A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell

Shuwang Li, John S. Lowengrub, Perry H. Leo

Research output: Contribution to journalArticlepeer-review

45 Scopus citations

Abstract

In this paper, we present a time and space rescaling scheme for the computation of moving interface problems. The idea is to map time-space such that the interfaces can evolve exponentially fast in the new time scale while the area/volume enclosed by the interface remains unchanged. The rescaling scheme significantly reduces the computation time (especially for slow growth), and enables one to accurately simulate the very long-time dynamics of moving interfaces. We then implement this scheme in a Hele-Shaw problem, examine the dynamics for a number of different injection fluxes, and present the largest and most pronounced viscous fingering simulations to date.

Original languageEnglish (US)
Pages (from-to)554-567
Number of pages14
JournalJournal of Computational Physics
Volume225
Issue number1
DOIs
StatePublished - Jul 1 2007

Keywords

  • Boundary integral method
  • Fractal
  • Hele-Shaw
  • Moving boundary problems
  • Saffman-Taylor instability
  • Self-similar

Fingerprint Dive into the research topics of 'A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell'. Together they form a unique fingerprint.

Cite this