PEGAFEM-V: A new petrov-galerkin finite element method for free surface viscoelastic flows

The recently proposed finite element (FE) formulation for viscoelastic flows that allows the use of equal order linear interpolants for all variables and simultaneously does not suffer from the high Weissenberg number problem, is extended to free surface flows. The coupling of this Petrov-Galerkin stabilized FE formulation with the quasi-elliptic mesh generator allows us to obtain stable numerical solutions in highly deformed meshes and for very high values of the Weissenberg number (Wi). We present benchmark solutions in three free surface flows: the axisymmetric filament stretching, the elastocapillary-driven formation of bead on a string, and the 2-dimensional, planar extrudate swell flow. In all cases, we attain converged solutions for values of Wi that have never been reached before by FE. The accuracy and robustness of the proposed numerical scheme are illustrated by achieving mesh and time step convergence under extreme mesh deformation conditions such as the bead-on-a-string (BOAS) formation during filament stretching. The formulation is enriched further with a discontinuity capturing scheme that enhances the quality of the solution around singularities dramatically. Finally, our simulations reveal for the first time the existence of lip-vortices in the steady planar extrudateswell flow of Oldroyd-B fluids, which converge with mesh refinement.