Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, p. 423-446

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.

DOI : https://doi.org/10.1051/m2an/2010060
Classification:  76M12,  35L65
Keywords: hyperbolic systems of conservation and balance laws, semi-discrete central-upwind schemes, Saint-Venant system of shallow water equations
@article{M2AN_2011__45_3_423_0,
author = {Bryson, Steve and Epshteyn, Yekaterina and Kurganov, Alexander and Petrova, Guergana},
title = {Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {45},
number = {3},
year = {2011},
pages = {423-446},
doi = {10.1051/m2an/2010060},
zbl = {1267.76068},
mrnumber = {2804645},
language = {en},
url = {http://www.numdam.org/item/M2AN_2011__45_3_423_0}
}

Bryson, Steve; Epshteyn, Yekaterina; Kurganov, Alexander; Petrova, Guergana. Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 45 (2011) no. 3, pp. 423-446. doi : 10.1051/m2an/2010060. http://www.numdam.org/item/M2AN_2011__45_3_423_0/

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