# Two-Relaxation Time

Hi every one
I am new in LB and I want to use Two-Relaxation time. I found the formulation in a paper but I couldn’t find what is the relation between the two relaxation times (symmetric and anti-symmetric ). ( if they are equal ,then we get BGK ).
If any one has any information or an idea will be highly appriciated.
Thank
Mas

Dear Mas,

Antisymmetric parameter is fixed by the problem you simulate - either diffusion for the advection-diffusion equation or viscosity for the Navier-Stokes equation. Another one is a free parameter, which can be controlled from the things you want to ensure. This parameter can be derived from the so-called “magic” parameter:
\Lambda = (\tau_anti-1/2)(\tau_sym-1/2)

\Lambda=1/4 - optimal stability
\Lambda=1/6 or 1/12 is for better approximations of advection-diffusion equations. Third (fourth) order spatial errors are canceled.

Hopefully it will help,
Alex

Dear Alex,
Thank you for your explanations and valuable information.
MAs