Stabilized Finite Element Methods of Gls Type for Maxwell-b and Oldroyd-b Viscoelastic Fluids

We evaluate the stabilized three-field stress-velocity-pressure Galerkin/LeastSquares finite element formulation for viscoelastic fluids, using a benchmark problem of Oldroyd-B flow past a cylinder at various Weissenberg numbers. 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, and study how such an approach affects the quality of computed results. We show that characteristic flow quantities obtained with the new formulation are in good agreement standard DAVSS and DEVSS results, while the cost of fully-implicit velocity gradient computation may be in some cases avoided.