Finite Element Solution of Saint-Venant Equations

A finite element solution based on the Galerkin method was developed for the Saint-Venant equations that approximately govern unsteady flow in rigid open channels. A predictor-corrector solution scheme produced theoretically stable and convergent results, and applications to test problems confirmed stability provided that time steps were not so large as to render invalid the Newton linearization scheme used for the friction factor. Linear elements were adequate for all problems solved. Time step limitations to produce accurate results were closely related to: (1) The degree to which piecewise linear functions describing the variation of depth and discharge in time could be fit to the actual curvilinear functions; and (2) the value given to the time step weighting factor. Values of this factor near 0.5 gave the best results.