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

On the streamfunction – vorticity formulation in sliding bi-period frames: application to bulk behavior for polymer blends. (English) Zbl 1136.76386

J. Comput. Phys. 212, No. 1, 268-287 (2006).
Summary: The Lees — Edwards description of bi-periodic boundary conditions [J. Phys. C 5, 1921 (1972)] 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.

Cited in 3 Documents

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T25 Granular flows

Keywords:

Lees – Edwards boundary conditions; streamfunction — vorticity formulation; Lagrangian multiplier; polymer blends

Software:

HSL
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Full Text: DOI

References:

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