A central scheme for shallow water flows along channels with irregular geometry
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 2, p. 333-351

We present a new semi-discrete central scheme for one-dimensional shallow water flows along channels with non-uniform rectangular cross sections and bottom topography. The scheme preserves the positivity of the water height, and it is preserves steady-states of rest (i.e., it is well-balanced). Along with a detailed description of the scheme, numerous numerical examples are presented for unsteady and steady flows. Comparison with exact solutions illustrate the accuracy and robustness of the numerical algorithm.

DOI : https://doi.org/10.1051/m2an:2008050
Classification:  65M99,  35L65
Keywords: hyperbolic systems of conservation and balance laws, semi-discrete schemes, Saint-Venant system of shallow water equations, non-oscillatory reconstructions, channels with irregular geometry
@article{M2AN_2009__43_2_333_0,
author = {Balb\'as, Jorge and Karni, Smadar},
title = {A central scheme for shallow water flows along channels with irregular geometry},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {43},
number = {2},
year = {2009},
pages = {333-351},
doi = {10.1051/m2an:2008050},
zbl = {1159.76026},
mrnumber = {2512499},
language = {en},
url = {http://www.numdam.org/item/M2AN_2009__43_2_333_0}
}

Balbás, Jorge; Karni, Smadar. A central scheme for shallow water flows along channels with irregular geometry. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 43 (2009) no. 2, pp. 333-351. doi : 10.1051/m2an:2008050. http://www.numdam.org/item/M2AN_2009__43_2_333_0/

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