Dear All,
Another turn of LB science)), and I would be very grateful for your comments.
MY SYSTEM:
I have a small obstacle of radius a~1mkm in water (I remember Timm’s post about LB for blood cells;
and in my case I have some artificial, but also soft, polymeric object). Because of small radius, Reynolds is also small, Re~1/10-1/100. (fluid velocity V ~1 cm/s, viscosity for water nu~1/100 cm2/s at room temperature).
In lattice units it gives the viscosity nu~10-100 and the relaxation time tau~3*nu~30-300,
if we take V~0.01-0.1 and a~10. So, tau is huge for small Re!
PROBLEMS:
-
From common sense it means that the fluid needs to propagate over about 30-300 lattice length
to come into equilibrium! With a~10 (that is <<300), it is clearly Knudsen regime and we can forget about
hydrodynamics (it’s kinetics). It’s bad, because in real water we have, of course, pure hydrodynamics for mkm scales. -
Also, with such a long tau I have to have an LB lattice of size L>300 (say, a lattice 1000x1000x1000),
because on smaller lattice the interaction of the objects through the fluid is strongly non-local,
that most probably leads to unphysical behavior. But such a lattice looks terribly huge.
I feel that computations on this lattice could be extremely lengthy.
My QUESTIONS are:
** Does this all mean that LB is inapplicable/unsuitable for such small Re numbers?
** Or, maybe, we can tune the LB parameters somehow, to use it for small objects/ small Re’s?
(I want LB because it gives huge advantages and is elegant))).
What do LB gurus think about it? What does the experience of others say in this case?
Best regards,
German