Chapter 12 showed how to circumvent two major stumbling blocks of the LGCA approach: statistical noise and exponential complexity of the collision rule. Yet, the ensuing LB still remains connected to low Reynolds flows, due to the low collisionality of the underlying LGCA rules. The high-viscosity barrier was broken just a few months later, when it was realized how to devise LB models top-down, i.e., based on the macroscopic hydrodynamic target, rather than bottom-up, from underlying microdynamics. Most importantly, besides breaking the low-Reynolds barrier, the top-down approach has proven very influential for many subsequent developments of the LB method to this day.
An Investigation into the Numerical Robustness of High-order Lattice Boltzmann Models
