A FINITE-ELEMENT MODEL OF ESTUARIAN AND RIVER FLOWS WITH MOVING BOUNDARIES

We present a robust and reliable algorithm that takes into account the moving boundary process in free surface flows. The basic model is a classical 2-D finite element representation of shallow water equations. The algorithm defines three types of elements: dry, partly dry and wet. Once the state of an element is established along the transient non-linear resolution process, one applies the full form of the mathematical model (wet element) or a reduced one adapted to the specific case. The mesh configuration and the matrix topology remain fixed. The main principles used in defining the mathematical formulation close to the boundary are the conservation of mass and the continuity of flow field. An academic example and a real life application to a tidal flow in the Manicouagan estuary in Canada are presented.