The simulation of some model viscoelastic extensional flows

The numerical simulation of three model viscoelastic extensional flows is considered : sink flow, model draw-down and conical section draw-down. A transient finite element scheme with a pressure correction method is employed to analyse the numerical treatment of such problems for Oldroyd-B and Phan-Thien/Tanner constitutive models. Both decoupled and coupled formulations are compared for these highly convective flows and effective mechanisms are proposed for removing numerical oscillations in the temporally developing solution. In pure viscoelastic extensional flow from an initial stress-free state, the maximum stress level attained decreases with increase in material relaxation time. When this is followed by stress relaxation, as in conical section draw-down, increasing the relaxation time inhibits stress decay.