Transport in Porous Media 44: 219–246, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands. 219 Coupled Groundwater Flow and Transport in Porous Media. A Conservative or Non-conservative Form? C. OLTEAN and M. A. BUÈS Laboratoire Environnement, Géomécanique et Ouvrages, École Nationale Supérieure de Géologie, Institut National Polytechnique de Lorraine, Rue du Doyen Marcel Roubault, BP 40, F, 54501 Vandœuvre-lès-Nancy, France (Received: 21 September 1999; in final form: 14 April 2000) Abstract. A new formulation for the modeling of density coupled flow and transport in porous media is presented. This formulation is based on the development of the mass balance equation by using the conservative form. The system of equations obtained by coupling the flow and transport equations using a state equation is solved by a combination of the mixed hybrid finite element method (MHFEM) and the discontinuous finite element method (DFEM). The former is applied in order to solve the flow equation and the dispersive part of the transport equation, whilst the latter is used to solve the advective part of the transport equation. Although the advantages of the MHFEM are known (efficiency calculation of velocity field and continuity of fluxes from one element to an adjacent one), its application in a classical development form (volumetric fluxes as unknowns) leads to the non- conservative version of the mass balance equation. The associated matrix of the system of equations obtained by hybridization is positive definite but non-symmetrical. By using a new approach (mass fluxes as unknowns) the conservative form of the continuity equation is preserved and the associated matrix of the system of equations obtained by hybridization becomes symmetrical. When applied to Elder’s problem involving a strong density contrast, this new approach, with a lower calculation cost, leads to similar or identical results to those found in the specialized literature. The comparison between the conservative and non-conservative formulations solved with the same MHFEM and DFEM combination emphasizes the rigor and the pertinence of this new approach. Furthermore, we show the existence of a limit refinement defining the stability of the numerical solution for Elder’s problem. Key words: flow and mass transport, conservative form, density driven flow, numerical simulation, Elder’s problem. 1. Introduction A wide variety of mathematical models have been developed for the simulation of contaminant transport in groundwater. When the pollutant can be considered as a ‘tracer’ and large dispersion values are used, most of these models simulate the transport accurately. Nevertheless, in many groundwater flow systems (e.g., saltwater intrusion, injection of liquid waste in deep saline aquifers or disposal of high level radioactive waste in salt formation) the liquid density and/or dynamic