Finite element simulation of die swell for a Maxwell fluid

The finite element formulation recently developed 1] for viscoelastic fluids of singly memory type has been extended to handle problems involving free surfaces. Previously 1], flows without free surfaces were demonstrated by solving the die entry and reverse entry flows. The single integral Maxwell fluid is retained here as the constitutive model for this further test of the technique. New work in this paper includes an algorithm to track particles on the free surface and a new free surface updating scheme. For the present die swell problem, the method successfully converged up to Deborah number of about 1. As in the previous problems, convergence appears to be limited by numerically induced incompatibility of large strains. The resulting errors in the computed stress field have a more pronounced impact on free surface flows.