  The lid-driven cavity flow is a well-known benchmark problem for the
validation of new numerical methods and techniques. In experimental and
numerical studies with viscoelastic fluids in such lid-driven flows,
purely-elastic instabilities have been shown to appear even at very low
Reynolds numbers. A finite-volume viscoelastic code, using the log-conformation
formulation, is used in this work to probe the effect of viscoelasticity on the
appearance of such instabilities in two-dimensional lid-driven cavities for a
wide range of aspect ratios (0.125 < height/length < 4.0), at different Deborah
numbers under creeping-flow conditions and to understand the effects of
regularization of the lid velocity. The effect of the viscoelasticity on the
steady-state results and on the critical conditions for the onset of the
elastic instabilities are described and compared to experimental results.
