October 15 – Florent Hédin: A hybrid high-order (HHO) method with non-matching meshes in discrete fracture networks

Florent Hédin: Thursday 15 October at 11:00, Gilles Kahn 1, Inria Paris.

We are interested in efficient numerical methods for solving flow in large scale fractured networks. Fractures are ubiquitous in the subsurface. Flow in fractured rocks are of interest for many applications (water resources, geothermal applications, oil/gas extraction, nuclear waste disposal). The networks are modeled as Discrete Fractures Networks (DFN). The main challenges of such flow simulations are the uncertainty regarding the geometry and properties of the subsurface, the observed wide range of fractures length (from centimeters to kilometers) and the number of fractures (from thousands to millions of fractures). In natural rocks, flow is highly channelled, which motivates to mesh finely the fractures that carry most of the flow, and coarsely the remaining fractures. But independent triangular mesh generation from one fracture to another yields non matching triangles at the intersections between fractures. Mortar methods have been developed in the past years to deal with non matching grids. In this presentation, we propose an alternative based on the recent HHO method which naturally handles general meshes (polygons/polyhedral) and face polynomials of order k ≥ 0. Combined with refining/coarsening strategies, we will show how the HHO method allows to save computational time in DFN flow simulations.

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