  In the finite element analysis with fast decoupled time integration scheme
for viscoelastic fluid (the Leonov model) flow, we investigate strong nonlinear
behavior in 2D creeping contraction flow. The algorithm is applicable in the
whole range of the retardation parameter. In the analysis of steady solutions,
there exists upper convergence limit of available numerical solutions in this
contraction flow that is free from the frustrating mesh dependence when we
incorporate the tensor-logarithmic formulation [Fattal and Kupferman, JNNFM,
2004]. With adjustment of a nonlinear parameter, 2 kinds of fluid have been
chosen for flow modeling such as highly shear thinning and Boger-type liquids.
According to the type of such property, the transient modeling has revealed
distinct flow dynamics of elastic instability. With pressure difference imposed
slightly below the steady limit, the result demonstrates fluctuating solution
without approaching steady state for the shear thinning fluid. From it, we
conclude that the existence of upper limit for convergent steady solution
possibly implies transition to spatially as well as temporally varying flow
field without steady asymptotic. Under the pressure fairly higher than the
limit, the result expresses severe fluctuation of flowrate, oscillation of
corner vortices and also asymmetric irregular wave propagation along the
downstream wall. In addition, flow dynamics seems quite stochastic with almost
no temporal correlation. For the Boger-type fluid, under the traction higher
than steady limit the flowrate and corner vortices exhibit periodic oscillation
with flow asymmetry. Both types of instability express purely elastic
instability in this inertialess flow approximation.
