Journal
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
Volume 223, Issue -, Pages 37-61Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.jnnfm.2015.05.003
Keywords
Incompressible viscoelastic flow; Streamfunction formulation; Log-conformation representation; Lid-driven cavity; High Weissenberg number; Elastic instability
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Funding
- Scientific Research Council on Technology and Production Sciences (FTP) (OPTIMAC), Danish Council for Independent Research (DFF) [09-072888]
- FTP [4005-00381]
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A new streamfunction/log-conformation formulation of incompressible viscoelastic flows is presented. The log-conformation representation guaranties the positive-definiteness of the conformation tensor and obviates the high Weissenberg number problem. The streamfunction is defined as a vector potential of the velocity field, and provides a pressureless formulation of the conservation laws, which automatically enforces the incompressibility. The resulting numerical method is free from velocity-pressure decoupling errors, and can achieve stable calculations for large Courant numbers, which improve the robustness and the efficiency of the solver. The two-dimensional flow of an Oldroyd-B fluid inside the lid-driven cavity is simulated for a large range of Weissenberg numbers. The numerical results demonstrate the second-order accuracy of our scheme, and our solutions are in good agreement with the available data from the literature for Weissenberg number 3 and below. Finally, the simulations at higher Weissenberg numbers 5 and 10 reveal a structural mechanism that sustains quasi-periodic elastic instabilities arising at the upstream corner of the moving lid. (C) 2015 Elsevier B.V. All rights reserved.
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