Oldroyd-BLog convergence limitations in high Wi

[Joe199999]

Dear Professor,

In the user guide, it is noted: "The four variants of the model are available in rheoTool, where both the Herschel–Bulkley and PTT variants can avoid the possible infinite Oldroyd-B elongational viscosity for Wi ≥ 0.5 in extensional flows of Oldroyd-B fluids."

In my 2D simulation of Oldroyd-B flow around a cylinder for Wi ≥ 5, I am observing anomalous flow structures with irregular oscillations in the parameters (the attached figure shows results for Wi = 5; for Wi > 5, the flow structure in front of the cylinder becomes highly variable and irregular). My question is: Are these results physical, or can physically meaningful results for the Oldroyd-B model at high Wi numbers be obtained using the log-conformation method, as implied by the guide?

I have implemented numerous numerical strategies to address this, including:
Extremely refined meshes.
Very small time steps (CFL numbers of 0.05 and 0.01).
Crank–Nicolson temporal discretization with blending factors of 0.5, 0.9, and 1 (implicit).

Despite these efforts, the irregular oscillations persist.

Additional question for context: In your experience, does this suggest a fundamental limitation of the Oldroyd-B constitutive model itself in such flow regimes, where its known stress divergence in extension makes steady numerical solutions unattainable? Would switching to a more realistic model like PTT (with a small ε) be the recommended path forward for studying high-Wi flows, as the user guide seems to indicate?