# Choice of LBM units

Hi,

I fairly new to LBM and I am trying to wrap my head around the choice of units for LBM. I am using the externalFlowAroundObstacle example case as a starting point but when I change the parameters to fit my case the simulation quickly diverges.

I am trying to simulate the following case:
Domain dimensions (length x width x depth) = 3.135 x 0.486 x 0.326 m
Inlet velocity = 0.183 m/s
Kinematic viscosity = 1.0e-6 (m^2/s) [i.e. Water]
Reynolds Number (based on depth) ~ 60000

Lattice Units:
Resolution = 98/0.486 = 200 nodes/m
dx = 4.96e-3
By fixing the lattice velocity at 0.01 to keep the mach number low (incompressible)
dt = 2.71e-4

This results in the relaxation parameter being:
tau = 0.500033057

I am assuming that the reason for the simulation diverging is that tau is too close to 0.5 but any any combination that I try to increase it either leaves me with a ridiculously high resolution or a very high Mach number either of which is unacceptable for the case I am trying to simulate.

Also LES modelling is activated with a Smagorinsky constant of 0.2

Any advice will be greatly appreciated.
Thank you

Hello,

although U=0.01 (velocity in lattice units) assures you a very low Mach number it is in practice of limited interest because of the value of tau which is too close to 0.5 and therefore a high instability. You could try to increse it. A value like 0.1 could be a good choice actually.

Best regards,

Hi,

Thanks for the advice, but if I increase the velocity to 0.1 like you suggest the value of tau only increases to 0.50033 and the simulation still diverges.

Kind regards,
NSangtani

Hi NSangtani and malaspin,
I’m also not familiar with the choice of latticeU. As we know the latticeU should be lower than sound speed.
I’m puzzled with the value of sound speed. I read in some books that it is calculated as below.
For example , in D3Q19, is the sound speed=1/sqrt(3)dx/dt ?
As in your case, is sound speed =1/sqrt(3)
4.96e-3 / 2.71e-4 = 10.56 ?
Is that right?

And how much lower should the latticeU be than sound speed in incompressible problems at least?

Please forgive my newbie’s question.

best wishes,
steed188