  In this paper, we discuss whether the instability of viscoelastic flow around
a circular cylinder is subcritical or supercritical by numerical simulation.
The Oldroyd-B model is selected to describe the viscoelastic constitutive
relationship. The Log-conformation reformulation is employed to stabilize
numerical simulation. The parameter ranges investigated are the Reynolds
numbers ($Re$) spanning from 5 to 100 and the Weissenberg number ($Wi$)
spanning from 0 to 10, with a fixed viscosity ratio of $\beta = 0.9$.
Simulations are performed under two paths, i.e., 1) increasing $Re$ (or $Wi$)
and 2) decreasing $Re$ (or $Wi$) slowly and gradually from one state to the
next. The results show that the statistical solutions such as the time-averaged
velocity obtained along the two paths are not identical over certain parameter
range, which is around the transition point from the steady to unsteady flow.
This loading path dependence behaviour indicates that the flow instability is
subcritical.
