A two-dimensional ®nite element drying-wetting shallow water model for rivers and estuaries

A new ®nite element model has been developed to simulate two-dimensional free surface ̄ow in rivers and estuaries. The variables of the model are the speci®c discharge and the water level. The algorithm takes into account the natural boundaries of the ̄ow, de®ned by the contour lines of zero depth, with a new approach that accepts positive and negative values for the water depth. In this way, we consider a wet or dry area when the water depth is positive or negative respectively. A 6-node triangular element and an implicit Euler scheme are respectively used for spatial and time discretization of the mathematical model. The solution procedure is based on the inexact Newton-GMRES type solver with incomplete factorization as preconditioning. The numerical results of the proposed approach are in good agreement with an analytic solution and also with the classical approach. Ó 2000 Elsevier Science Ltd. All rights reserved.