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A central scheme for shallow water flows along channels with irregular geometry

Published online by Cambridge University Press:  18 December 2008

Jorge Balbás and
Smadar Karni
Jorge Balbás
Affiliation:
Department of Mathematics, California State University, Northridge, CA 91330, USA. jorge.balbas@csun.edu
Smadar Karni
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA. karni@umich.edu
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Abstract

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.

Keywords

Hyperbolic systems of conservation and balance lawssemi-discrete schemesSaint-Venant system of shallow water equationsnon-oscillatory reconstructionschannels with irregular geometry.

Information

Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 43 , Issue 2 , March 2009, pp. 333 - 351
Copyright
© EDP Sciences, SMAI, 2009

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