Reference for D3Q7(D3Q6) advection-diffusion LBM

Hello everyone,

Does anyone know of the paper(s) which first investigated the use of the D3Q7(or D3Q6) BGK-LBMs for the advection-diffusion equation? I found many articles mentioning them briefly, but I cannot track it down for referencing…

Many thanks,

Dear Dragos,

It depends what you want - I don’t have the initial reference, but I have the specifications for D3Q7 (equilibrium functions and so on). Please let me know if you need the paper with the equilibrium functions specified.


Dear Alex,

That would be great! I found bits and pieces, but not the whole model specification.

Best wishes,

You should definitly start here:

I. Ginzburg, Equilibrium-type and Link-type Lattice Boltzmann models for generic advection and anisotropic-dispersion equation, Adv Water Resour, 28, 2005

but I have to warn you, I. Ginzburgs papers a hard to read. This would also be a good starting point:

Stiebler et al., Advection–diffusion lattice Boltzmann scheme for hierarchical grids

Good luck!