Implicit level set schemes for modeling hydraulic fractures using the XFEM

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Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model (2016, methodology): “Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model Sanghyun Lee ∗ Mary F. Wheeler † Thomas Wick ‡ This work presents phase field fracture modeling in heterogeneous porous media.”
Enrichment strategies and convergence properties of the XFEM for hydraulic fracture problems (2015, methodology): “During the development of the fully coupled XFEM schemes applicable to both fluid lag and coalescent front situations [33,34] we identified two key boundary value problems that need to be solved repeatedly during the modeling of a propagating HF using the XFEM.”
A non-singular integral equation formulation to analyse multiscale behaviour in semi-infinite hydraulic fractures (2015, methodology): “This technique has also been used in the context of the extended finite element method to model the propagation of hydraulic fractures (Gordeliy & Peirce 2013).”