An entropy-correction free solver for non-homogeneous shallow water equations
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 5, p. 755-772

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.

DOI : https://doi.org/10.1051/m2an:2003043
Classification:  65N06,  76B15,  76M20,  76N99
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {37},
number = {5},
year = {2003},
pages = {755-772},
doi = {10.1051/m2an:2003043},
zbl = {1033.76032},
mrnumber = {2020863},
language = {en},
url = {http://www.numdam.org/item/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: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 37 (2003) no. 5, pp. 755-772. doi : 10.1051/m2an:2003043. http://www.numdam.org/item/M2AN_2003__37_5_755_0/

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