Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography
type: Item
instance of: scholarly article
title: Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography
zbMATH Open document ID: 1464.65096
author: Alina Chertock
author: Alexander Kurganov
author: Tong Wu
published in: Communications in Mathematical Sciences
publication date: 2021-05-03T00:00:00Z
review text: The authors study the shallow water system with time-dependent bottom topography. They consider the simplest case, in which the shallow water waves are modeled by the Saint-Venant system and the bottom topography movement is governed by the Exner equation. The resulting system is hyperbolic and its Jacobian matrices typically contain both large and small eigenvalues. The largest eigenvalues determine the speed of the fast surface waves and the smallest eigenvalue reflects the (slow) speed of the bottom topography propagation. A finite volume method is presented to approximate the underlying system using an explicit scheme. The time steps, which are inversely proportional to the maximum of the spectral radius of the Jacobians over the entire computational domain, would be too small. An operator splitting approach is developed which allows to deal with large time steps in the bottom evolution stages, while keeping the small CFL-controlled time steps in the hydrodynamics stages. The method presented here is based on the application of a finite-volume central-upwind scheme introduced in [\textit{A. Kurganov} and \textit{G. Petrova}, Commun. Math. Sci. 5, No. 1, 133--160 (2007; Zbl 1226.76008)]. Some numerical tests in one- and two-dimensions are presented to demonstrate the performance of the proposed method.
reviewed by: Abdallah Bradji
Mathematics Subject Classification ID: 65M08
Mathematics Subject Classification ID: 35L65
Mathematics Subject Classification ID: 76M12
Mathematics Subject Classification ID: 86-08
Mathematics Subject Classification ID: 86A05
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35R37
zbMATH DE Number: 7342285
zbMATH Keywords: Saint Venant system of shallow water equations
zbMATH Keywords: moving bottom topography
zbMATH Keywords: Exner equation
zbMATH Keywords: operator splitting method
zbMATH Keywords: semi-discrete central-upwind schemes
MaRDI profile type: Publication
full work available at URL: cms.2020.v18.n8.a3
OpenAlex ID: W3115071728
DOI: 10.4310/CMS.2020.V18.N8.A3
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description: scientific article; zbMATH DE number 7342285