Numerical modeling of viscoelastic flows using equal low-order finite elements

A mixed finite element scheme abbreviated as I_PS_DEVSS_CNBS scheme for modeling viscoelastic flow problems is presented. The finite incremental calculus (FIC) pressure stabilization process and the discrete elastic-viscous stress-splitting method (DEVSS) are introduced into the general framework of the iterative version of the fractional step algorithm with the use of the Crank–Nicolson-based splitting. Inconsistent streamline upwinding method (SU) is employed to spatially discretize the constitutive equation of viscoelastic fluids. Equal low-order finite elements which violate the LBB compatibility conditions are successfully used in the proposed scheme. In addition, the Oldroyd-B and the PTT models have been integrated into the proposed scheme to solve the 4:1 sudden contraction flow problem. The numerical results demonstrate prominent stability and accuracy of both pressure and stress distributions over the flow domains provided by the proposed scheme within the Weissenberg number range studied in the present work, as compared with the reference solutions reported in the literatures.