Finite domain solution of a KGD hydraulic fracture in the viscosity-dominated regime

Cexuan Liu, Emmanuel Detournay, Fengshou Zhang

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This paper describes a numerical algorithm for solving the classic problem of a plane strain (KGD) fracture propagating in an impermeable elastic medium with zero toughness. The method, which takes advantage of the self-similar nature of the solution, combines a domain-based scheme to solve the elasticity equations and a finite volume method to solve the nonlinear lubrication equation. This work represents a first step towards developing a model able to account for pore pressure diffusion in the medium and corresponding poroelastic effects, noting that these processes are more efficiently solved using a domain-based rather than a boundary integral method. To enhance the efficiency and accuracy of the numerical scheme, the far-field crack asymptotics is embedded in the discretized elastic relationship between the fluid pressure and the crack opening, while the coupled fluid-solid tip asymptote is enforced in a weak form when solving the nonlinear lubrication equation. The proposed technique yields results that closely match the analytical solution, even with a coarse mesh. This approach offers potential for addressing more complex hydraulic fracturing problems in the future.

Original languageEnglish (US)
Article number100095
JournalRock Mechanics Bulletin
Issue number1
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2023 Chinese Society for Rock Mechanics & Engineering.


  • Domain-based method
  • Far-field asymptotic boundary
  • Hydraulic fracturing
  • Numerical simulation
  • Tip asymptote


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