Asymptotic freedom in the lattice Boltzmann theory

Abstract

Asymptotic freedom is a feature of quantum chromodynamics that guarantees its well-posedeness. We derive an analog of asymptotic freedom enabling unconditional stability of lattice Boltzmann simulation of hydrodynamics. For the lattice Boltzmann models of nearly-incompressible flow, we show that the equilibrium based on entropy maximization is uniquely renormalizable. This results in a practical algorithm of constructing unconditionally stable lattice Boltzmann models.