On modeling hydraulic fracture in proper variables: Stiffness, accuracy, sensitivity

Gennady Mishuris*, Michał Wróbel, Alexander Linkov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

34 Citations (SciVal)


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 e-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. 

Original languageEnglish
Pages (from-to)10-23
Number of pages14
JournalInternational Journal of Engineering Science
Publication statusPublished - Dec 2012


  • Speed equation
  • Sensitivity analysis
  • Accuracy
  • Stiffness
  • Hydraulic fractures


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