Well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. Application to the dam-break of Aznalcóllar.

In this paper, we introduce a class of well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. We extend the derivation of standard finite volume solvers for homogeneous systems to non-homogeneous ones using the method of lines. We study conservation and some well-balanced pro...

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Bibliographic Details
Authors: Castro Díaz, Manuel Jesús, Chacón Rebollo, Tomás, Fernández Nieto, Enrique Domingo, González Vida, José Manuel, Parés Madroñal, Carlos
Format: article
Status:Versión aceptada para publicación
Publication Date:2008
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32145
Online Access:http://hdl.handle.net/11441/32145
https://doi.org/10.1016/j.cma.2008.03.026
Access Level:Open access
Keyword:Finite volume method
Well-balanced
Upwinding
Shallow water
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Summary:In this paper, we introduce a class of well-balanced finite volume schemes for 2D non-homogeneous hyperbolic systems. We extend the derivation of standard finite volume solvers for homogeneous systems to non-homogeneous ones using the method of lines. We study conservation and some well-balanced properties of the numerical scheme. We apply our solvers to shallow water equations: we prove that these exactly compute the water at rest solutions. We also perform some numerical tests, by comparing with 1D solutions, simulating the formation of a hydraulic drop and a hydraulic jump, and studying a real dam break: Aznalcóllar, an ecological disaster happened in the province of Seville, Spain in 1998.