Efficient geometric reconstruction of complex geological structures

CutFEM: Discretizing geometry and partial differential equations

“…Similar challenging and computationally costly preprocessing steps are required to transform geological image data into conforming domain discretizations, which respect complex structures such as faults and large scale networks of fractures; see, for instance, [2].…”

“…For instance, the simulation of blood flow dynamics in vessel geometries requires a series of highly non-trivial steps to generate a high quality, full 3D finite element mesh from biomedical image data [1]. Similar challenging and computationally costly preprocessing steps are required to transform geological image data into conforming domain discretizations, which respect complex structures such as faults and large scale networks of fractures; see, for instance, [2].…”

Analysis of a mimetic finite difference approximation of flows in fractured porous media

“…We give a wellposedness result that does not rely on the imposition of pressure in part of the boundary of the fracture network, thus including a fully immersed fracture network. We present and analyze a mimetic finite difference formulation for the problem, providing convergence results and numerical tests.Article published by EDP Sciences c EDP Sciences, SMAI 2018Even if the use of a geometrically reduced model avoids the need for extremely refined or anisotropic grids inside the fractures, the construction of a computational grid for realistic cases is a challenging task (see, for instance, [22]): a fractured oil reservoir can be cut by several thousands of fractures, often intersecting or very close together. A computational grid conforming to the fractures can thus be characterized by very small elements and low quality, due to high aspect ratios and small angles.…”

“…Even if the use of a geometrically reduced model avoids the need for extremely refined or anisotropic grids inside the fractures, the construction of a computational grid for realistic cases is a challenging task (see, for instance, [22]): a fractured oil reservoir can be cut by several thousands of fractures, often intersecting or very close together. A computational grid conforming to the fractures can thus be characterized by very small elements and low quality, due to high aspect ratios and small angles.…”

A hybrid finite volume – finite element method for bulk–surface coupled problems

“…However, a straightforward application of this technique to model transport and diffusion along a fracture would require fitting the mesh or triangulating the surface. For a large and complex net of fractures cutting through the porous matrix this is a difficult task [14], and an efficient method avoids mesh fitting and surface triangulations. Recently, extended finite element method approximations have been extensively studied in transport and flow problems in fractured porous media, see the review [19] and references therein.…”