Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7061254 | Journal of Non-Newtonian Fluid Mechanics | 2015 | 25 Pages |
Abstract
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.
Related Topics
Physical Sciences and Engineering
Chemical Engineering
Fluid Flow and Transfer Processes
Authors
Raphaƫl Comminal, Jon Spangenberg, Jesper Henri Hattel,