Geodesic
A central scheme for shallow water flows along channels with irregular geometry
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 2, pp. 333-351

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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 : 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 
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     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 },
     pages = {333--351},
     publisher = {EDP-Sciences},
     volume = {43},
     number = {2},
     year = {2009},
     doi = {10.1051/m2an:2008050},
     mrnumber = {2512499},
     zbl = {1159.76026},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/m2an:2008050/}
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Balbás, Jorge; Karni, Smadar. A central scheme for shallow water flows along channels with irregular geometry. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 43 (2009) no. 2, pp. 333-351. doi: 10.1051/m2an:2008050

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