Generalized Onsager-regularized lattice Boltzmann framework

This work presents a novel strategy to address Navier–Stokes modeling errors arising in first-nearest neighbor lattice Boltzmann 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 modeling 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, regularized, and uncorrected OReg-GEq schemes, thus presenting a promising avenue for OReg based thermohydrodynamic extensions.