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.
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.
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
let us take, Number of lattice units=100
my doubts are:
- How to decide number of time steps require to get temperature distribution at 40 sec?
- In LBM, most popular method is to use unity for delta x and delta t, how these are related to number of lattice units?
- 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?