Revisiting the open boundary problem in computational fluid dynamics

International audienceThe overall context of this work is the design of e cient open boundary conditions (OBCs) for limited area models of the ocean circulation. In these limited areas, complex systems of equations are solved using a high resolution grid. On the arti cial boundaries, boundary conditions with some available external information, must be prescribed. Such external information is generally available from previous simulations of large scale low resolution models. Ideally, the OBC must evacuate the outgoing information reaching the boundary, and must take into account the incoming part of the external information. In this talk, we propose a reformulation of this problem in which the link with absorbing boundary conditions is highlighted. This formulation allows a complete treatment of the problem in simple cases like the 1D Laplace equation, which illustrates in particular the context in which absorbing conditions may be or not e cient OBCs. Moreover some numerical applications for shallow water systems will be give