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.
Mots-clés : finite volume method, upwinding, shallow water, Harten regularization, source terms, entropy-correction
@article{M2AN_2003__37_5_755_0,
author = {Rebollo, Tom\'as Chac\'on and Delgado, Antonio Dom{\'\i}nguez and Fern\'andez Nieto, Enrique D.},
title = {An entropy-correction free solver for non-homogeneous shallow water equations},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {755--772},
publisher = {EDP-Sciences},
volume = {37},
number = {5},
year = {2003},
doi = {10.1051/m2an:2003043},
mrnumber = {2020863},
zbl = {1033.76032},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/m2an:2003043/}
}
TY - JOUR AU - Rebollo, Tomás Chacón AU - Delgado, Antonio Domínguez AU - Fernández Nieto, Enrique D. TI - An entropy-correction free solver for non-homogeneous shallow water equations JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2003 SP - 755 EP - 772 VL - 37 IS - 5 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/m2an:2003043/ DO - 10.1051/m2an:2003043 LA - en ID - M2AN_2003__37_5_755_0 ER -
%0 Journal Article %A Rebollo, Tomás Chacón %A Delgado, Antonio Domínguez %A Fernández Nieto, Enrique D. %T An entropy-correction free solver for non-homogeneous shallow water equations %J ESAIM: Modélisation mathématique et analyse numérique %D 2003 %P 755-772 %V 37 %N 5 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/m2an:2003043/ %R 10.1051/m2an:2003043 %G en %F M2AN_2003__37_5_755_0
Rebollo, Tomás Chacón; Delgado, Antonio Domínguez; Fernández Nieto, Enrique D. An entropy-correction free solver for non-homogeneous shallow water equations. ESAIM: Modélisation mathématique et analyse numérique, Tome 37 (2003) no. 5, pp. 755-772. doi : 10.1051/m2an:2003043. http://archive.numdam.org/articles/10.1051/m2an:2003043/
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