EVSS‐Based Simulation Techniques for the Viscoelastic Fluids With Pure Polymer Melts Using Three‐Field Approach

ABSTRACT To obtain the numerical solution of viscoelastic fluid simulations 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 article is to present a mixed finite element method for solving the three‐field Stokes flow with zero solvent viscosity using 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. A common approach to address this issue is to expand the problem size to a four‐field formulation by introducing the strain‐rate tensor as an additional variable, which increases the computational cost. In contrast, our approach reformulates the convective term by explicitly taking into account the divergence‐free nature of the velocity field and shifts the higher order derivatives to the test function in the weak formulation. This approach retains the problem as a three‐field formulation, avoiding the need to treat the strain‐rate tensor as an independent equation. As a result, it reduces the number of degrees of freedom and lowers the overall computational cost. The velocity, pressure and stress are discretized by the higher order stable FEM triplet . The proposed scheme is tested for Oldroyd‐B, Giesekus, and exponential PTT models using both the decoupled and monolithic solution approaches. The numerical results are obtained on the 4:1 contraction configuration for highly viscoelastic fluids with the aim to analyze the shear‐thinning effect as the relaxation parameter increases.