A stable and convergent scheme for viscoelastic flow in contraction channels

  • Authors:

  • D. Trebotich;P. Colella;G. H. Miller

  • Affiliations:

  • Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94551, USA;Applied Numerical Algorithms Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA;Department of Applied Science, University of California, One Shields Avenue, Davis, CA 95616, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

We present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels. In our approach we split the viscoelastic terms of the Oldroyd-B constitutive equation using Duhamel's formula and discretize the resulting PDEs using a semi-implicit finite difference method based on a Lax-Wendroff method for hyperbolic terms. In particular, we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well-posed. A projection method is used to impose the incompressibility constraint. We are able to compute the full range of unsteady elastic flows in an abrupt contraction channel - from the viscous limit to the elastic limit - in a stable and convergent manner. We demonstrate the range of our method for unsteady flow of a Maxwell fluid with and without viscosity in planar contraction channels. We also demonstrate stable and convergent results for benchmark high Weissenberg number problems at We=1 and We=10.