LBM and first order equilibrium

Lattice Boltzmann Method LBM: Theory
#1

Hello together,

I have a question regarding BGK LBM and its equilibrium. If one truncates the equilibrium after the linear velocity terms, the Chapman-Enskog analysis yields the Navier-Stokes equation without the quadratic velocity term (convective term). All other macroscopic quantities are not affected. However, this does not mean that the Reynolds number is zero since the partial time derivative of the velocity is still present. It cannot be removed because LBM is a kinematic Navier-Stokes solver and intrinsically time dependent. Still, a truncated equilibrium could be used at small Re in order to save computing time.
My question: Has anybody used a linearized equilibrium to simulate low Re flows, and what are the experiences? I have noticed that the code is about 25% faster, but I am not sure whether additional problems arise when the linearization is employed. Of course I wouldn’t use a linearized equilibrium for higher Re (I am working at Re << 1).

Thanks,
Timm

#2

Dear Timm,

As I know the truncated equilibrium just works fine with some flows as Poiseuille flow in low-Reynolds regime. It represents the Stokes equation. It’s good to ask about it Dr. Ginzburg by emailing her irina.ginzburg@cemagref.fr - she worked a lot with Stokes equilibrium.

Cheers,
Alex

#3

Thank you Alex, I will try to find some references by Irina or contact her.