ABSTRACT
ABSTRACT: Runge-Kutta discontinous Galerkin (RKDG) schemes are finite element methods using also finite volume (FV) techniques such as: Riemann solver, slope limiter andTotal-VariationDiminishing (TVD) Runge-Kutta time discretization. The intension of this survey is to establish a one-dimensional numerical computation of the shallow water equations (SWE) by means of a second order Runge-Kutta discontinuous Galerkin (RKDG2) scheme. Hence, this method is briefly described and incorporated with a robust handling of the boundary conditions (BC) which was performed by the use of the characteristics theory. By the support of: (a) results reported in the literature; (b) applications to the SWE, we illustrate the effectiveness of the proposed numerical scheme near the results of recent and traditional FV methods.
