Multi-scale meshing for 3D discrete fracture networks

by Pedro Lima, Phillippe R. B. Devloo, José Villegas, presented at XLI Ibero-Latin American Congress Computational Methods in Engineering, November 2020


The geometric description of a Discrete Fracture Network (DFN) in the context of multi-scale methods, involves the ability of inserting multiple fractures in a predefined coarse mesh, while building volumetrical elements of smaller scale around the surface of these fractures in order to create sub-meshes inside the coarse elements. This paper presents an approach for automatic finite element meshing of fractured reservoirs suited to Multi-scale Hybrid-Mixed methods (MHM). The code is written in C++ and largely relies on two open source finite element libraries: NeoPZ and Gmsh. The main steps to the method involve: locating intersections and re-fining elements at those points, building a data structure that associates each element of a fracture surface to the coarse volume that encloses it, and then generate a sub-mesh of fine elements around the fractures to fill these coarse elements, without altering originally defined nodes in the coarse mesh. In order to improve the quality of geometrical elements to be generated, strategies of moving intersection points and features simplifications are also presented. Results show that the proposed technique can efficiently construct adequate 3D meshes. While relying on neighbourhood information and consistent element topologies available from NeoPZ’s geometric meshes, enables optimization of multiple algorithms of geometric search that would, otherwise, require a considerable amount of floating-point operations.

Error estimations for multiscale hybrid-mixed finite element methods for Darcy’s problems on polyhedral meshes

by Denise de Siqueira, Gustavo A. Batistela, Paulo R. Bösing, Phillippe R. B. Devloo, Sônia M. Gomes, presented at XLI Ibero-Latin American Congress on Computational Methods in Engineering, November 2020


A posteriori error estimation for multiscale hybrid-mixed formulations for Darcy’s problems is discussed. The method adopts two-scale finite element spaces: refined discretizations are adopted inside polygonal subregions, but flux approximations are constrained over the mesh interfaces by a given coarse normal trace space. For stability, pressure and flux approximations are divergence compatible. The error estimation is based on potential reconstruction, which is a popular technique for this kind of analysis in the context of mixed methods. Numerical experiments are presented in order to illustrate the efficiency of the proposals.