The molecular rheological characteristics of branched polymer melts (low density polyethylene

LDPE) are described by the extended Pom-Pom (XPP) model based on the tube theory

which results in the bridging scale simulation from the molecular-scale structure to macroscopic flow responses. The finite increment calculus (FIC) procedure is introduced to reformulate the mass conservation equation and to overcome spurious oscillations of pressure field due to incompressibility of fluids. In order to retain an elliptic contribution in the weak form of the momentum equation in the absence of a purely viscous contribution or as the viscous contribution is negligible in comparison with the viscoelastic contribution

the discrete elastic viscous stress splitting (DEVSS) technique is employed. Inconsistent streamline-upwind (SU) method is applied to spatially discretize the constitutive equation of the XPP model with modified stretch dynamics. Moreover

mass

momentum and constitutive equations are discretized and solved by the iterative stabilized fractional step algorithm based on Crank-Nicolson implicit difference scheme. Thus the finite elements with equal low-order interpolation approximation for velocitypressurestress variables are adopted to calculate the 4∶1 planar contraction transient viscoelastic flows. The influences of Weissenberg number

the amount of branched-arms (q) at the end of the Pom-Pom molecule and the molecularscale structure parameters on the rheological behavior generated in this complex flow are discussed. Numerical results demonstrate good agreement with those given in the literatures.