ABSTRACT
The stabilized Galerkin/Least-Squares finite element formulation for viscoelastic fluids circumvents inf-sup conditions on all three fields involved - stress, velocity and pressure - allowing the use of low- and equal-order interpolations, and provides necessary stability in the high Weissenberg number regime. A new definition of stabilization parameter for the stabilized form of the constitutive equation is evaluated using a benchmark problem of Oldroyd-B flow past a cylinder in a channel. To address the issue of weak consistency exhibited by low-order velocity interpolations in the context of stabilized formulations, we also employ velocity gradient recovery for the Newtonian solvent. We show that the proposed parameter improves the agreement of the GLS formulation results with standard DEVSS results, especially in the high-Weissenberg number limit. In contrast to DEVSS, fully-implicit velocity gradient computation is not crucial for stability.