The study investigates numerical simulation of viscoelastic fluids that are pure polymer melts, i.e. fluids with no solvent contribution to the viscosity. The authors employ the Elastic Viscous Stress Splitting (EVSS) formulation to recover velocity coupling in the momentum equation while keeping the problem size at three fields – velocity, pressure and stress. The EVSS approach introduces a split of the extra‑stress tensor into a viscous part, (2eta_p D(u)), and an elastic part, (E). This change of variables restores the missing viscous term in the Stokes momentum balance and allows the use of both decoupled and monolithic solution strategies. A key technical contribution is the reformulation of the convective term in the constitutive equation. By exploiting the divergence‑free property of the velocity field, the authors shift the second‑order velocity derivatives to the test function in the weak form, thereby avoiding the need for higher‑order finite‑element spaces and keeping the problem size minimal.

The discretisation uses a stable mixed finite‑element triplet: Q2 for velocity, discontinuous Q1 for pressure, and Q3 for the stress tensor. This choice satisfies the additional inf‑sup condition required for the three‑field formulation. The method is applied to three standard viscoelastic models: Oldroyd‑B, Giesekus and the PTT exponential model. For the Oldroyd‑B case, the authors present a detailed performance comparison between the decoupled and monolithic approaches. At a relaxation parameter (lambda=0.0) the decoupled solver needs 8 iterations and 0.951 s of runtime, while the monolithic solver requires 13 iterations and 1.551 s. As (lambda) increases to 0.5, 1.0, 3.0 and 5.0 the decoupled solver requires 167, 334, 1048 and 6222 iterations, with runtimes of 1.119, 1.121, 1.131 and 1.129 s respectively, and memory consumption rising from 13 GB to 2048 GB. The monolithic solver, in contrast, fails to converge at (lambda=5.0) and shows a steady increase in iterations and memory from 13 to 2048 GB as (lambda) grows. These results demonstrate that the decoupled approach is computationally cheaper and uses less memory for moderate (lambda), but the monolithic method remains more robust for very high relaxation times, provided a Newton solver is employed instead of the fixed‑point iteration used in the study.

Shear‑thinning behaviour is clearly captured by the Giesekus and PTT exponential models. At downstream channel positions (x=20) the velocity profiles deviate from the parabolic shape, with pronounced thinning observed for (lambda=5) and (lambda=10). The PTT exponential model, in particular, reproduces realistic flow behaviour even at high (lambda) values when solved with the decoupled scheme. Convergence plots for the Oldroyd‑B model at (lambda=0.5) show that the monolithic solver is largely insensitive to the EOFEM stabilization parameter, whereas the decoupled solver’s convergence is strongly affected by the added stabilization.

The computations were carried out on a high‑performance server equipped with an Intel Xeon E5‑2640 v3 processor (16 cores) and 218 GB of DDR4 memory. The research was conducted by R. Ahmad, P. Zajac and S. Turek at the Institute for Applied Mathematics, LS III, TU Dortmund University. While the report does not specify external funding or a formal partnership, the collaboration among the three authors within the university’s applied mathematics department underpins the development and validation of the EVSS‑based simulation framework.