| Issue |
ESAIM: M2AN
Volume 45, Number 3, May-June 2011
|
|
|---|---|---|
| Page(s) | 423 - 446 | |
| DOI | https://doi.org/10.1051/m2an/2010060 | |
| Published online | 11 October 2010 | |
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
1
NASA Ames Research Center, Moffett Field, CA 94035, USA. Stephen.T.Bryson@nasa.gov
2
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. rina10@andrew.cmu.edu
3
Mathematics Department, Tulane University, New Orleans, LA 70118, USA. kurganov@math.tulane.edu
4
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. gpetrova@math.tamu.edu
Received:
20
November
2008
Revised:
3
May
2010
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Mathematics Subject Classification: 76M12 / 35L65
Key words: Hyperbolic systems of conservation and balance laws / semi-discrete central-upwind schemes / Saint-Venant system of shallow water equations
© EDP Sciences, SMAI, 2010
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