On the streamfunction-vorticity formulation in sliding bi-period frames: Application to bulk behavior for polymer blends

  • Authors:

  • Patrick D. Anderson;Bert J. Keestra;Martien A. Hulsen

  • Affiliations:

  • Materials Technology, Dutch Polymer Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Materials Technology, Dutch Polymer Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Materials Technology, Dutch Polymer Institute, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2006

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Abstract

The Lees-Edwards description of bi-periodic boundary conditions has been extended to the streamfunction and streamfunction-vorticity formulation in sliding bi-periodic frames. The required compatibility conditions are formulated and uniqueness of the solution is shown. The model has been implemented in a spectral element method context to describe bulk shear behavior far away from walls, where no simple periodic boundary conditions can be used. In the numerical model a Lagrangian multiplier is introduced to couple the shearing boundaries. The proposed method has been validated for a mathematical test problem; convergence is shown and the influence of the order of approximation of the Lagrangian multiplier is studied. Finally, results are presented for drop coalescence across the boundaries of the bi-periodic frame.