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In this paper we present a new approach to describe the behaviour of a pollutant slick at the sea surface. To this end, we consider that the pollutant and the water are immiscible and we propose a two-layer model where the lower layer corresponds to the water and the upper layer represents the pollutant. Since the dimension of the pollutant slick is generally much smaller than the domain occupied by the sea, we propose to compute the motion of the pollutant with a shallow water model with free boundary only in the domain occupied by the pollutant. To discretize in time the problem with free boundary, we use an ALE formulation coupled with the characteristic method. Then, to solve the space discretized problem, we approximate the pollutant velocity by using a Galerkin method with a special basis which verifies the boundary conditions and simplifies significantly the resolution. Finally we test this work in a real situation: the dam of Calacuccia (Corsica). [ABSTRACT FROM AUTHOR]