Asymptotic freedom in the lattice Boltzmann theory

TL;DR

This paper introduces an analog of asymptotic freedom for lattice Boltzmann models, ensuring unconditional stability and providing a practical algorithm for simulating nearly-incompressible hydrodynamics.

Contribution

It develops a novel asymptotic freedom concept for lattice Boltzmann models, enabling unconditionally stable simulations of hydrodynamics.

Findings

Unconditional stability in lattice Boltzmann models achieved.

Entropy-based equilibrium is uniquely renormalizable.

Practical algorithm for stable hydrodynamic simulations developed.

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.