THE LAGRANGIAN PARTICLE METHOD FOR MACROSCOPIC AND MICRO-MACRO VISCOELASTIC FLOW COMPUTATIONS

We propose a new numerical technique, referred to as the Lagrangian Pa rticle Method (LPM), for computing time-dependent viscoelastic flows u sing either a differential constitutive equation (macroscopic approach ) or a kinetic theory model (micro-macro approach). In LPM, the Euleri an finite element solution of the conservation equations is decoupled from the Lagrangian computation of the extra-stress at a number of dis crete particles convected by the flow. In the macroscopic approach, th e extra-stress carried by the particles is obtained by integrating the constitutive equation along the particle trajectories. In the micro-m acro approach, the extra-stress is computed by solving along the parti cle paths the stochastic differential equation associated with the kin etic theory model. Results are given for the start-up flow between sli ghtly eccentric rotating cylinders, using the FENE and FENE-P dumbbell models for dilute polymer solutions. (C) 1998 Elsevier Science B.V. A ll rights reserved.