November 17, 2016
Laboratoire de Mathématiques J.A. Dieudonné, Université de Nice Sophia Antipolis, France
||Seminarraum 2, Universität Stuttgart
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In France, high radioactive wastes are planned to be stored in deep geological repositories that will be operated and kept reversible for a period of 150 years. To guarantee the safety of workers during the repository exploitation phase, it is important to take into account the interactionsbetween the porous medium and the ventilated galleries of the repository.Many works have been performed to model and discretize the coupling of single phase Darcy and free flows, however there is very little work so far on the coupling of a two phase gas liquidcompositional Darcy flow with a single phase compositional gas free flow. Such a coupled model has been proposed in  using matching conditions at the interface between the porous medium and the free flow regions. In , the coupled system is solved fully implicitly. In this talk, we are interested by iterative or sequential approaches which decouple the computations of the porous medium andfree flow models in order to be able to use a different code in each domain.Usual approaches to solve iteratively the coupled model are based on Dirichlet Neumann algorithms. However these methods are not stable due to the strong coupling at the interface betweenthe vapor molar fraction in the gallery and the liquid flux in the porous medium induced by the liquidgas thermodynamical equilibrium.We propose a new iterative algorithm to solve the coupled system which is based on a non overlapping Robin Robin domain decomposition method. The computation of the Robin coefficientsis based on a simplified model coupling the Richards equation in the porous medium to the convection diffusion of vapor molar fraction in the gallery. Our algorithm is assessed in the caseof the modelling of the mass exchanges at the interface between the storage and the ventilated galleries in radioactive waste deposits.
 K. Mosthaf, K. Baber, B. Flemisch, R. Helmig, A. Leijnse, I. Rybak, and B. Wohlmuth. Acoupling concept for two-phase compositional porous-medium and single-phase compositionalfree flow. Water Resources Research, 2011.