P. Kusmierczyk, G. Mishuris, M. Wrobel
The problem of hydraulic fracture for the PKN model is considered within the framework of approach presented recently by Linkov (2011). The modified formulation is further enhanced by employing an improved regularized boundary condition near the crack tip. This increases solution accuracy especially for singular leak-off regimes. A new dependent variable having clear physical sense is introduced. A comprehensive analysis of numerical algorithms based on various dependent variables is provided.
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http://arxiv.org/abs/1211.6474
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