The finite volume method in the non-staggered grid was applied to the prediction of the two-dimensional branched polymer melts through a 4∶1 planar contraction and planar contraction with inset.The constitutive equation followed the extended pom-pom model (XPP model)

which was developed from the Doi-Edwards model based on the rheology molecular theory.The decoupling about velocity-pressure and velocity-stress was removed by a new interpolation technique inspired by that of Rhie and Chow.Moreover

some numerical terms were added in order to promote the stability of the finite volume schemes.With the help of contour about stream function

backbone stretch

the first normal stress difference and the second normal stress difference

the development tendency of the polymer melts in 4∶1 planar contraction and planar contraction with inset was presented.The influence of inset on viscoelasticity of concentrated liquids was also discussed in detail.The numerical result indicated that the quantities describing viscoelasticity of polymer melts

especially for the size and shape of the salient corner vortex and backbone stretch behind inset

had obvious changes if the central position of inset was different.