Fitted Finite Volume Method for Unsaturated Flow Parabolic Problems with Space Degeneration

In the present work, we discuss a question of correct boundary conditions and adequate approximation of parabolic problems with space degeneration in porous media. To the Richards equation, as a typical problem, we apply a time discretization, linearize the obtained nonlinear problem and introduce correct boundary conditions. Then, we develop fitted finite volume method to get the space discretization of the model problem. A graded space mesh is also deduced. We illustrate experimentally that the proposed method is efficient in the case of degenerate permeability.