General boundary conditions for a Boussinesq model with varying bathymetry

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
David Lannes, Mathieu Rigal
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引用次数: 0

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.

水深变化的布森斯克模型的一般边界条件
本文致力于对用于描述沿海地区波浪的方程系统,即存在地形的 Boussinesq-Abbott 系统的初始边界值问题进行理论和数值研究。我们提出了一种程序,可以处理非常一般的线性或非线性边界条件。它包括将问题简化为一个具有非局部通量并与常微分方程耦合的守恒定律系统。利用这种重述方法,分别提出了两种一阶和二阶混合有限体积/有限差分方案。利用使用多种边界条件的可能性,对边界条件的渐近稳定性进行了数值研究,这在沿岸海洋 学中是一个具有实际意义的问题,因为渐近稳定的边界条件可以使人们仅根据边界数据重建波 场,即使不知道初始数据。
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来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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