A mixed finite element scheme for viscoelastic flows with XPP model

A mixed finite element formulation for viscoelastic flows is derived in this paper, in which the FIC (finite incremental calculus) pressure stabilization process and the DEVSS (discrete elastic viscous stress splitting) method using the Crank-Nicolson-based split are introduced within a general framework of the iterative version of the fractional step algorithm. The SU (streamline-upwind) method is particularly chosen to tackle the convective terms in constitutive equations of viscoelastic flows. Thanks to the proposed scheme the finite elements with equal low-order interpolation approximations for stress-velocity-pressure variables can be successfully used even for viscoelastic flows with high Weissenberg numbers. The XPP(extended Pom-Pom) constitutive model for describing viscoelastic behaviors is particularly integrated into the proposed scheme. The numerical results for the 4:1 sudden contraction flow problem demonstrate prominent stability, accuracy and convergence rate of the proposed scheme in both pressure and stress distributions over the flow domain within a wide range of theWeissenberg number, particularly the capability in reproducing the results, which can be used to explain the "die swell" phenomenon observed in the polymer injection molding process. The project supported by the National Natural Science Foundation of China (10672033, 10590354, 90715011 and 10272027) and the National Key Basic Research and Development Program (2002CB412709).