# Increasing the Reynolds number

Dear guys,

I would like to increase the time step of my simulations, i.e. I want to increase the physical length of each LB step. The advantage is that the computing times would be shorter (and the simulations less accurate).
The point is that I cannot do this by changing the lattice viscosity or the spatial resolution, since other restrictions prevent me from that.
The idea is to artificially increase the Reynolds number by a given factor (say 5 or 10). One can show that by increasing Re, the time step can be increased, but the relaxation parameter and the lattice constant can remain the same. However, modifying Re would change the physics of the problem. In my case, the physics is mainly dictated by the Capillary number, not the Reynolds number, and Re is very small (<< 1). I can now manage to increase Re but keep Ca, which should preserve the dominant physical effects in my system.
Before I start with a series of benchmark simulations: Does anybody have experience with this kind of manipulation?

Thank you,
Timm

Hello,

since your Re number is very small the right way to adimensionalize your problem is indeed to use the viscosity (and not the velocity) as a adimensionalization constant (caracteristic lengthscale). This will give you the following N-S equations (in the incompressible case):

\p_t u + Re (u*nabla) u = - nabla p + nabla^2 u.

(If the adimensionalization is done with respect to the velocity then the 1/Re is in front of nabla^2 u.)

You therefore see that as long as Re remains small the physics are more or less the same. The only thing that is needed is to rescale the velocity a posteriori.

Note that I never did such thing, but I’m pretty convinced that it should work. In order to give you more details I would need more details about the meaning of this capillary number and your physical setup.

I hope it helps a bit,
Orestis

Hello Orestis,

thanks for your reply. The capillary number in my setup is the ratio of the external body force to the fluid viscous force. Keeping it fixed ensures that the right-hand side of the NSE is invariant. As you clearly state, only the convective term is modified by a time step rescaling, IF the remaining terms are re-defined in a proper way.
I will tell you more about the exact definition of the capillary number, when this issue becomes more pressing. This cannot be explained in two or three sentences.

Timm