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On well-balanced finite volume methods for non-conservative non-homogeneous hyperbolic systems

 

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Opened Access On well-balanced finite volume methods for non-conservative non-homogeneous hyperbolic systems
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Título alternativo: Well-balanced Finite volume solvers
Author: Chacón Rebollo, Tomás
Fernández-Nieto, Enrique D.
Parés Madroñal, Carlos
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2007
Published in: SIAM journal on scientific computing, 29 (3), 1093-1126
Document type: Article
Abstract: In this work we introduce a general family of finite volume methods for non-homogeneous hyperbolic systems with non-conservative terms. We prove that all of them are “asymptotically well-balanced”: They preserve all smooth stationary solutions in all the domain but a set whose measure tends to zero as ∆x tends to zero. This theory is applied to solve the bilayer Shallow-Water equations with arbitrary cross-section. Finally, some numerical tests are presented for simplified but meaningful geometries, comparing the computed solution with approximated asymptotic analytical solutions.
Size: 720.7Kb
Format: PDF

URI: http://hdl.handle.net/11441/32920

DOI: http://dx.doi.org/10.1137/040607642

This work is under a Creative Commons License: 
Attribution-NonCommercial-NoDerivatives 4.0 Internacional

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