Simulation techniques for the viscoelastic fluids with pure polymer melts based on EVSS approach

Abstract

To obtain the solution of the viscoelastic fluid simulation with pure polymer melts is a highly challenging task due to the lack of the solvent contribution to the viscosity in the standard viscoelastic formulation. The aim of this paper is to present a mixed finite element method for solving the three field Stokes flow with zero solvent viscosity employing the Elastic Viscous Stress Splitting (EVSS) formulation. On one hand, the EVSS formulation helps to recover the velocity coupling back into the momentum equation by the application of the change of variables in the standard viscoelastic formulation. On the other hand, additional terms containing the second order velocity derivatives appear in the convective part of the constitutive equation for stress. We have reformulated the convective term by considering the divergence-free nature of the velocity field and shifted the higher order derivatives to the test function in the weak formulation. The velocity, pressure and stress are discretized by the higher order stable FEM triplet Q2/P1disc/Q3. The proposed scheme is tested for Oldroyd-B, Giesekus and PTT exponential fluids employing both the decoupled and the monolithic solution approaches. The numerical results are obtained on four to one contraction for highly viscoelastic fluids with the aim to observe the shear-thinning effect as the relaxation parameter increases.