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An entropy-correction free solver for non-homogeneous shallow water equations

Published online by Cambridge University Press:  15 November 2003

Tomás Chacón Rebollo ,
Antonio Domínguez Delgado  and
Enrique D. Fernández Nieto
Tomás Chacón Rebollo
Affiliation:
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, C/ Tarfia, s/n, 41080 Sevilla, Spain. chacon@numer.us.es.
Antonio Domínguez Delgado
Affiliation:
Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura Avda, Reina Mercedes s/n, 41012 Sevilla, Spain. domdel@us.es.
Enrique D. Fernández Nieto
Affiliation:
Departamento de Matemática Aplicada I, Universidad de Sevilla, E.T.S. Arquitectura. Avda, Reina Mercedes, s/n, 41012 Sevilla, Spain. edofer@us.es.
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Abstract

In this work we introduce an accurate solver for the Shallow Water Equations with source terms. This scheme does not need any kind of entropy correction to avoid instabilities near critical points. The scheme also solves the non-homogeneous case, in such a way that all equilibria are computed at least with second order accuracy. We perform several tests for relevant flows showing the performance of our scheme.

Keywords

Finite Volume Methodupwindingshallow waterHarten Regularizationsource termsentropy-correction
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 5 , September 2003 , pp. 755 - 772
Copyright
© EDP Sciences, SMAI, 2003

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