A moving overset grid method for interface dynamics applied to non-Newtonian Hele-Shaw flow

  • Authors:

  • Petri Fast;Michael J. Shelley

  • Affiliations:

  • Lawrence Livermore National Laboratory, Center for Applied Scientific Computing, P.O. Box 808, L-365 Livermore, CA;Courant Institute of Mathematical Sciences, New York University, New York, NY

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2004

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Abstract

We present a novel moving overset grid scheme for the accurate and efficient long-time simulation of an air bubble displacing a non-Newtonian fluid in the prototypical thin film device, the Hele-Shaw cell. We use a two-dimensional generalization of Darcy's law that accounts for shear thinning of a non-Newtonian fluid. In the limit of weak shear thinning, the pressure is found from a ladder of two linear elliptic boundary value problems, each to be solved in the whole fluid domain. A moving body fitted grid is used to resolve the flow near the interface, while most of the fluid domain is covered with a fixed Cartesian grid. Our use of body-conforming grids reduces grid anisotropy effects and allows the accurate modeling of boundary conditions.