I would like to understand how can we deal with high Schmidt numbers when trying to use a passive scalar Diffusion problem.

For example, for my hydrodynamic problem of a flow past a cylinder corresponding to a Reynolds = 230 and a mesh resolution on yDim = 80 nodes. I have a relaxation time tau_fluid = 0.513,

If I want to couple this hydrodynamic problem with a passive scalar diffuion mesh with a Schmidt = 7300, then I realize that my corresponding relaxation time for the diffusion is tau_diffusion = 0.500001785, which obviously is too narrow to the 0.5 threshold and therefore there are no results of my diffusion problem.

I tried to increase my mesh resolution, but still is not enough. What can I do?

higher mesh resolution -> better computers and parallel code

different collision operator (MRT, TRT, I’m not sure if the entropic or cascaded LBM can be used for diffusion as well?)

decouple the hydrodynamic and mass transfer lattices so you can tune the relaxation times separately (this will mean you will have to interpolate the velocities between grids somehow, which can be a problem in unsteady flows)

modify the weighting factors as suggested by Ronald Blaak, Peter M.A. Sloot, Lattice dependence of reaction-diffusion in lattice Boltzmann modeling, Computer Physics Communications 129 (2000) 256–266. Also check S.P. Sullivan, F.M. Sani, M.L. Johns, L.F. Gladden, Simulation of packed bed reactors using lattice Boltzmann methods, Chemical Engineering Science 60 (2005) 3405 – 3418 who argue it would be possible to achieve Peclet numbers as high as 10⁸ with this modification.

compute the scalar diffusion with a different method for example finite volume, only using LBM for the flow, check J. J. Derksen, The Lattice-Boltzmann Method for Multiphase Fluid Flow Simulations and Euler-Lagrange Large-Eddy Simulations. Here also the possibility of filtering and subgrid scale models inside LBM are explained.

I was solving a diffusion problem some time ago where I had the same problem. These were the possible solutions but I never tried any of them. With BGK and a regular laptop I think you should be able to get to around Pe = ~ 1500 without too much hassle.