M. Amara, F. El Dabaghi, and C. Kada Kloucha (France)
Navier-Stokes, free surface, characteristics method, finiteelement, dry and wet element.
In this work, we analyse a numerical model of a free sur face water flow in a lake. The main difficulty resides in set ting a numerical scheme sufficiently stable, for describing the evolution of the free surface and consequently to find the water elevation at each moment. The water phase sim ulator is based on a velocity-pressure Ե variational for mulation of incompressible Navier-Stokes equations; the approximation is achieved by the characteristics method for the time discretization, combined to a mixed finite el ement ȽBubble-Ƚ in space. After a synthetic review of several methods used in this framework, we present our approach based on a wetting-drying algorithm on a fixed grid of the whole Air-Water domain. We present some nu merical results, validating our approach on a bidimensional case.
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