Ecoulement bidimensionnel a surface libre, Approche h-s : Partie I - Mefta, Khouane; Dhatt, Gouri; Tanguy, Jean-Michel (European Journal of Computational Mechanics, 1999)
The works that are the object of the present paper consist of developing a model to simulate free surface flows applicable at sea, river, and lake, under loads as various as floods, density gradient between salt water -fresh water, marine coast or gales. This model based upon finite element method, implies an approach that we called h-s. This latter privileges, as it occurs in nature for the problems that we wish to study, the horizontal dimension to vertical dimension, which under goes a special treatment. We note that the pressure can be hydrostatic or not. This method is based upon a finite element approximation along with x and upon analytical one along with z. The choice of the series and the number of its terms depend on the physics of the problem and the required accuracy. We have used a hybrid element L3L for the spatial discretization. For the time discretization, we have used two schemes. The first one is that of backward Euler, and the second is explicit of LaxWendrofftype which can better fit the non stationary problems.