Comparison and application of non-conforming mesh models for flow in fractured porous media using dual Lagrange multipliers. (English) Zbl 07524771
Summary: Geological settings, such as reservoirs, include fractures with different material properties and geometric features. Hence, numerical simulations in applied geophysics demands for computational frameworks which efficiently allow us to integrate various fracture geometries in a porous medium matrix. This study focuses on a modeling approach for single-phase flow in fractured porous media and its application to different types of non-conforming mesh models. We propose a combination of the Lagrange multiplier method with variational transfer techniques for simulating flow through fractured porous media by employing complex non-conforming geometries as well as hybrid- and equi-dimensional models and discretizations. The variational transfer is based on the \(L^2\)-projection and enables an accurate and highly efficient parallel projection of fields between non-conforming meshes (e.g., between fracture and porous matrix domain).
We present the different techniques as a unified mathematical framework with a practical perspective. By means of numerical examples we discuss both, performance and applicability of the particular strategies. Comparisons of finite element simulation results to widely adopted 2D benchmark cases show good agreement and the dual Lagrange multiplier spaces show good performance. In an extension to 3D fracture network, we first provide complementary results to a recently developed benchmark case and afterwards we explore a complex scenario which leverages the different types of fracture meshes. Complex and highly conductive fracture networks are found more suitable in combination with embedded hybrid-dimensional fractures. However, thick and blocking fractures are better approximated by equi-dimensional embedded fractures and the equi-dimensional mortar method, respectively.
We present the different techniques as a unified mathematical framework with a practical perspective. By means of numerical examples we discuss both, performance and applicability of the particular strategies. Comparisons of finite element simulation results to widely adopted 2D benchmark cases show good agreement and the dual Lagrange multiplier spaces show good performance. In an extension to 3D fracture network, we first provide complementary results to a recently developed benchmark case and afterwards we explore a complex scenario which leverages the different types of fracture meshes. Complex and highly conductive fracture networks are found more suitable in combination with embedded hybrid-dimensional fractures. However, thick and blocking fractures are better approximated by equi-dimensional embedded fractures and the equi-dimensional mortar method, respectively.
MSC:
| 65Nxx | Numerical methods for partial differential equations, boundary value problems |
| 76Sxx | Flows in porous media; filtration; seepage |
| 76Mxx | Basic methods in fluid mechanics |
Keywords:
discrete fracture model; non-matching meshes; flow in fractured porous media; finite element method; non-conforming meshes; Lagrange multiplier methodReferences:
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