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Explicit-implicit XFEM for Hydraulic Fracturing with emphasis on transport models on curved crack surfaces

Banff International Research Station for Mathematical Innovation and Discovery

The eXtended Finite Element Method (XFEM) has developed to a standard tool in fracture mechanics. The method enriches the approximation space such that inner-element cracks are considered without loss of accuracy. The hybrid explicit-implicit XFEM uses both, an explicit surface mesh and the implicit level-set method for the description of the crack geometry. The implicit description is needed for the integration in cut elements and it defines where to enrich and how. The explicit description facilitates the (non-planar) crack propagation and provides the basis for solving general transport models on the surface mesh in order to consider for the fluid in Hydraulic Fracturing. One may span the full range from the Reynolds equation, general scalar advection-diffusion equations up to Stokes and Navier-Stokes equations. Because the crack surfaces in hydraulic fracturing may be non-planar, these models have to be extended from the flat case to the situation on curved manifolds. Tangential differential calculus and surface operators play an important role and approximations based on finite elements have to be provided. Future research will show which of these transport models are necessary and sufficient in the field of hydraulic fracturing.

Mathematics; Mechanics of deformable solids; Fluid mechanics

video/mp4

Author affiliation: Graz University of Technology

2019-03-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68916

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/