A finite volume approach with local adaptation scheme for the simulation of free surface flow in porous media

We present a method for solving steady-state flow with a free surface in porous media. This method is based on a finite volume approach and is halfway between a fixed and an adaptive mesh method, taking advantage of both approaches: computational efficiency and localization accuracy. Most of the mesh remains fixed during the iterative process, while the cells in contact with the free surface (free surface cells) are being reshaped. Based on this idea, we developed two methods. In the first one, only the volumes of the free surface cells are adapted. In the second one, the computational nodes of the free surface cells are relocated exactly at the free surface. Both adaptations are designed for a better application of the free surface boundary conditions. Implementation details are given on a regular finite volume mesh for the case of homogeneous and heterogeneous rectangular dams in 2D and 3D. Accuracy and convergence properties of the proposed approach are demonstrated by comparison with an analytical solution and with existing references.