An arbitrary order Mixed Virtual Element formulation for coupled multi-dimensional flow problems

• Published in: Computer methods in applied mechanics and engineering Vol. 391; p. 114204
• Main Authors: Benedetto, M.F., Borio, A., Kyburg, F., Mollica, J., Scialò, S.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-03-2022; Elsevier BV
• Subjects: DFN; Finite element method; Flow simulation; Fractures; Inter-dimensional coupling; Mathematical models; Mesh generation; Mixed VEM; Partial differential equations; Porous media; Subsurface flow; Two dimensional models; Subsurface flow; DFN; Mixed VEM; Inter-dimensional coupling
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2021.114204

Discrete Fracture and Matrix (DFM) models describe fractured porous media as complex sets of 2D planar polygons embedded in a 3D matrix representing the surrounding porous medium. The numerical simulation of the flow in a DFM requires the discretization of partial differential equations on the three dimensional matrix, the planar fractures and the one dimensional fracture intersections, and suitable coupling conditions between entities of different dimensionality need to be added at the various interfaces to close the problem. The present work proposes an arbitrary order implementation of the Virtual Element method in mixed formulation for such multidimensional problems. Details on effective strategies for mesh generation are discussed and implementation aspects are addressed. Several numerical results in various contexts are provided, which showcase the applicability of the method to flow simulations in complex multidimensional domains.
•The formulation for a multi-dimensional flow problem is established.•An outline of the mixed Virtual Element Method (VEM) is given, including implementation details.•A set of numerical applications emphasizing inter-dimensional coupling is studied and its results analyzed.•The performance of the proposed methodology is assessed, highlighting its advantages.