Flood routing using finite differences and the fourth order Runge-Kutta method

The Saint-Venant continuity and momentum equations are solved numerically by discretising the time variable using finite differences and then the Runge-Kutta method is employed to solve the resulting ODE. A model of the Rufiji river downstream on the proposed Stiegler Gourge Dam is used to provide numerical results for comparison. The present approach is found to be superior to an earlier analysis using finite differences in both space and time. Moreover, the steady and unsteady flow analyses give almost identical predictions for the stage downstream provided that the variations of the discharge and stage upstream are small. (author)