LBM Sample code for diffusion

Lattice Boltzmann Method LBM: Theory
#1

Hi,

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)

thanks a lot!
Liang

#2

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.

You can find more information in this thesis.

#3

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?

PLEASE HELP ME .

#4

Hello Jonas,

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,:,:slight_smile: = 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.

Sincere gratitude for creating this forum!

Regards,

Nitesh

#5

Hello,

it depends on what macroscopic equation one wants to simulate.

If one wants pure diffusion : d/dt rho = kappa * Laplacian(rho)
or advection-diffusion : d/dt rho + u*grad rho = kappa Laplacian(rho).

In the first case feq = t(i)*rho in the other feq=t(i)rho(1+c_i * u/cs^2).

#6

Hello Orestis,

Thanks for the reply.

Completely agree with you and Jonas. I understood the point.

Regards,

Nitesh

#7

alireza378 Wrote:

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?

PLEASE HELP ME .

#8

hi
I am new lbm user.
I need simple code by lbm for start.

#9

hello
for the cavity code there is maxT=40000
what this number of iterations physically means ? and how it is chosen?
thanks