Conforming Delaunay Triangulation of Stochastically Generated Three Dimensional Discrete Fracture Networks: A Feature Rejection Algorithm for Meshing Strategy

We introduce the feature rejection algorithm for meshing (FRAM) to generate a high quality conforming Delaunay triangulation of a three-dimensional discrete fracture network (DFN). The geometric features (fractures, fracture intersections, spaces between fracture intersections, etc.) that must be resolved in a stochastically generated DFN typically span a wide range of spatial scales and make the efficient automated generation of high-quality meshes a challenge. To deal with these challenges, many previous approaches often deformed the DFN to align its features with a mesh through various techniques including redefining lines of intersection as stair step functions and distorting the fracture edges. In contrast, FRAM generates networks on which high-quality meshes occur automatically by constraining the generation of the network. The cornerstone of FRAM is prescribing a minimum length scale and then restricting the generation of the network to only create features of that size and larger. The process is fully automated, meaning no adjustments of the mesh are performed, and the meshing of the individual fractures has been parallelized. Reported mesh statistics show that the computational meshes generated using FRAM are of high quality. Furthermore, the method does not require solving additional systems of linear equations which is needed if a nonconforming mesh is used. Details of the FRAM approach are provided, including its mathematical underpinnings and an algorithm for its implementation. We demonstrate the method's applicability by generating a DFN with similar statistics as the fractured granite at the Forsmark site in Sweden containing 6 700 fractures, and also solve the fully saturated Darcy flow equations to show the quality of the flow solutions which result from computation on the mesh.