Finite element simulation of three-dimensional viscoelastic flow at high Weissenberg number based on the log-conformation formulation

Viscoelasticity is an important characteristic of many complex fluids such as polymer solutions and melts. Understanding the viscoelastic behavior of such complex fluids presents mathematical, modeling and computational challenges, particularly in the case of fluids affected by elastic turbulence at high Weissenberg number. A numerical methodology based on the penalty finite element method with a decoupled algorithm is presented in the study to simulate three-dimensional flow of viscoelastic fluids. The discrete elastic viscous split stress (DEVSS) formulation in cooperating with log-conformation formulation transformation is employed to improve computational stability at high Weissenberg number. The momentum equation is calculated after introducing an ellipticity factor and the constitutive equation is calculated based on the logarithm of the conformation tensor. The finite element-finite difference formulations of governing equations are derived. The planar contraction as a representative benchmark problem is used to test the robustness of the numerical method to predict real flow patterns of viscoelastic fluids at different Weissenberg numbers. The simulation results predicted with differential constitutive models based on the logarithm of the conformation tensor agree well with Quinzani's experimental results. Both the stability and the accuracy are improved compared with traditional calculation method. The numerical methodology proposed in the study can well predict complex flow patterns of viscoelastic fluids at high Weissenberg number.