A Three-Field based optimization formulation for flow simulations in networks of fractures on non conforming meshes

TL;DR

This paper introduces a novel three-field numerical scheme for simulating flow in complex fracture networks, capable of handling non conforming meshes and ensuring local mass conservation, with an iterative solver suitable for parallel computing.

Contribution

It presents a new three-field formulation and a coupling enforcement method for flow simulation in fracture networks on non conforming meshes, improving flexibility and accuracy.

Findings

Handles non conforming meshes independently built on each fracture.

Ensures local mass conservation at fracture intersections.

Compatible with parallel computing architectures.

Abstract

A new numerical scheme is proposed for flow computation in complex discrete fracture networks. The method is based on a three-field formulation of the Darcy law for the description of the hydraulic head on the fractures and uses a cost functional to enforce the required coupling condition at fracture intersections. The resulting method can handle non conforming meshes, independently built on each geometrical object of the computational domain, and ensures local mass conservation properties at fracture intersections. An iterative solver is devised for the method, ready for parallel implementation on parallel computing architectures.