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Comptes Rendus Mathématique
Volume 338, n° 1
pages 85-90 (janvier 2004)
Doi : 10.1016/j.crma.2003.11.008
Received : 30 June 2003 ;  accepted : 4 November 2003
Asymptotically balanced schemes for non-homogeneous hyperbolic systems - application to the Shallow Water equations

Tomás  Chacón Rebollo a ,  Antonio  Domínguez Delgado b ,  Enrique D.  Fernández Nieto b
aDpto Ecuaciones Diferenciales y Análisis Numérico, Universidad de Sevilla, c/Tarfia s/n, 41012 Sevilla, Spain 
bDpto Matemática Aplicada I, Universidad de Sevilla, Avda. Reina Mercedes N. 2, 41012 Sevilla, Spain 


In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).


Dans ce travail nous introduisons une classe de schémas numériques equilibrés au second ordre pour la solution de systèmes hyperboliques de lois de conservation. Nous donnons une technique générale pour construire ce type de schémas. Nous prouvons que ces schémas équilibrent au second ordre une grande classe de solutions stationaires, dans tout le domaine, excepté un sous-ensemble de mesure qui tend vers zéro lorsque la taille de la maille tend vers zéro. Nous présentons finalement une application aux équations de Saint-Venant qui montre les bonnes performances de quelques-uns des schémas présentés. Pour citer cet article : T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).

© 2003  Académie des sciences@@#104156@@

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