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 journalArticle

44 Citations (Scopus)

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

Fingerprint

cells
simulation
Fluxes
injection

Keywords

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

Cite this

A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell. / Li, Shuwang; Lowengrub, John S.; Leo, Perry H.

In: Journal of Computational Physics, Vol. 225, No. 1, 01.07.2007, p. 554-567.

Research output: Contribution to journalArticle

@article{96468cc3b5464ee59a8472a2072692a1,
title = "A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell",
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.",
keywords = "Boundary integral method, Fractal, Hele-Shaw, Moving boundary problems, Saffman-Taylor instability, Self-similar",
author = "Shuwang Li and Lowengrub, {John S.} and Leo, {Perry H}",
year = "2007",
month = "7",
day = "1",
doi = "10.1016/j.jcp.2006.12.023",
language = "English (US)",
volume = "225",
pages = "554--567",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - A rescaling scheme with application to the long-time simulation of viscous fingering in a Hele-Shaw cell

AU - Li, Shuwang

AU - Lowengrub, John S.

AU - Leo, Perry H

PY - 2007/7/1

Y1 - 2007/7/1

N2 - 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.

AB - 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.

KW - Boundary integral method

KW - Fractal

KW - Hele-Shaw

KW - Moving boundary problems

KW - Saffman-Taylor instability

KW - Self-similar

UR - http://www.scopus.com/inward/record.url?scp=34447284554&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34447284554&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2006.12.023

DO - 10.1016/j.jcp.2006.12.023

M3 - Article

AN - SCOPUS:34447284554

VL - 225

SP - 554

EP - 567

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -