Galerkin least-squares approximations for upper-convected Maxwell fluid flows

In this work finite element approximations for upper-convected Maxwell fluid flows are presented. The mechanical model is approximated by a Galerkin least-squares formulation in extra-stress, pressure and velocity. This formulation has the advantage of remaining stable in locally elastic-dominated flow regions even employing a combination of equal-order finite element interpolations. The performance of the proposed formulation is evaluated by analyzing the flow around a cylinder kept by two parallel plates, for the Deborah number ranging from 0 to 0.9. The numerical results confirm the good features of the GLS formulation, since stable solutions are obtained for increasing elastic effects.

Research highlights▶ Multi-field Galerkin least-squares approximations for upper-convected Maxwell flows. ▶ Creeping flow of UCM fluid around a cylinder between two parallel plates. ▶ Stable solutions for increasing elastic effects.