A numerical tool for the study of the hydrodynamic recovery of the Lattice Boltzmann Method

TL;DR

This paper introduces a numerical approach to analyze the hydrodynamic recovery of the Lattice Boltzmann Method in turbulence, validating it against spectral methods and exploring its potential for implicit subgrid-scale modeling.

Contribution

It develops an exact balance relation-based method for studying LBM hydrodynamics and benchmarks its performance in turbulence simulations, highlighting its applicability for implicit SGS modeling.

Findings

Validated the approach on decaying turbulence against spectral simulations.

Benchmark results for forced turbulence at increasing Reynolds numbers.

Potential for quantifying implicit SGS models within LBM.

Abstract

We investigate the hydrodynamic recovery of Lattice Boltzmann Method (LBM) by analyzing exact balance relations for energy and enstrophy derived from averaging the equations of motion on sub-volumes of different sizes. In the context of 2D isotropic homogeneous turbulence, we first validate this approach on decaying turbulence by comparing the hydrodynamic recovery of an ensemble of LBM simulations against the one of an ensemble of Pseudo-Spectral (PS) simulations. We then conduct a benchmark of LBM simulations of forced turbulence with increasing Reynolds number by varying the input relaxation times of LBM. This approach can be extended to the study of implicit subgrid-scale (SGS) models, thus offering a promising route to quantify the implicit SGS models implied by existing stabilization techniques within the LBM framework.