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

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...

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Detalles Bibliográficos
Autores: Chacón Rebollo, Tomás, Fernández Nieto, Enrique Domingo, Parés Madroñal, Carlos
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2007
País:España
Institución:Universidad de Sevilla (US)
Repositorio:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/32920
Acceso en línea:http://hdl.handle.net/11441/32920
https://doi.org/10.1137/040607642
Access Level:acceso abierto
Palabra clave:Well-balanced
Finite Volume Method
upwinding
shallow water
source terms
two-layer flows
Descripción
Sumario: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.