Simulation of 2D transient viscoelastic flow using the CONNFFESSIT approach

In this paper, a modified form of the time-dependent DEVSS-G/SUPG scheme associated with the penalty function method was developed to simulate the viscoelastic flow under the high Weissenberg number by using the Calculation of Non-Newtonian Flow: Finite Elements and Stochastic Simulation Technique (CONNFFESSIT) approach. The element condensation method is used to eliminate the velocity gradient term and still maintain good stability. The variance reduction method was also taken for the Brownian configuration field (BCF) equation to reduce the noise level in calculating the polymer stresses. A planar 4:1 abrupt contraction flow was taken as a benchmark case to verify this modified scheme. The stress contours and vortex evolution with the Hookean dumbbell model were compared with the literature results. The simulation was also extended to the finitely extendable non-linear elastic (FENE) dumbbell model. The second case is the planar flow around a confined cylinder at non-zero Reynolds and Weissenberg numbers. Both the inertial and viscoelastic effects were examined in the second case. For the Hookean and FENE dumbbell models, it was found that without the convective term, the streamlines shift upstream behind the cylinder compared with the Newtonian fluid flow, while an opposite result is observed at a high Reynolds number (i.e., Re = 10).