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{\bf Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular
Grids for the Saint-Venant System}

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Steve Bryson\\
 NASA Ames Research Center\\
 Moffett Field, CA 94035\\
Stephen.T.Bryson@nasa.gov\\

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Yekaterina Epshteyn\\
Department of Mathematical Sciences\\
Carnegie Mellon University\\
Pittsburgh, PA 15213\\
rina10@andrew.cmu.edu\\

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Alexander Kurganov\\
Mathematics Department\\
Tulane University\\
New Orleans, LA 70118\\
kurganov@math.tulane.edu

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Guergana Petrova\\
Department of Mathematics\\
Texas A\&M University\\
College Station, TX 77843\\
gpetrova@math.tamu.edu

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\noindent {\bf Abstract}:  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 stationary steady states (lake at rest) 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.

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