The Lagrangian particle method for macroscopic and micro-macro viscoelastic flow computations

We propose a new numerical technique, referred to as the Lagrangian Particle Method (LPM), for computing time-dependent viscoelastic flows using either a differential constitutive equation (macroscopic approach) or a kinetic theory model (micro-macro approach). In LPM, the Eulerian finite element solution of the conservation equations is decoupled from the Lagrangian computation of the extra-stress at a number of discrete particles convected by the flow. In the macroscopic approach, the extra-stress carried by the particles is obtained by integrating the constitutive equation along the particle trajectories. In the micro-macro approach, the extra-stress is computed by solving along the particle paths the stochastic differential equation associated with the kinetic theory model. Results are given for the start-up flow between slightly eccentric rotating cylinders, using the FENE and FENE-P dumbbell models for dilute polymer solutions. (C) 1998 Elsevier Science B.V. All rights reserved.