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

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.

References in corpus (5)

• Benchmarks for single-phase flow in fractured porous media
• Conforming, non-conforming and non-matching discretization couplings in discrete fracture network simulations
• Estimating Flow Rates through Fracture Networks using Combinatorial Optimization
• Call for participation: Verification benchmarks for single-phase flow in three-dimensional fractured porous media
• A hierarchy of models for simulating experimental results from a 3D heterogeneous porous medium

Cited by in corpus (7)

• MOOSE: Enabling Massively Parallel Multiphysics Simulation
• Verification benchmarks for single-phase flow in three-dimensional fractured porous media
• A hybrid-mixed finite element method for single-phase Darcy flow in fractured porous media
• A hybridizable discontinuous Galerkin method on unfitted meshes for single-phase Darcy flow in fractured porous media
• Modelling of hydro-mechanical processes in heterogeneous fracture intersections using a fictitious domain method with variational transfer operators
• The hybrid dimensional representation of permeability tensor: a reinterpretation of the discrete fracture model and its extension on nonconforming meshes
• A novel equi-dimensional finite element method for flow and transport in fractured porous media satisfying discrete maximum principle and conservation properties