Numerical stability in multicomponent diffusion

Lattice Boltzmann Method LBM: Theory
#1

Hi all,

I was interested in simulating diffusion in a ternary mixture with palabos, but I’m having problems with numerical (in)stability. My first thought was to try and modify the multiComponent2d example included in palabos source files, however, the system i’m interested in has one component (ethyl glycol) which is much more viscous than the others (about an order of magnitude apart). Therefore when I compute


tau=3*nuLB+0.5;

I get ratios of TauMax/TauMin ranging from 2 to 10, depending on how I make my physical units dimensionless. however if I try to make this ratio small, the values of the relaxation times come very close to 0.5, which is also numerically unstable.
So far I’ve only been able to simulate a ternary mixture with the Shan-Chen model by choosing unphysical values for tau. Is there a better way to simulate this situation with palabos?

#2

Hi Asasuser,

I would not use the shan-chen model for diffusion… Even if I read it can be used you will find difficulties in relate physical parameters (i.e diffusion coefficient) to you relaxation time. As far as I know, lattice-boltzmann has a scheme for Advection-diffusion problems which is proved recovers the advection-diffusion equation in the continuum limit.

In palabos the advection-diffusion is already implemented and, the most common, is under the dynamics “AdvectionDiffusionBGKDynamic”. Bascally, if you can describe your problem using a sort of advection-diffusion equation you should defenetly use that dynamic.

Let me know if you need more information…