Finite volume multigrid method of the planar contraction flow of a viscoelastic fluid

This paper reports on a numerical algorithm for the steady flow of viscoela stic fluid. The conservative and constitutive equations are solved using th e finite volume method (FVM) with a hybrid scheme for the velocities and fi rst-order upwind approximation for the viscoelastic stress. A non-uniform s taggered grid system is used. The iterative SIMPLE algorithm is employed to relax the coupled momentum and continuity equations. The non-linear algebr aic equations over the flow domain are solved iteratively by the symmetrica l coupled Gauss-Seidel (SCGS) method. In both, the full approximation stora ge (FAS) multigrid algorithm is used. An Oldroyd-B fluid model was selected for the calculation. Results are reported for planar 4:1 abrupt contractio n at various Weissenberg numbers. The solutions are found to be stable and smooth. The solutions show that at high Weissenberg number the domain must be long enough. The convergence of the method has been verified with grid r efinement. All the calculations have been performed on a PC equipped with a Pentium III processor at 550 MHz. Copyright (C) 2001 John Wiley & Sons, Lt d.