Discontinuous Galerkin Method for the one dimensional simulation of shallow-water flows

TASSI PA; VIONNET CA

Bahia Blanca

Congreso; ENIEF 2003; 2003

AMCA - Asociación Argentina de Mecánica Computacional

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 techniques, 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 ability to capture discontinuities without producing spurious oscillations. In this paper, we consider some scalar conservation equations to illustrate 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.