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

A new finite element model has been developed to simulate two-dimensional free surface flow in rivers and estuaries. The variables of the model are the specific discharge and the water level. The algorithm takes into account the natural boundaries of the flow, defined 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. (C) 2000 Elsevier Science Ltd. All rights reserved.