  Geological settings with reservoir characteristics include fractures with
different material and geometrical properties. Hence, numerical simulations in
applied geophysics demands for computational frameworks which efficiently allow
to integrate various fracture geometries in a porous medium matrix. This study
presents 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 to allow for complex non-conforming geometries as well as hybrid- and
equi-dimensional models and discretizations of flow through fractured porous
media. 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 networks, we first provide complementary results
to a recently developed benchmark case, before 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.

Computational Physics;Computational Engineering, Finance, and Science