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.
@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},
volume = {43},
year = {2009},
pages = {333-351},
doi = {10.1051/m2an:2008050},
mrnumber = {2512499},
zbl = {1159.76026},
language = {en},
url = {http://dml.mathdoc.fr/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, Tome 43 (2009) pp. 333-351. doi : 10.1051/m2an:2008050. http://gdmltest.u-ga.fr/item/M2AN_2009__43_2_333_0/
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