  We study numerically two-dimensional creeping viscoelastic flow past a
biperiodic square array of cylinders within the Oldroyd B, FENE-CR and FENE-P
constitutive models of dilute polymer solutions. Our results capture the
initial mild decrease then dramatic upturn ('thickening') seen experimentally
in the drag coefficient as a function of increasing Weissenberg number. By
systematically varying the porosity of the flow geometry, we demonstrate two
qualitatively different mechanisms underpinning this thickening effect: one
that operates in the highly porous case of widely spaced obstacles, and another
for more densely packed obstacles, with a crossover between these two
mechanisms at intermediate porosities. We also briefly consider 2D creeping
viscoelastic flow past a linear array of cylinders confined to a channel, where
we find that the flow is steady for all Weissenberg numbers explored.

Soft Condensed Matter;Fluid Dynamics