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Weak entropic solution to a scalar hyperbolic-parabolic law.

Guy Vallet (2003)

RACSAM

In this paper we are interested in the Dirichlet problem of a hyperbolic-parabolic degenerate equation. Thanks to a global entropic formulation in the sense of F. Otto, we propose a result of existence and uniqueness of the entropic measure valued solution and of the entropic weak solution in the space DM2.

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

Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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.

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

Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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.

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