Conservative upwind difference schemes for the shallow water equations
نویسندگان
چکیده
منابع مشابه
Hydrostatic Upwind Schemes for Shallow–Water Equations
We consider the numerical approximation of the shallow–water equations with non–flat topography. We introduce a new topography discretization that makes all schemes to be well–balanced and robust. At the discrepancy with the well–known hydrostatic reconstruction, the proposed numerical procedure does not involve any cut–off. Moreover, the obtained scheme is able to deal with dry areas. Several ...
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The proposed work concerns the numerical approximations of the shallow-water equations with varying topography. The main objective is to introduce an easy and systematic technique to enforce the well-balance property and to make the scheme able to deal with dry areas. To access such an issue, the derived numerical method is obtained by involving the free surface instead of the water height and ...
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We derive a second-order semi-discrete central-upwind scheme for oneand two-dimensional systems of two-layer shallow water equations. We prove that the presented scheme is wellbalanced in the sense that stationary steady-state solutions are exactly preserved by the scheme, and positivity preserving, that is, the depth of each fluid layer is guaranteed to be nonnegative. We also propose a new te...
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In this paper, certain well-known upwind schemes for hyperbolic equations are extended to solve the two-dimensional Saint-Venant (or shallow water) equations. We consider unstructured meshes and a new type of nite volume to obtain a suitable treatment of the boundary conditions. The source term involving the gradient of the depth is upwinded in a similar way as the ux terms. The resulting schem...
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We introduce a central-upwind scheme for oneand two-dimensional systems of shallow-water equations with horizontal temperature gradients (the Ripa system). The scheme iswell-balanced, positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps, that is, near the contact waves. Such oscillations would typically appear when a conventional God...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2000
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(00)00053-5