Cell-vertex discretization of shallow water equations on mixed unstructured meshes

Cell-vertex discretization of shallow water equations on mixed unstructured meshes

Finite-volume discretizations can be formulated on unstructured meshes composed of different polygons. A staggered cell-vertex finite-volume discretization of shallow water equations is analyzed on mixed meshes composed of triangles and quads. Although triangular meshes are most flexible geometrically, quads are more efficient numerically and do not support spurious inertial modes of triangular...

Numerical discretizations for shallow water equations with source terms on unstructured meshes

In the following lines we introduce two frictional schemes for the discretization of the 2D Shallow Water system, on unstructured meshes. The starting point consists in writing both of them as convex combinations of 1D schemes. Then, we propose to include the resistance effects proceeding to a slight adaptation of the gathered convex components, using the frictional approach recently developed ...

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...

Upwind schemes for the two-dimensional shallow water equations with variable depth using unstructured meshes

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...

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