Almost all (99%) write a BGK term as -(f-fsup[/sup])/tau.

Why not to write down more naturally (fsup[/sup]-f)/tau?

Because (f - f^eq) / tau = f^neq / tau is the non-equilibrium part

You can write it as you wish, but using the additional minus sign is actually more natural from a physical point of view.

Thanks, but both expressions are completely equivalent. Probably the first record is simply historical tradition without any physical sense?