Conversion problem (Lattice to Dimensionless) in thermal problem

Lattice Boltzmann Method LBM: Theory
#1

Hi all,

I have another problem I can not figure out …
Before starting, I precise I read most of topics on the forum, the Edmonton scaling, papers, etc … without founding the answer.

The context is the following :

I perform simulation of Rayleigh-Bénard convection in the heated cavity. The only data I have are the dimensionless parameters : Ra, Pr and the cavity length.
I starts form the lattice convection tutorial written by JLatt. The initialization is correct : I found the correct Nusselt number, the same flow structure as in the literature for different Rayleigh numbers and the good ratio of horizontal velocity u over vertical velocity v (in plane sections).

My problem is that I want to recover the dimensionless values of the velocity and I can’t manage this particular point …

In most example the (poiseuille flow, lid driven cavity) the reference velocity is known and makes the conversion “easy”. Here, I don’t understand how to process to get back the correct dimensionless values. I guess the Mach number is the key but I don’t clearly see how to use it.

Maybe this is a trivial point, but conversion is not still clear in my head …

Thanks

Best regards,

Ben

#2

Hello Ben

First of all: Do you want to recover the ‘dimensionless’ or the ‘dimensional’ velocity? The dimensionless velocity you should already have.

Timm

#3

Hi Ben,

You introduced a discrete space step dx and time step dt to set up your simulation (as described in the tutorial), right? Then the dimensionless velocity is simply u = dx/dt uLB, where uLB is the velocity in lattice units.