[Une limitation de la reconstruction hydrostatique pour la résolution du système de Saint-Venant]
De par leur capacité à préserver les états dʼéquilibre, les schémas équilibres connaissent actuellement un fort développement dans la résolution des équations de Saint-Venant. En particulier, la reconstruction hydrostatique proposée dans Audusse et al. (2004) [1], couplée à un flux numérique positif, permet de garantir certaines propriétés comme la positivité de la hauteur dʼeau et, donc, dʼéviter certaines instabilités pour traiter les zones sèches. Dans cette note, nous montrons que cette méthode présente un défaut pour certaines combinaisons de pente, taille de maillage et hauteur dʼeau.
Because of their capability to preserve steady states, well-balanced schemes for Shallow Water equations are becoming popular. Among them, the hydrostatic reconstruction proposed in Audusse et al. (2004) [1], coupled with a positive numerical flux, allows to verify important mathematical and physical properties like the positivity of the water height and, thus, to avoid instabilities when dealing with dry zones. In this note, we prove that this method exhibits an abnormal behavior for some combinations of slope, mesh size and water height.
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@article{CRMATH_2012__350_13-14_677_0,
author = {Delestre, Olivier and Cordier, St\'ephane and Darboux, Fr\'ed\'eric and James, Fran\c{c}ois},
title = {A limitation of the hydrostatic reconstruction technique for {Shallow} {Water} equations},
journal = {Comptes Rendus. Math\'ematique},
pages = {677--681},
publisher = {Elsevier},
volume = {350},
number = {13-14},
year = {2012},
doi = {10.1016/j.crma.2012.08.004},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2012.08.004/}
}
TY - JOUR AU - Delestre, Olivier AU - Cordier, Stéphane AU - Darboux, Frédéric AU - James, François TI - A limitation of the hydrostatic reconstruction technique for Shallow Water equations JO - Comptes Rendus. Mathématique PY - 2012 SP - 677 EP - 681 VL - 350 IS - 13-14 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2012.08.004/ DO - 10.1016/j.crma.2012.08.004 LA - en ID - CRMATH_2012__350_13-14_677_0 ER -
%0 Journal Article %A Delestre, Olivier %A Cordier, Stéphane %A Darboux, Frédéric %A James, François %T A limitation of the hydrostatic reconstruction technique for Shallow Water equations %J Comptes Rendus. Mathématique %D 2012 %P 677-681 %V 350 %N 13-14 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2012.08.004/ %R 10.1016/j.crma.2012.08.004 %G en %F CRMATH_2012__350_13-14_677_0
Delestre, Olivier; Cordier, Stéphane; Darboux, Frédéric; James, François. A limitation of the hydrostatic reconstruction technique for Shallow Water equations. Comptes Rendus. Mathématique, Tome 350 (2012) no. 13-14, pp. 677-681. doi : 10.1016/j.crma.2012.08.004. http://www.numdam.org/articles/10.1016/j.crma.2012.08.004/
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