Moving-water equilibria preserving central-upwind 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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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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This note aims at demonstrating the advantage of moving-water well-balanced schemes over still-water well-balanced schemes for the shallow water equations. We concentrate on numerical examples with solutions near a moving-water equilibrium. For such examples, still-water well-balanced methods are not capable of capturing the small perturbations of the moving-water equilibrium and may generate s...
متن کاملEfficient well-balanced hydrostatic upwind schemes for shallow-water equations
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 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: Communications in Mathematical Sciences
سال: 2016
ISSN: 1539-6746,1945-0796
DOI: 10.4310/cms.2016.v14.n6.a9