We present a novel hybridizable discontinuous Galerkin (HDG) method on unfitted meshes for single-phase Darcy flow in a fractured porous media. In particular we apply the HDG methodology to the recently introduced reinterpreted discrete fracture model (RDFM) [Xu, Yang 2020] that use Dirac-delta functions to model both conductive and blocking fractures. Our numerical scheme naturally allows for unfitted meshes with respect to the fractures, which is the major novelty of the proposed scheme. Moreover, the scheme is locally mass conservative and is relatively easy to implement comparing with existing work on the subject. In particular, our scheme is a simple modification of an existing regular Darcy flow HDG solver by adding the following two components: (i) locate the fractures in the background mesh and adding the appropriate surface integrals associated with these fractures into the stiffness matrix, (ii) adjust the penalty parameters on cells cut through conductive and blocking fractures (fractured cells). Despite the simplicity of the proposed scheme, it performs extremely well for various benchmark test cases in both two- and three-dimensions. This is the first time that a truly unfitted finite element scheme been applied to complex fractured porous media flow problems in 3D with both blocking and conductive fractures without any restrictions on the meshes. This is a joint work with Yang Yang from Michigan Tech.
Guosheng Fu is the Robert and Sara Lumpkins Assistant Professor in the Department of Applied and Computational Mathematics and Statistics at the University of Notre Dame. Before that, he was the Prager Assistant Professor in the Division of Applied Mathematics at Brown University. He got his Ph.D. degree in Mathematics from University of Minnesota with Prof. Bernardo Cockburn in 2016.