J. Non-Newtonian Fluid Mech., 75 (1998) 1–23 A finite element method for computing the flow of multi-mode viscoelastic fluids: comparison with experiments C. Be ´raudo a , A. Fortin b , T. Coupez a , Y. Demay c , B. Vergnes a , J.F. Agassant a, * a Centre de Mise en Forme des Mate ´riaux, URA CNRS 1374, E ´ cole des Mines de Paris, BP 207 06904 Sophia Antipolis Cedex, France b De ´partement de Mathe ´matiques et de Ge ´nie Industriel, E ´ cole Polytechnique de Montre ´al, C.P. 6079, Succursale Centre -Ville, H3C 3A7 Montre ´al, Canada c Institut Non Line ´aire de Nice, UMR CNRS 129, 1361, route des Lucioles, 06560 Valbonne, France Received 3 February 1997; received in revised form 9 September 1997 Abstract The numerical computation of viscoelastic fluid flows with differential constitutive equations presents various difficulties. The first one lies in the numerical convergence of the complex numerical scheme solving the non-linear set of equations. Due to the hybrid type of these equations (elliptic and hyperbolic), geometrical singularities such as reentrant corner or die induce stress singularities and hence numerical problems. Another difficulty is the choice of an appropriate constitutive equation and the determination of rheological constants. In this paper, a quasi-Newton method is developed for a fluid obeying a multi-mode Phan-Thien and Tanner constitutive equation. A confined convergent geometry followed by the extrudate swell has been considered. Numerical results obtained for two-dimen- sional or axisymmetric flows are compared to experimental results (birefringence patterns or extrudate swell) for a linear low density polyethylene (LLDPE) and a low density polyethylene (LDPE). © 1998 Elsevier Science B.V. Keywords: Viscoelastic fluid flows; Geometrical singularities; Extrudate swell; Birefringence patterns 1. Introduction The numerical simulation of polymer processing needs to take into account their complex viscoelastic rheological behavior. A large number of constitutive equations have been proposed and the selection of an adequate model is obviously a critical step in the simulation of viscoelastic flows. Different criteria have to be considered but the constitutive equation should at least give satisfactory predictions in simple rheometrical flows. Furthermore, a numerical solution of the resulting governing set of equations must be possible. Generally speaking, * Corresponding author. Fax: +33 493654304. 0377-0257/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0377-0257(97)00083-9