LBM to Physical Temperature Conversion

How can we convert Physical temperatures to LB? ( for example I want to insert my physical boundary condition temperatures into my LB code)
For velocity, in a lid driven cavity problem for instance, we use (u/Ucavity)_physical=(u/Ucavity)_LB. Where Ucavity_LB is obtained by Re and nu_LB independent from its physical value. But no such ability is available for temperature to be computed.
I have not found an answer despite so many unit conversion discussions, except natural convection case in which we can use Ra number that has deltaT term in it.

Hi Omish,

the general way to convert units in LBM to the physical units is using a dimensionless number like Re, Gr, Ra and etc.

the calculation you mentioned doesn’t convert units “(u/Ucavity)_physical=(u/Ucavity)_LB)”, it normalizes the velocity in both units.

for the temperature, you can use a dimensionless number like Ra or Gr. but if you know the high and the low value of temperature in the physical unit follow the below calculation:

T_phy = T_LBM * Diff_T_phy + T_low_phy.

for example:

T_low_phy = 20
T_high_phy = 100
Diff_T_phy = 100 - 20 = 80

T_low_LBM = 0
T_high_LBM = 1

T_LBM = 0.5

T_phy = 0.5 * 80 + 20 = 60

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Yes maybe as you say the calculations are not called “conversion”, but by it I meant that I can find physical velocities from LBM code results by using 0 to 1 scale.
The method you mentioned had come to my mind since it’s also the same 0 to 1 scaling for temperature; However I thought it is mandatory to use a dimensionless number to get a LB temperature independently first (just like finding Ucavity_LB independent from its physical values), and then use this variable change (frequently called theta) as a scale; I couldn’t find such a dimosionless number that contains T or delta T for a general case, so in fact that was the problem.
Thanks for your answer

Hi Arman, I am developing a code for melting of phase change material. In that case, the code is running, but after some time it becomes unstable . I think the problem is in unit conversion. Will you help me, how to convert units?