# 3D non-conforming mesh model for flow in fractured porous media using Lagrange multipliers

## TL;DR

This paper introduces a novel 3D modeling approach for simulating flow in fractured porous media using non-conforming meshes, combining Lagrange multipliers with an $L^2$-projection transfer for accurate, parallel variable coupling.

## Contribution

It presents a new method integrating Lagrange multipliers and $L^2$-projection for efficient, accurate simulation of flow in complex 3D fracture networks with non-conforming meshes.

## Key findings

- Good agreement with 2D benchmarks
- Validated on 3D fracture networks against conforming mesh results
- Capable of modeling realistic 3D fracture networks

## Abstract

This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel $L^2$-projection variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The $L^2$-projection variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the method is further validated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the $L^2$-projection method, is capable of modeling single-phase flow through realistic 3D fracture networks.