| Issue |
ESAIM: M2AN
Volume 43, Number 2, March-April 2009
|
|
|---|---|---|
| Page(s) | 333 - 351 | |
| DOI | https://doi.org/10.1051/m2an:2008050 | |
| Published online | 18 December 2008 | |
A central scheme for shallow water flows along channels with irregular geometry
1
Department of Mathematics, California State University, Northridge, CA 91330, USA. jorge.balbas@csun.edu
2
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA. karni@umich.edu
Received:
25
September
2007
Revised:
27
June
2008
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.
Mathematics Subject Classification: 65M99 / 35L65
Key words: Hyperbolic systems of conservation and balance laws / semi-discrete schemes / Saint-Venant system of shallow water equations / non-oscillatory reconstructions / channels with irregular geometry.
© EDP Sciences, SMAI, 2009
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