question about dimensionless equations and units

[Cecilia Bejarano]

Hi Axel and everyone,
I have a very quick question (maybe it is a silly question
but it is certainly a very important issue).
In order to study saturation states in 2D/3D configurations (for shear
flows with Hall effect) we set some paramters in a very different way
than the previous simulations (pencil-code/samples/1d-tests/hallmri).
So now, we set, for example,
cs0=1e-4
Sshear=(-)1e-3
in the start.in file for eos_init_pars and shear_init_pars,
respectively (also for magnetic_init_pars,
we set B_ext=cs0 in order
to perform runs with beta parameter equal to 1)

I understand that the code uses the sound speed as the velocity unit
and the inverse of the shear rate as time unit.
Is this correct?
Then, if we set cs0 and Sshear not equal to 1, this implies that the
length unit also changes, doesn't it?
So, in addition, we have to change the values of the Hall parameter
and the wavenumbers in order to study the same problem with the same
spatial scales than before when cs0=1 (=B0) and Sshear=-1.

However, nothing goes as we expected, so we are doing something
wrong. I think we are misunderstanding the meaning of cs0 and Sshear
when they are different from 1.

Any suggestion or clarification?

Thanks in advance!
Cecilia

[Tobias Heinemann]

Hi Cecilia,

> I understand that the code uses the sound speed as the velocity unit
> and the inverse of the shear rate as time unit.
> Is this correct?

It's not, actually. The code uses the sound speed as the unit of
velocity only if cs0=1. You should think of cs0 as "the speed of sound
divided by the unit of velocity". So if, as in your example, cs0=1e-4,
then this means that you've chosen the unit of velocity to be the
10000th multiple of the speed of sound.

Best,
Tobi