A large time-step and well-balanced Lagrange-projection type scheme for the shallow water equations

A Subsonic-Well-Balanced Reconstruction Scheme for Shallow Water Flows

We consider the Saint-Venant system for shallow water flows with non-flat bottom. In the past years, efficient well-balanced methods have been proposed in order to well resolve solutions close to steady states at rest. Here we describe a strategy based on a local subsonic steady-state reconstruction that allows to derive a subsonic-well-balanced scheme, preserving exactly all the subsonic stead...

A well-balanced scheme for the shallow-water equations with topography

A non-negativity preserving and well-balanced scheme that exactly preserves all the smooth steady states of the shallow water system, including the moving ones, is proposed. In addition, the scheme must deal with vanishing water heights and transitions between wet and dry areas. A Godunov-type method is derived by using a relevant average of the source terms within the scheme, in order to enfor...

A Well–Balanced Stable GRP Scheme for Shallow Water Equations for Adaptive Unstructured Triangular Meshes

A fully well-balanced, positive and entropy-satisfying Godunov-type method for the shallow-water equations

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A robust well-balanced scheme for multi-layer shallow water equations

The numerical resolution of the multi-layer shallow water system encounters two additional difficulties with respect to the one-layer system. The first is that the system involves nonconservative terms, and the second is that it is not always hyperbolic. A splitting scheme has been proposed by Bouchut and Morales, that enables to ensure a discrete entropy inequality and the wellbalanced propert...