I have written general codes for predicting temperature on 1D and 2D using D1Q3 , D2Q4

I have few doubts regarding number of iterations in LBM and duration of predictions

tau(relaxation time)= thermal diffusivity/(c**2)+(delta t/2)

where c is dx/dt

and omega =dt/tau

Suppose I take dx=L/(number of grid points -1) and dt=time/(number of time steps)

and not as dx=1 , dt=1

Will it be correct ?

If not , can someone explain why dx=dt=1 and how one can relate number of iteration and time ?

Problem in 1D

alpha=1e-6 , t=10 seconds (prediction at), How to compute omega ?