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channels with irregular geometry.

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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A central scheme for shallow water flows along channels with irregular geometry
Jorge Balbás, Smadar Karni
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 43 / Issue 2 / March 2009

Published online by Cambridge University Press:

18 December 2008, pp. 333-351

Print publication:

March 2009
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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.