Third M.I.T. Conference on Computational Fluid and Solid Mechanics June 14–17, 2005  

GLS-type finite element methods for viscoelastic fluid flow simulation

M. Behra,*, D. Arorab, O.M. Coronadoc, M. Pasqualic
aChair for Computational Analysis of Technical Systems, CCES, RWTH Aachen, 52056 Aachen, Germany bDepartment of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77005, USA cDepartment of Chemical and Biomolecular Engineering, Rice University, Houston, TX 77005, USA

  Full Text
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.

Keywords:  Stabilized FEM; Viscoelastic fluids; Galerkin/Least-Squares

* Corresponding author. Tel.: +49 241 80 94505; Fax: +49 241 80 92126; E-mail: