A diffuse interface approach to Hele-Shaw flow

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47 Scopus citations


A diffuse interface model for the one-phase Hele-Shaw problem is derived from a gradient flow characterization due to Otto (1998 Arch. Rat. Mech. Anal. 141 63). The resulting dynamical model yields a generalized form of Darcy's law, and reduces to a degenerate version of the well-known Cahn-Hilliard equation. Formal asymptotics illustrate the connection to the classical Hele-Shaw free boundary problem. Some example computations are carried out to demonstrate the flexibility of the modelling framework.

Original languageEnglish (US)
Pages (from-to)49-66
Number of pages18
Issue number1
StatePublished - Jan 2003

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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