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 so...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 1998-11, Vol.79 (2), p.387-403
Main Authors: Halin, P, Lielens, G, Keunings, R, Legat, V
Format: Article
Language:English
Subjects:
Computational methods in fluid dynamics
Exact sciences and technology
FENE dumbbells
Finite element method
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Non-newtonian fluid flows
Physics
Stochastic simulation
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Summary: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.
ISSN:0377-0257
1873-2631
DOI:10.1016/S0377-0257(98)00123-2