Numerical Simulation of Contraction Flow for Viscoelastic Fluids at High Weissenberg Number by the Streamline-Upwind Finite Element Method

Numerical simulation of viscoelastic flow at high Weissenberg number (We) was carried out by the streamline-upwind finite element method with the sub-elements for stress components proposed by Marchal and Crochet. This method and the Galerkin finite element method were applied to the stick-slip flow with the singular point in order to examine the effectiveness of this method. The Oldroyd-B model was used as a constitutive equation. This model incorporates strong elasticity and numerical solutions sometimes diverge. When the Galerkin finite element method was used, the numerical solutions had oscillation and the loss of convergence occurred at relatively low value of We. On the other hand, when the streamline-upwind method was used with the stress sub-elements, the oscillation of numerical solutions did not appear and the solution could be obtained up to a high value ofWe. Using the latter method, the calculation of the tapered contraction flow was carried out with the Giesekus model as a constitutive equation. The limit values of We were not encountered and we could calculate even at We> 100 using various values of model parameters. It was concluded that the streamline-upwind finite element method with the stress sub-elements was very useful to simulate the contraction flow up to high values of We.