Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm

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A non-singular integral equation formulation to analyse multiscale behaviour in semi-infinite hydraulic fractures (2015, methodology): “A partial solution was obtained (Peirce 2015) in which the pre-computed semi-infinite fracture toughness-to-viscous solution was interpolated to capture the multiscale fracture tip behaviour in the hydraulic fracturing simulator ILSA.”
Hydraulic fracture revisited: Particle velocity based simulation (2015, background): “Furthermore, in the hydraulic fracture problem, the nature of the moving boundary results in degeneration of the governing equations and the boundary conditions at the crack tip, which makes tracing the fracture front an extremely difficult task (Detournay & Peirce, 2014; Peirce, 2015).”
On the moving boundary conditions for a hydraulic fracture (2014, methodology): “The algorithm is able to use the multi-scale hydraulic fracture tip asymptotic solution (Lecampion et al., 2013; Peirce, 2014) and can thus automatically capture the different types of propagation regimes with a relatively coarse mesh.”