Dual virtual element method for discrete fractures networks

TL;DR

This paper introduces a dual virtual element method for simulating fluid flow in discrete fracture networks, allowing flexible grid construction and improved computational efficiency.

Contribution

It presents two models for pressure and velocity computation in fracture networks using virtual element discretization, simplifying grid requirements and incorporating a coarsening algorithm.

Findings

Method effectively handles arbitrary grid shapes.

Simplifies fracture network flow discretization.

Achieves faster computation with coarsening algorithm.

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.