Peter Wapperom, Roland Keunings, and Vincent Legat
The Backward-tracking Lagrangian Particle Method for Transient
Journal of Non-Newtonian Fluid Mechanics 91 (2000) 273-295
A new Lagrangian particle method for solving transient viscoelastic flow
for both macroscopic and microscopic stress equations is proposed.
In this method, referred to as the Backward-tracking Lagrangian Particle
Method (BLPM), we specify the particle locations and calculate the
trajectories leading to these locations.
This backward tracking process is stopped after a specified time
(possibly only a single time step), and the initial configuration for the
integration of the stress is obtained by interpolating a stored Eulerian
field at that time.
In order to demonstrate the accuracy, efficiency and stability of the
method, we consider two benchmark problems in the context of the FENE
dumbbell kinetic theory
of dilute polymer solutions and its FENE-P approximate constitutive
equation: the high eccentricity journal bearing flow and the 4:1
contraction flow. With the help of these examples, we show in which manner
accurate and stable results can be obtained, for transients of both
polymer stress and stream function, with a minimum number of particles and
a minimum particle path length.
Lagrangian particle method; backward tracking;
viscoelastic fluids; kinetic theory; constitutive models