A Well-Balanced FVC Scheme for 2D Shallow Water Flows on Unstructured Triangular Meshes

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

Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on Unstructured Triangular Meshes

The shallow water equations model flows in rivers and coastal areas and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. In [36], the authors constructed high order discontinuous Galerkin methods for the shallow water equations which can maintain the still water steady state exactly, and at the same time can preserve the nonnegativity of the water height without...

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 Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows

We consider the Saint-Venant system for shallow water flows, with nonflat bottom. It is a hyperbolic system of conservation laws that approximately describes various geophysical flows, such as rivers, coastal areas, and oceans when completed with a Coriolis term, or granular flows when completed with friction. Numerical approximate solutions to this system may be generated using conservative fi...

A robust and well-balanced scheme for the 2D Saint-Venant system on unstructured meshes with friction source term

In the following lines we propose a numerical scheme for the shallow water system supplemented by topography and friction source terms, in a 2d unstructured context. This work proposes an improved version of the well-balanced and robust numerical model recently introduced in [J. Comp. Phys., 235, 565–586, 2013] for the pre-balanced Shallow Water Equations, accounting for varying topography. The...