A nonlinear domain decomposition method to couple compositional gas liquid Darcy and free gas flows

Nabil Birgle (1, 2) , Roland Masson (1, 2) , Laurent Trenty (3)

1 LJAD - Laboratoire Jean Alexandre Dieudonné
2 COFFEE - COmplex Flows For Energy and Environment
3 ANDRA - Agence Nationale pour la Gestion des Déchets Radioactifs

A domain decomposition algorithm is proposed to couple at the interface a gas liquid compositional Darcy flow and a compositional free gas flow. At each time step, our algorithm solves iteratively the nonlinear system coupling the compositional Darcy flow in the porous medium, the RANS gas flow in the free flow domain, and the convection diffusion of the species in the free flow domain. In order to speed up the convergence of the algorithm, the transmission conditions at the interface are replaced by Robin boundary conditions. Each Robin coefficient is obtained from a diagonal approximation of the Dirichlet to Neumann operator related to a scalar simplified model in the neighbouring subdomain. The efficiency of our domain decomposition algorithm is assessed in the case of the modelling of the mass exchanges at the interface between the geological formation and the ventilation galleries of geological radioactive waste disposal.

Mots clés: Drying model; Coupling algorithm; Nonlinear domain decomposition method; Compositional gas liquid darcy flow; Free gas flow

Domaines: Analyse numérique [math.NA]

Nabil Birgle, Roland Masson, Laurent Trenty. A nonlinear domain decomposition method to couple compositional gas liquid Darcy and free gas flows. FVCA: International Conference on Finite Volumes for Complex Applications VIII, Jun 2017, Lille, France. ⟨10.1007/978-3-319-57397-7⟩. ⟨hal-01541149⟩