Numerical simulations of the planar contraction flow for a polyethylene melt using the XPP model

The Discrete Elastic Viscous Stress Splitting technique in combination with the Discontinuous Galerkin (DEVSS/DG) method is used to simulate a low density polyethylene melt flowing in a transientcontraction flow problem.Numerical results using the original and a modified form of the eXtended Pom-Pom (XPP) model are compared to numerical results obtained with the exponential form of the Phan-Thien Tanner (PTT-a) and the Giesekus model and to experimental data of velocities and stresses. These models are known to be well capable of predicting all characteristic features encountered experimentally.Curiously, the eXtended Pom-Pom mode, formulated with the same non-affine or irreversible stretch dynamics as the original Pom-Pom model, encounters convergence problems using the DEVSS/DG method. A slight modification of the stretch dynamics such that it becomes consistent with other viscoelastic models and in agreement with a modification of the stretch dynamics based on non-equilibrium thermodynamics by van Meerveld [J. Non-Newtonian Fluid Mech.,108: 291-299, 2002] gives a more numerical stable behavior and steady state could be reached. From this it is clear that physical and numerical issues still play a mixed role in numerical viscoelastic flow problems