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saint-venant system ofshallow water equations

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 45 / Issue 3 / May 2011

Published online by Cambridge University Press:

11 October 2010, pp. 423-446

Print publication:

May 2011
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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.