Dynamic p-adaptive Runge–Kutta discontinuous Galerkin methods for the shallow water equations

A well-balanced Runge–Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying

Discontinuous Galerkin Method for 1D Shallow Water Flow with Water Surface Slope Limiter

A water surface slope limiting scheme is tested and compared with the water depth slope limiter for the solution of one dimensional shallow water equations with bottom slope source term. Numerical schemes based on the total variation diminishing RungeKutta discontinuous Galerkin finite element method with slope limiter schemes based on water surface slope and water depth are used to solve one-d...

A wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations

This paper proposes a wetting and drying treatment for the piecewise linear Runge–Kutta discontinuous Galerkin approximation to the shallow water equations. The method takes a fixed mesh approach as opposed to mesh adaptation techniques and applies a post-processing operator to ensure the positivity of the mean water depth within each finite element. In addition, special treatments are applied ...

Space-time discontinuous Galerkin discretization of rotating shallow water equations

A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the finite element boundaries. When discontinuities are present, we locally apply dissipation around t...

Notes on RKDG Methods for Shallow-Water Equations in Canal Networks

PDE models for network flows are used in a number of different applications, including modeling of water channel networks. While the theory and first-order numerics are well developed, high-order schemes are not well developed. We propose a Runge-Kutta discontinuous Galerkin method as an efficient, effective and compact numerical approach for numerical simulations of 1-D models for water flow i...