Computer simulation of hydraulic fractures

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An extended finite element method for hydraulic fracture problems (2009, background): “The numerical simulation of the propagation of hydraulic fractures is a notoriously difficult problem having non-linear and non-local properties enhanced by the presence of a moving boundary [1].”
Phase-field modeling of a fluid-driven fracture in a poroelastic medium (2015, positive): “Detailed discussion of the development of hydraulic fracturing models for use in petroleum engineering can be found in [1] and in mechanical engineering and hydrology in [5, 11, 18] and in references therein.”
Modeling multi-scale processes in hydraulic fracture propagation using the implicit level set algorithm (2015, background): “Mathematical models of HF involve a degenerate system of hyper-singular integro-partial differential equations defined on a domain with a moving boundary [4].”
Phase-field modeling of hydraulic fracture (2016, background): “Several commercial production codes are based on these ideas and are in use today([14]).”