Convection diffusion with large variation of Peclet number

I work on the convection diffusion equation using the LB method, I vary the Peclet from 0.1 to 10 ^ 5, the concentration profile that I obtain is not always fair
i use the f eq = w(k)c(i,j)(1+3cU/ck)
with c(i,j) the concentration
c=velocity nodes
U macroscopic velocity u0y
and omega= dt/((3dx²/(Pe
ican’t varied with this for a large Peclet
but i find for Pe=1000 to Pe=5000 a concentration profile that can be coherent
for other peclet i can’t find a solution
thank you for your support


I do not really understand what you want to say, could you please explain this more clearly?


Thanks Timm,
I must solve the convection diffusion equation with Lattice Boltzmann.
The non dimensional equation that i use is:
C is the concentration
I use D2Q9
I must plot the Concentration profile in the channel for a large variation of Peclet number ie: from Pe=0.1 to Pe=10^5.
Im not sure if the equilibrum function that i use is correct.
im not sure too that omega=dt/(relaxation time) is adequate
and how can I do this large variation without divergent result
Thank you for your support

There should be a lot of articles in the literature about advection-diffusion and the corresponding equilibrium in the LBM. A large Peclet number means that you need a diffusion relaxation time very close to 0.5. The Peclet number you can reach depends on the minimum tau you can take for diffusion. I am not sure if this is possible without additional numerical tricks. Anybody else with experience in this field?

Can I vary Peclet number and dt in the same time?
i means for a Peclet chosen i chose a dt ?

Yes, you can.
For a system without diffusion, the time step is uniquely defined by the spatial resolution, the relaxation time, and the Reynolds number. The diffusivity is then introduced as an additional, independent parameter (via an additional relaxation time). There are many threads in this forum about the unit conversion and control about the simulation parameters. You should have a look.

im a beginner in this fields, I found this forum by chance and I find it very interesting
thank you

Dear Wafikos,

TRT is a real remedy to use with type flows with largely varying Peclet numbers. Try Google Scholar to find some articles. You can obtain stable and accurate simulations. BGK in this case produces inaccurate results.


dear Alex,
I tried to use TRT but i found great difficulty in assimilating and understanding the expression of equilibriuim function, can you help me in this field please?
Thank you

Dear Wafikos,

Send me your scanned calculations and the article you used. I will correct them for the equilibrium function. Please indicate the model you want to use.

My email is