Decoupled algorithm for transient viscoelastic flow modeling and   description of elastic flow instability
  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. 
Youngdon Kwon
physics.flu-dyn