A posteriori estimator and adaptive mesh refinement for finite volume finite element method for monophasic flow and solute transport in porous media

Document available in extended abstract form only. The disposal of high level, long lived waste in deep underground clay formations is investigated by several countries including France. In the safety assessment of such geological repositories, a thoughtful consideration must be given to the mechanisms and possible pathways of migration of radionuclides released from waste packages. However, when modelling the transfer of radionuclides throughout the disposal facilities and geological formations, the numerical simulations must take into consideration, in addition to long durations of concern, the variety in the properties as well as in geometrical scales of the different components of the overall disposal, including the host formation. This task presents significant computational challenges. Numerical methods used in the MELODIE software The MELODIE software is developed by IRSN, and constantly upgraded, with the aim to assess the long-term containment capabilities of underground and surface radioactive waste repositories. The MELODIE software models water flow and the phenomena involved in the transport of radionuclides in saturated and unsaturated porous media in 2 and 3 dimensions; chemical processes are represented by a retardation factor and a solubility limit, for sorption and solubility respectively, integrated in the computational equations. These equations are discretized using a so-called Finite Volume Finite Element method (FVFE), which is based on a Galerkin method to discretize time and variables, together with a Finite Volume method using the Godunov scheme for the convection term. The FVFE method is used to convert partial differential equations into a finite number of algebraic equations that match the number of nodes in the mesh used to model the considered domain. It is also used to stabilise the numerical scheme. In order to manage the variety in properties and geometrical scales of underground disposal components, an a posteriori error estimator using an adaptive mesh refinement strategy was introduced in MELODIE for the simulation of groundwater flow and solute transport in saturated porous media in 2 dimensions. The selected estimator, based on the explicit residual error, is expected to allow local refinements and thus minimization of the discretization error at an optimal computational cost. Test case: a realistic heterogeneous case with fracturing. In addition to theoretical test cases a more complex case was tested. The purpose of this test case was twofold: - to move from pure theoretical work to an illustrative case within a realistic generic context; however parameter values for hydrodynamic characteristics were chosen so as to highlight the investigated phenomena; - to account for large time and space scales, representative for those required for the simulation of radioactive waste repositories. The general shape of the geological media was designed to cover main features representative of sedimentary formations. Three distinct radionuclide source locations were chosen in order to obtain a set of flow and transport configurations. The entire layer sequence was structured into three hydrogeological units intersected by three sub-vertical faults. The vertical 2D cross-section dimensions are 5 km long by 500 m thick. Two source terms are located in a 100 m-thick layer in the right part of the domain and another one is located in a larger layer in the left part. These two 'host rock' layers consist of the same sedimentary unit with a low permeability, though an offset due to the middle fault. Faults are considered as conductive features. Radionuclides are assumed to be instantaneously released from the three source term locations at t = 0. The a posteriori error estimator and the adaptive mesh algorithm were applied to this heterogeneous problem. Preliminary calculations showed that the implemented a posteriori error estimator method is efficient to solve the equations of flow and advective-diffusive transport in this highly heterogeneous porous media. Indeed, as expected, the shapes of the contaminant plumes are very contrasted depending on the hydrogeological characteristics of the source term locations. The mesh was dynamic in time to match the investigated problem: it is refined in sensitive zones and unrefined in non-sensitive zones, thus leading to optimal CPU time compared to a very fine mesh built with static elements. Complementary results dealing with flow calculations and CPU time will be given in the final paper