Towards nonlinear thermohydrodynamic simulations via the Onsager-Regularized Lattice Boltzmann Method

TL;DR

This paper develops a theoretical framework for the Onsager-Regularized lattice Boltzmann method, improving accuracy and reducing errors in nonlinear thermohydrodynamic simulations without external corrections.

Contribution

It provides a generalized, assumption-free analysis of the OReg LB method, demonstrating enhanced accuracy and automatic correction of lattice isotropy issues for standard lattices.

Findings

OReg scheme yields more accurate macroscopic dynamics than BGK model.

Automatic compensation for lattice isotropy deficiencies in D2Q9 lattice.

Numerical validation on shear wave and shocktube problems.

Abstract

This work presents a generalized, assumption-free, and stencil-independent theoretical analyses of the recently proposed Onsager-Regularized (OReg) lattice Boltzmann (LB) method [Jonnalagadda et al., Phys. Rev. E 104, 015313 (2021)] and demonstrates its ability to mitigate spurious errors associated with the insufficient isotropy of standard first-neighbor lattices without the inclusion of any external correction terms. The hydrodynamic limit recovered by the OReg scheme is derived for two equilibrium distribution functions, namely the so-called thermal guided equilibrium and the popular second order polynomial equilibrium, to show that the OReg scheme yields macroscopic dynamics that are O(u) times more accurate than that of the bare BGK collision model. Specifically, we show that, with the guided equilibrium on the D2Q9 standard lattice, the OReg scheme inherently compensates for the insufficient lattice isotropy of the standard D2Q9 lattice by automatically adjusting the lattice viscosity, yielding O(u4) and O(u2) accurate kinetic models when operated at the reference and arbitrary temperatures respectively. Further, we also show that the OReg scheme presents an O(u3) accurate kinetic model for the D2Q9 lattice when used with the second order polynomial equilibrium formulation. Thereafter, the accuracy of the OReg-guided-equilibrium kinetic model is numerically demonstrated for quasi-one-dimensional simulations of the rotated decaying shear wave and isothermal shocktube problems. The present work lays the theoretical foundation of a generic framework which can enable fully local, correction-free, nonlinear thermohydrodynamic LB simulations on standard lattices, thereby facilitating scalable simulations of physically challenging fluid flows.