I am new user on the LBM modeling. I got the sample code of flow past cylinder online and I am familiar with the code now.

I need solve diffusion problem using LBM model. Does anyone know where I can find the sample LBM code for diffusion phenomena? (Matlab or Fortran version)

Actually, here’s a funny fact about lattice Boltzmann: you can use just any LB code which was written for fluid dynamics and use it to solve a diffusion equation (or, an advection-diffusion equation if you want).

Here’s the procedure: take for example the Matlab code for the lid-driven cavity. Then, take the density rho as your diffused scalar, erase all terms in which the velocity u appears, and re-interpret the viscosity nu as being the diffusivity constant D. That’s it.

For example, the computation of the equilibrium

cu = 3*(cx(i)*ux+cy(i)*uy);
fEq(i,:,:) = rho .* t(i) .* ...
( 1 + cu + 1/2*(cu.*cu) - 3/2*(ux.^2+uy.^2) );

is simply replaced by

fEq(i,:,:) = rho .* t(i);

Once your code works, you can make it more efficient by switching from a 9-neighbor lattice to a 4-neighbor lattice.

hi
for a cavity cod with lid driven and size 100*100 and nu=0.05 and vilocity of lid driven is uw=0.05 and itteriton is (timestep=15000)
how much reynolds number ( RE=?)

with changing of uw how changing RE number ?
how relation between RE , NU , UW ,SIZE OF CAVITY , TIME STEP?

With the equilibrium distribution function in your reply, we cannot recover the macroscopic velocities. So, I believed the equilibrium distribution function will be:

fEq(i,:, = rho .* t(i).*(1+cu);

I am writing it from my very naive understanding so please correct me if I am wrong and please explain on this issue.

hi
for a cavity cod with lid driven and size 100*100
and nu=0.05 and vilocity of lid driven is
uw=0.05 and itteriton is (timestep=15000)
how much reynolds number ( RE=?)

with changing of uw how changing RE number ?
how relation between RE , NU , UW ,SIZE OF CAVITY
, TIME STEP?