Lattice units

Lattice Boltzmann Method LBM: Theory
#1

Dear all,

I’ve just begun to use the LBM and I’m currently stucked with the lattice units.
I’m doing a code for the advection diffusion heat equation and for this, I have to do it in dimensionless system i.e my curve must be between 0 and 1, not 0 and N (number of nodes) because I have to compare with a FD code.

From the physical parameters, I calculated them in dimensionless parameters. Then, I deduced the dx and dt from u_lbm=0.1 and tau_lbm=0.6 that I chose. When I got the dt and dx, I made the inverse in order to get N (number of nodes) and Nt (number of steps).
I tried to follow the paper from Jonas, however I’m confused with the dx which is equal to 1/N instead to 1.
Could you tell me if the approach I described is good and where I am wrong.

Thanks.

#2

Dear all,

finally I think I’ve understood why we don’t change anything for the dx=1/N and dt=1/Nt.
Indeed, we assume that dx_lbm=1 and dt_lbm=1 and we know that dx=dx_lbm*Ch with Ch=1/N.
So we have dx=Ch.