Positivity-Preserving Well-Balanced Discontinuous Galerkin Methods for the Shallow Water Equations on 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...

Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations

Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas, as standard numerical methods may fail in the presence of these areas. These equations also have steady state solutions in which the flux gradients are nonzero but exactly balanced by the ...

A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations

In this paper, we consider the development of central discontinuous Galerkin methods for solving the nonlinear shallow water equations over variable bottom topography in one and two dimensions. A reliable numerical scheme for these equations should preserve still-water stationary solutions and maintain the non-negativity of the water depth. We propose a high-order technique which exactly balanc...

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

Well-balanced Finite Volume Evolution Galerkin Methods for the 2d Shallow Water Equations on Adaptive Grids

Abstract. We extend a well-balanced finite volume evolution Galerkin (FVEG) method to nonuniform grids. As a model problem, we consider the two-dimensional shallow water equations with a source term modelling the bottom topography. Our work is based on the well-balanced scheme proposed in (Lukáčová, Noelle, Kraft, J.Comp.Physics, 221, 2007). We present selected test cases to demonstrate the cap...