A diffuse interface approach to Hele-Shaw flow

Karl Glasner

doi:10.1088/0951-7715/16/1/304

A diffuse interface approach to Hele-Shaw flow

Karl Glasner

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51 Scopus citations

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 language	English (US)
Pages (from-to)	49-66
Number of pages	18
Journal	Nonlinearity
Volume	16
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/16/1/304
State	Published - Jan 2003
Externally published	Yes

ASJC Scopus subject areas

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

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AB - 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.

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A diffuse interface approach to Hele-Shaw flow

Abstract

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