A finite volume approach with local adaptation scheme for the simulation of free surface flow in porous media E. Bresciani* ,† , P. Davy and J. R. de Dreuzy UMR CNRS 6118, Geosciences Rennes, Université de Rennes 1, 35042 Rennes Cedex, France SUMMARY 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. Copyright © 2011 John Wiley & Sons, Ltd. Received 9 June 2010; Revised 9 May 2011; Accepted 10 May 2011 KEY WORDS: free surface; porous flow; finite volume; numerical simulation 1. INTRODUCTION Free surface flow in porous media is of great importance for many applications. This problem can be considered by formulating the flow equations either in both saturated and unsaturated zones (variably saturated approach) or only in the saturated zone (free boundary approach). The variably saturated approach has been developed and followed by numerous authors [1–5]. It presents different characteristics from the free boundary approach and can give different results under certain conditions [6]. In this study, we present a new free boundary approach. Classically, numerical methods used to solve free boundary problems in porous media are classified into two broad categories: adaptive mesh methods in which only the part below the free surface is meshed [7–12], and fixed mesh methods in which the whole domain considered is meshed [13–16]. The former are generally regarded as more intuitive and accurate than the latter [9], because the mesh matches the free surface position during the whole solution process. They have, however, several drawbacks. First, continuously adapting the whole mesh as the free surface moves is computationally more intensive, owing to the fact that the whole linear system has to be reconstructed in every iteration, in addition to the mesh generation itself [9, 17]. Second, when dealing with heterogeneous media, this requires to continuously reinterpolating the hydraulic conductivity field at the computational nodes. Third, when a stress analysis has to be performed in addition to the seepage analysis, it is convenient to use the same mesh, which is not possible if the mesh evolves [17]. Finally, stability issues have been *Correspondence to: E. Bresciani, UMR CNRS 6118, Geosciences Rennes, Université de Rennes 1, 35042 Rennes Cedex, France. † E‐mail: etienne.bresciani@univ‐rennes1.fr Copyright © 2011 John Wiley & Sons, Ltd. INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/nag.1065