Generalized Onsager-Regularized Lattice Boltzmann Method for error-free Navier-Stokes models on standard lattices

TL;DR

This paper introduces a new Onsager-Regularized lattice Boltzmann method that corrects modeling errors on standard lattices, significantly improving accuracy and stability for Navier-Stokes simulations.

Contribution

It develops fully local correction strategies for lattice Boltzmann models, enabling error-free Navier-Stokes simulations on standard lattices with improved accuracy.

Findings

Partially corrected models improve accuracy by 2-4 orders of magnitude.

Fully corrected models eliminate stress tensor errors.

Numerical benchmarks show enhanced stability and precision.

Abstract

This work presents a novel strategy to address Navier-Stokes modelling errors arising on first-nearest neighbour lattice Boltzmann (LB) methods and introduces fully local corrections through Onsager-Regularized (OReg) non-equilibrium populations. The proposed mechanism, which admits partially and completely corrected OReg models, is used to develop representative partially and completely corrected models for the six-moment-constrained guided equilibrium (GEq) representation on the D2Q9 lattice. The former realization only addresses compatibility condition violations and improves the accuracy by two/four orders of magnitude at reference/arbitrary lattice temperatures respectively, while the latter additionally corrects stress tensor modelling errors, resulting in a fully corrected exact model. Numerical benchmarks of the corrected schemes demonstrate improved accuracy and stability in comparison to the Lattice-BGK and uncorrected OReg-GEq schemes thus presenting a promising avenue for OReg based thermohydrodynamic extensions.