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

Abstract

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.

HDGlab: An Open-Source Implementation of the Hybridisable Discontinuous Galerkin Method in MATLAB

“…An alternative to GMsHDG is the HHO framework for highly oscillatory elliptic problems introduced in [73]. Moreover, in the context of coupled problems involving porous media, HHO simulations of passive transport of a solute in a fractured medium are presented in [52], whereas nonlinear poroelastic phenomena in a saturated porous medium with a slightly compressible fluid are described in [33,35].…”

Comparison of the response to geometrical complexity of methods for unstationary simulations in discrete fracture networks with conforming, polygonal, and non-matching grids

“…This approach, named non-conforming mesh discretization, requires more advanced numerical schemes based on the mortar technique. In this case, we relax the actual generation of the fracture meshes which usually gives fewer discrete elements than the conforming mesh approach [6,22,23,[51][52][53]. This method may still suffer in the presence of severe geometries.…”

Numerical Study of the Fracture Diffusion-Dispersion Coefficient for Passive Transport in Fractured Porous Media

“…In this paper, we focus on the reduced model introduced in [1,3] describing the Passive Transport of a solute in a Fractured Porous Media, which will be now refered to as (PTFPM). By reduced model, we assume that the fracture is treated as a surface of codimension one.…”

“…Indeed, in (PTFPM) those coefficients are assumed to be independent from the surrounding unknowns: this is irrelevent since they play an important role in the description of (i) the exchanges between the porous media and the fracture, and (ii) the behavior of the solute at the neighborhood of the fracture. The aim of this paper is to propose a more physical definition of the fracture diffusion-dispersion coefficient, and to present some test cases based on the previous works [2,3]. The rest of this paper is organized as follows: in Section 2 we present the main equations and in Section 3 we perform numerical experiments.…”