How to convert physical units in to LBM units

Lattice Boltzmann Method LBM: Theory
#1

Hello everyone,

Being a beginer in LBM, i am missing the important link between physical units and LBM units

I solved ‘1-D unsteady conduction in slab’ using finite volume method.

Physical Data:

slab thickness= 2 cm
Thermal conductivity= 10 W/m.K
Heat capacity (rho*c)= 10x10^6 J/m^3.K
at time t=0, Temperature of slab=200 degree Celcius
at time t>0, Left boundary= adiabatic, Right boundary temperature=0 degree Celcius
I want to analyse temperature distribution along slab thickness at 40 sec.

FVM units:
Number of nodes=5
hence, Delta x=0.004 m
delta t<8 sec to get stable solution, let us say delta t=2 sec
hence, number of time step=20
Remaining material properties are as above

LBM Units:
let us take, Number of lattice units=100
my doubts are:

  1. How to decide number of time steps require to get temperature distribution at 40 sec?
  2. In LBM, most popular method is to use unity for delta x and delta t, how these are related to number of lattice units?
  3. It is said that thermal diffusivity is related to relaxation time. Thermal diffusivity of most of the material are of the order of 10^-6, should we have to convert it into Lattice diffusivity in order to calculate relaxation time?

Thank you.

#2

Hello,

You can find a large number of similar threads in this forum. Please take a look around. I guess that this document can also help you.

Best wishes,
Timm

#3

Hello,
Works of R. Djebali et al. may help you surely, such as this paper
or Djebali thesis in this link at page 125 of 160.
For other query follows any of emails in http://www.ridhadjebali.sitew.com.
Best.

#4

Thank you very much Timm and Djebali for your support.
My result matches with that of FVM for constant temperature boundary condition.