Dual virtual element method for discrete fractures networks

Abstract

Discrete fracture networks is a key ingredient in the simulation of physical processes which involve fluid flow in the underground, when the surrounding rock matrix is considered impervious. In this paper we present two different models to compute the pressure field and Darcy velocity in the system. The first allows a normal flow out of a fracture at the intersections, while the second grants also a tangential flow along the intersections. For the numerical discretization, we use the mixed virtual finite element method as it is known to handle grid elements of, almost, any arbitrary shape. The flexibility of the discretization allows us to loosen the requirements on grid construction, and thus significantly simplify the flow discretization compared to traditional discrete fracture network models. A coarsening algorithm, from the algebraic multigrid literature, is also considered to further speed up the computation. The performance of the method is validated by numerical experiments.

References in corpus (1)

• Mathematical analysis of a discrete fracture model coupling Darcy flow in the matrix with Darcy-Forchheimer flow in the fracture

Cited by in corpus (7)

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• The Mixed Virtual Element Method on curved edges in two dimensions
• A mathematical model for thermal single-phase flow and reactive transport in fractured porous media
• Cut Finite Elements for Convection in Fractured Domains
• A multiscale flux basis for mortar mixed discretizations of reduced Darcy-Forchheimer fracture models
• Dual virtual element method in presence of an inclusion