetary Sciences

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,330

Funder: Agence Nationale de la Recherche