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

  • Authors:

  • Shuwang Li;John S. Lowengrub;Perry H. Leo

  • Affiliations:

  • Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA;Department of Mathematics, University of California at Irvine, Irvine, CA 92697, USA;Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2007

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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.