Prsentation PowerPoint

1
3D viscoelastic fluids with complex free
surfaces Andrea Bonito and Marco
Picasso Institut dAnalyse et de Calcul
Scientifique, EPFL
1
THE MODEL
SPACE-TIME DISCRETIZATION
The problem unknowns are the volume fraction of
liquid in the whole cavity plus the
velocity , the pressure and the
extra-stress in the liquid region
Time discretization
Prediction step
Correction step
The liquid particles move with the fluid
Incompressible Navier-Stokes equations in the
liquid domain
or
or
Space discretization
Constitutive law in the liquid domain
Prediction step (left) forward characteristic
method on a structured grid improved by SLIC.
Oldroyd-B
Correction step (right) classical P1-P1-P1
finite element with GLS-EVSS stabilization.
Hookean dumbbells (with a Wiener process)
EXISTENCE AND CONVERGENCE
3D NUMERICAL SIMULATIONS
Filament stretching
Oldroyd-B (without advection terms)
Assuming
The flow of an Oldroyd-B fluid contained between
two parallel coaxial circular disks with radius
of is considered. At
the initial time, the distance between the two
end-plates is
and the liquid is at rest. Then, the top
end-plate is moved vertically with velocity
small enough ( compatibility conditions) with
, there exist an unique
and a unique approximating solution
such that
The comparison at different times between a
Newtonian fluid (top) and a non Newtonian fluid
(bottom) is done on the left
Computations with an initial aspect ratio equal
to 120. Numerical results clearly show that
non-axisymmetric fingering instabilities take
place, leading to branched structures.
Hookean dumbbells (without advection terms)
Assuming
small enough ( compatibility conditions) with
and ,
there exist a unique
and a unique
Jet buckling
The transient flow of a jet injected into a
parallelepiped cavity is reproduced. The
injection velocity is . The
comparison between Newtonian fluid (left) and a
non Newtonian fluid (right) is showed
REFERENCES
A. Bonito, M. Laso and M. Picasso, J. Comp.
Phys., 2005, Submitted.
A. Bonito, P. Clément and M. Picasso, Numer.
Math., 2005, Submitted.
1
Corresponding author supported by the Swiss
National Science Foundation andrea.bonito_at_epfl.ch