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

•Stabilized finite element method for viscoelastic flows with free surfaces using equal order polynomials, 2nd order accurate.•Stable numerical simulations under large mesh deformation and high Weissenberg numbers.•Discontinuity-capturing directional dissipation (DCDD) for the constitutive equation....

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Published inJournal of non-Newtonian fluid mechanics Vol. 284; p. 104365
Main Authors Varchanis, S., Syrakos, A., Dimakopoulos, Y., Tsamopoulos, J.
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 01.10.2020
Elsevier BV
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ISSN0377-0257
1873-2631
DOI10.1016/j.jnnfm.2020.104365

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Summary:•Stabilized finite element method for viscoelastic flows with free surfaces using equal order polynomials, 2nd order accurate.•Stable numerical simulations under large mesh deformation and high Weissenberg numbers.•Discontinuity-capturing directional dissipation (DCDD) for the constitutive equation.•Bead-on-a-string instability captured using 2D axisymmetric simulations.•Existence of lip vortex just before the die exit in the extrudate swell flow. 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 extrudate-swell flow of Oldroyd-B fluids, which converge with mesh refinement.
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ISSN:0377-0257
1873-2631
DOI:10.1016/j.jnnfm.2020.104365