2012/03/26 by Gennady Mishuris, Mishuris, Gennady, Michał Wróbel +5
Engineering · Mathematics · Physics and Astronomy · #37M05 #65P40 #74A45 #86-08 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geophysics (physics.geo-ph) #Hydraulic Fracturing and Reservoir Analysis #Numerical methods in engineering #math.AP #math.DS #msc:37M05 #msc:65P40 #msc:74A45 #msc:86-08 #physics.geo-ph
paper · pdf · doi:10.48550/arxiv.1203.5691
18 pages, 4 figures
arxiv created 2012/03/26 · openalex publication_date 2012/03/26 · arxiv updated 2012/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The problem of hydraulic fracture propagation is considered by using its recently suggested modified formulation in terms of the particle velocity, the opening in the proper degree, appropriate spatial coordinates and ε-regularization. We show that the formulation may serve for significant increasing the efficiency of numerical tracing the fracture propagation. Its advantages are illustrated by re-visiting the Nordgren problem. It is shown that the modified formulation facilitates (i) possibility to have various stiffness of differential equations resulting after spatial discretization, (ii) obtaining highly accurate and stable numerical results with moderate computational effort, and (iii) sensitivity analysis. The exposition is extensively illustrated by numerical examples.