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Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system

Published online by Cambridge University Press:  11 October 2010

Steve Bryson ,
Yekaterina Epshteyn ,
Alexander Kurganov  and
Guergana Petrova
Steve Bryson
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA. Stephen.T.Bryson@nasa.gov
Yekaterina Epshteyn
Affiliation:
Department of Mathematical Sciences, Carnegie Mellon University, Pittsburgh, PA 15213, USA. rina10@andrew.cmu.edu
Alexander Kurganov
Affiliation:
Mathematics Department, Tulane University, New Orleans, LA 70118, USA. kurganov@math.tulane.edu
Guergana Petrova
Affiliation:
Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. gpetrova@math.tamu.edu
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Abstract

We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove thatthe scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be appliedto models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as itshigh resolution and robustness in a number of numerical examples.

Keywords

Hyperbolic systems of conservation and balance lawssemi-discrete central-upwind schemesSaint-Venant system ofshallow water equations
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 3 , May 2011 , pp. 423 - 446
Copyright
© EDP Sciences, SMAI, 2010

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