Stress boundary layers in the viscoelastic flow past a cylinder in a channel:limiting solutions

The flow past a cylinder in a channel with the as-pect ratio of 2:1 for the upper convected Maxwell（UCM）fluid and the Oldroyd-B fluid with the viscosity ratio of 0.59is studied by using the Galerkin/Least-square finite elementmethod and a ρ-adaptive refinement algorithm.A posteri-ori error estimation indicates that the stress-gradient errordominates the total error.As the Deborah number,D;,ap-proaches 0.8 for the UCM fluid and 0.9 for the Oldroyd-Bfluid,strong stress boundary layers near the rear stagnationpoint are forming,which are characterized by jumps of thestress-profiles on the cylinder wall and plane of symmetry,huge stress gradients and rapid decay of the gradients acrossnarrow thicknesses.The origin of the huge stress-gradientscan be traced to the purely elongational flow behind the rearstagnation point,where the position at which the elonga-tion rate is of 1/2D;approaches the rear stagnation pointas the Deborah number approaches the critical values.Theseobservations imply that the cylinder problem for the UCMand Oldroyd-B fluids may have physical limiting Deborahnumbers of 0.8 and 0.9,respectively.