A Hybrid High-Order method for passive transport in fractured porous media

Florent Chave (1, 2) , Daniele Di Pietro (1) , Luca Formaggia (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Dipartimento di Matematica "Francesco Brioschi" - Laboratorio di Modellistica e Calcolo Scientifico MOX

In this work, we propose a model for the passive transport of a solute in a fractured porous medium, for which we develop a Hybrid High-Order (HHO) space discretization. We consider, for the sake of simplicity, the case where the flow problem is fully decoupled from the transport problem. The novel transmission conditions in our model mimic at the discrete level the property that the advection terms do not contribute to the energy balance. This choice enables us to handle the case where the concentration of the solute jumps across the fracture. The HHO discretization hinges on a mixed formulation in the bulk region and on a primal formulation inside the fracture for the flow problem, and on a primal formulation both in the bulk region and inside the fracture for the transport problem. Relevant features of the method include the treatment of nonconforming discretizations of the fracture, as well as the support of arbitrary approximation orders on fairly general meshes.

Mots clés: Darcy flow; Fractured porous media; Hybrid High-Order methods; Finite element methods; Finite volume methods

Domaines: Analyse numérique [math.NA]; Mécanique des fluides [physics.class-ph]

Florent Chave, Daniele Di Pietro, Luca Formaggia. A Hybrid High-Order method for passive transport in fractured porous media. GEM - International Journal on Geomathematics, 2019, 10 (1), ⟨10.1007/s13137-019-0114-x⟩. ⟨hal-01784181v3⟩