Discontinuous Galerkin Method For The One Dimensional Simulation Of Shallow Water Flows.

Abstract

A numerical solution for the one-dimensional (1D) hyperbolic conservation
law is presented, based on the Runge Kutta Discontinuous Galerkin Method (RKDG).
The RKDG scheme combines some properties of the finite element and finite-volume tech-
niques, resulting on a very attractive method because of its formal high-order accuracy, its
ability to handle complicated geometries, its adaptability to parallelization, and its abil-
ity to capture discontinuities without producing spurious oscillations. In this paper, we
consider some scalar conservation equations to ilustrate the method's properties in one
spatial dimension (1-D). Finally, the 1-D shallow water equations are discretized with the
RKDG. A comparison with an exact solution is made to illustrate the capability of the
method to handle strong discontinuities with relative small number of elements.