HHO-DFN : a Hybrid High Order (HHO) method for the simulation of flow in large tridimensional Discrete Fracture Networks (DFN)

Abstract : In fractured rocks, fluid flows mostly within a complex arrangement of fractures, classically modeled as a Discrete Fracture Network (DFN) [1]. In this model, the fractures are distributed in a three-dimensional domain and are modeled as ellipses whose position and orientation are evaluated from statistical laws given by geological studies. For large size production networks provided by external industrial partners, the network under study may contain millions of fractures generating millions of intersections (Figure 1, left). Solving flow within these large 3D DFNs requires robust and efficient numerical methods and software (Figure 1, right). Figure 1: A DFN with 1,176,566 fractures and 2,410,537 of intersections. Fractures are modeled using ellipses (left), the hydraulic head (right) is computed with the NEF-Flow software, which implements the Mixed-Hybrid Finite Element Method for DFNs. So far, the hydraulic head and velocity fields have been computed using the Mixed-Hybrid Finite Element (MHFEM) method, by the means of the software NEF-Flow [2]. As the flow in fractured rocks is highly chanelled, a reduction of the computational cost is achieved by meshing the fractures independently, the fractures with the fine meshes are the ones that carry most of the flow. It yields non matching meshes at the intersections between fractures [3]. To further gain in flexibility in the mesh generation, in the management of non conforming meshes and in the number of degrees of freedom, we propose to solve the same problem with a HHO (Hybrid High Order) method[4]. HHO is closely related to Hybridizable Dis-continuous Galerkin methods (HDG)[5], allowing general meshes (including polytopal cells and nonmatching interfaces) and arbitrary polynomial orders.
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Submitted on : Monday, October 14, 2019 - 4:13:33 PM
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Florent Hédin, Géraldine Pichot, Alexandre Ern. HHO-DFN : a Hybrid High Order (HHO) method for the simulation of flow in large tridimensional Discrete Fracture Networks (DFN). ENUMATH - European Numerical Mathematics and Advanced Applications Conference 2019, Sep 2019, Egmond ann Zee, Netherlands. ⟨hal-02315491⟩

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