In the BGK collision model for the Lattice Boltzmann Method, the solution becomes unstable when the relaxation time approaches 0.5. This happens when I increase my Reynolds number, $$Re =UL/\nu$$ which gives me my viscosity and is related to the relaxation time, tau, with $\Delta x$ and $\Delta t$ set to unity: $$\tau = 3\nu +0.5$$
I've read that the MRT collision model is able to simulate flows of higher Reynolds numbers using multiple relaxation times.
My question is, how does MRT bypass the limitation of the BGK model of tau being >0.5 and have it only depend on the Reynolds number? Right now, I am limited to Re of around 200 for cylinder in incompressible external flow using BGK, and I'd like to extend my code to simulating airfoils which can reach Re of 10^6.