Simulation of an oil slick movement using a shallow water model

The behaviour of an oil slick on the sea surface is studied using a shallow water model with free boundary. This model is solved by coupling the Arbitrary Lagrangian Eulerian method (ALE) with the characteristic method and by using a Galerkin spatial discretization. A special basis, which permits to obtain easily the solution by solving a scalar eigenvalue problem, is then proposed. Finally, a numerical experiment is presented in a realistic configuration.