CALCULATION OF STEADY VISCOELASTIC FLOW USING A MULTIMODE MAXWELL MODEL - APPLICATION OF THE EXPLICITLY ELLIPTIC MOMENTUM EQUATION (EEME) FORMULATION

The finite element method based on the explicitly elliptic momentum equation (EEME) formulation for solution of viscoelastic flow problem is extended to the calculation of flows using a multimode upper convected Maxwell (UCM) model. The generalized EEME for the multimode model makes explicit the elliptic character of momentum transport in creeping flows. Mixed finite-element approximations for the velocity, pressure and stress are used to discretize the EEME and continuity equations by Galerkin's method and the constitutive equation by the streamline-upwind Petrov-Galerkin (SUPG) technique. Sample calculations are described for a two-mode model for flow between eccentric rotating cylinders. The numerical method is stable and the solutions convergent with mesh refinement. The flow structure predicted for a single-mode UCM model is largely unchanged by the addition of the second mode, although the magnitude of the stresses is affected significantly. © 1990.