Most fluids used in industrial processing have a polymeric microstructure. When polymeric fluids are subjected to flow, the dynamics of their microstructure usually produces a viscoelastic response. Since Beris and coworkers achieved a breakthrough in the 1980’s with regard to solving viscoelastic fluid models in complex flows at Deborah numbers much larger than unity, considerable experience has been gained in the mathematical formulation of viscoelastic fluid flow problems as well as their discretization in space and time. In the classical approach used to solve nonlinear systems arising from the discretization of viscoelastic fluid flow problems, one of the different implementations of the Newton method is adopted. Direct methods, e.g., some variants of lower-upper decomposition, are commonly employed to solve the linear Jacobian system within the Newton iterations. The disadvantage of such implementations of the Newton method is that they do not scale satisfactorily with the problem size. Moreover, they tend to oversolve the linear Jacobian system if the initial estimate is not sufficiently close to a solution of the nonlinear system.

In this talk, we propose the application of a novel implementation of the Newton method to benchmark simulations. This implementation is unique in that the linear system of discretized algebraic flow equations is solved iteratively using a Krylov subspace method along with an inverse-based incomplete lower-upper preconditioner. We selected the eccentric Taylor-Couette system as a benchmark geometry. We show that our iterative solution strategy is capable of successfully solving the upper-convected Maxwell model at the largest Deborah number for which boundary-layer solutions are available in literature at a moderate eccentricity ratio of the cylinder system.

Additionally, we simulated the dynamics of polymeric solutions, melts, and blends with droplet morphology at different length scales. In this talk, we discuss interesting phenomena that occur because of the highly eccentric configuration of the cylinder system and the viscoelastic nature of the fluid. The findings presented in this talk are expected to help us gain a more fundamental understanding of the process-rheology-microstructure interrelationship of polymeric fluids under industrially relevant conditions. However, experimental data would be needed to verify the model predictions.