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.

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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