An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems

TL;DR

This paper introduces an arbitrary order mixed Virtual Element method for simulating flow in complex fractured porous media, effectively handling multi-dimensional domains and interfaces.

Contribution

It presents a novel arbitrary order Virtual Element formulation for coupled multi-dimensional flow problems in fractured media, with detailed implementation and meshing strategies.

Findings

Method successfully simulates flow in complex fractured domains.

Effective mesh generation strategies are discussed.

Numerical results demonstrate applicability to real-world problems.

Abstract

Discrete Fracture and Matrix (DFM) models describe fractured porous media as complex sets of 2D planar polygons embedded in a 3D matrix representing the surrounding porous medium. The numerical simulation of the flow in a DFM requires the discretization of partial differential equations on the three dimensional matrix, the planar fractures and the one dimensional fracture intersections, and suitable coupling conditions between entities of different dimensionality need to be added at the various interfaces to close the problem. The present work proposes an arbitrary order implementation of the Virtual Element method in mixed formulation for such multidimensional problems. Details on effective strategies for mesh generation are discussed and implementation aspects are addressed. Several numerical results in various contexts are provided, which showcase the applicability of the method to flow simulations in complex multidimensional domains.