A diffuse interface approach to Hele-Shaw flow

Research output: Contribution to journalArticle

35 Citations (Scopus)

Abstract

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
JournalNonlinearity
Volume16
Issue number1
DOIs
StatePublished - Jan 2003

Fingerprint

Hele-Shaw Flow
Diffuse Interface
Hele-Shaw
Darcy's Law
Cahn-Hilliard Equation
arches
Gradient Flow
free boundaries
Arch
Arches
Free Boundary Problem
Dynamical Model
flexibility
Flexibility
gradients
Modeling
Demonstrate
Model
Framework
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

A diffuse interface approach to Hele-Shaw flow. / Glasner, Karl B.

In: Nonlinearity, Vol. 16, No. 1, 01.2003, p. 49-66.

Research output: Contribution to journalArticle

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