Mass conservation

Lattice Boltzmann Method LBM: Theory
#1

Dear All.

It seems from the book of Dieter A. Wolf-Gladrow:
“Lattice-Gas Cellular Automata and Lattice Boltzmann Models - An Introduction”, pag 173-174, that the collision operator and the body forces don’t contribute to the mass conservation equation. By running the matlab code “Rayleigh-Bénard convection” i tried to consider their contribution. By summing the 9 terms for the distribution equation:

fOut(i,:,:slight_smile: = fIn(i,:,:slight_smile: - omegaNS .* (fIn(i,:,:)-fEq(i,:,:)) + force(i,:,:);

it seems that, while the body force sum is zero, the streaming and the collision operator contribution have the same value. I get confused about that so maybe someone may help me. Thanks,

Stefano

#2

Hi Stefano,

What do you mean about streaming operator contribution? The collision operator doesn’t contribute because:
-omegaNS. \sum_k (fln(i,j,k)-fEq(i,j,k))=-omegaNS (\rho - \rho)=0

The body force doesn’t contribute so you need to have the following summation to equal zero \sum_k{force(i,j,k)}=0. fOut is actually postcollision values. It means that with the body force the summation of postcollision populations and precollision one conserves density which inherently should be satisfied by collision operator and force contributions (see above).

Hopefully it will help,
Alex