This paper describes a new decoupled finite element method, which has been developed based on previous work and applied successfully to the high Weissenberg number problem of die-swell flow simulation using a single relaxation mode Giesekus model. The method is a modified version of the 2×2-subelement/non-consistent streamline upwind (2×2SU) scheme. To improve the convergence behavior, several additional techniques are incorporated: (1) unification of the number of Gaussian points to evaluate integrations with same accuracy for momentum equation and for constitutive equation, (2) as for discritization of momentum equation with the rearranged form substitution and for getting diagonal dominant matrices, treatment of velocity (v) as known and treatment of velocity gradient (∇v) (and its transpose) as unknown, both of which appear in the definition of upper convected derivative of the elastic part of extra-stress tensor (E∇), and (3) stepwise reduction of the relaxation factors for velocity-stress fields and for free surface shape, respectively. The new method enables us to predict die-swell flow simulations at Weissenberg numbers over 400.
