Reduced Subgrid-Scale Terms for Turbulence Simulations with the Lattice Boltzmann Method
Abstract
Turbulent flows span a wide range of scales, making direct numerical simulation (DNS) prohibitively expensive at high Reynolds numbers. Large eddy simulation (LES) offers a pragmatic alternative by only resolving the large-scale motions, but its accuracy hinges on the subgrid-scale (SGS) model. We introduce the Tau-orthogonal (TO) framework to the lattice Boltzmann method (LBM) using a macroscopic-velocity forcing. The TO method shifts the modeling target from a high-dimensional SGS field to the time dynamics of a small set of spatially integrated quantities of interest (QoIs). Training data are generated by a predictor-corrector tracking procedure that nudges coarse simulations toward reference QoI trajectories. Lightweight linear regression models with stochastic, multivariate Gaussian residuals (LRS) then drive the LES autonomously. Compact convolution-based kernels replace the sharp Fourier filters of the original formulation, lifting its restriction to rectangular periodic domains. We first evaluate the closure on two-dimensional Kolmogorov flow, where TO-LRS yields stable, statistically accurate online LES. However, bounded high-frequency oscillations are observed in the solution fields. The decisive test is three-dimensional turbulent channel flow, simulated on a grid five times coarser in every direction than the high-fidelity reference. Here the plain BGK solver is unstable, and even calibrated Smagorinsky and WALE models over-dissipate the near-wall flow. TO-LRS, applied on top of an eddy-viscosity substrate and with the QoI set augmented by mean-profile QoIs, reproduces the reference distributions and holds the DNS mean velocity profile, at 40× lower online cost per simulated time unit than the high-fidelity simulation. These results establish reduced, QoI-based closures as an interpretable and inexpensive alternative to high-dimensional neural SGS models for LBM.
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BibTeX
@misc{hoekstra2026reduced,
title = {{Reduced Subgrid-Scale Terms for Turbulence Simulations with the Lattice Boltzmann Method}},
author = {Rik Hoekstra and Xiao Xue and Peter V. Coveney and Wouter Edeling},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32892},
eprint = {2609.32892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32892},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Reduced Subgrid-Scale Terms for Turbulence Simulations with the Lattice Boltzmann Method
AU - Rik Hoekstra
AU - Xiao Xue
AU - Peter V. Coveney
AU - Wouter Edeling
PY - 2026
DA - 2026/09/26
PB - arXiv
DO - 10.48550/arxiv.2609.32892
UR - https://arxiv.org/abs/2609.32892
AB - Turbulent flows span a wide range of scales, making direct numerical simulation (DNS) prohibitively expensive at high Reynolds numbers. Large eddy simulation (LES) offers a pragmatic alternative by only resolving the large-scale motions, but its accuracy hinges on the subgrid-scale (SGS) model. We introduce the Tau-orthogonal (TO) framework to the lattice Boltzmann method (LBM) using a macroscopic-velocity forcing. The TO method shifts the modeling target from a high-dimensional SGS field to the time dynamics of a small set of spatially integrated quantities of interest (QoIs). Training data are generated by a predictor-corrector tracking procedure that nudges coarse simulations toward reference QoI trajectories. Lightweight linear regression models with stochastic, multivariate Gaussian residuals (LRS) then drive the LES autonomously. Compact convolution-based kernels replace the sharp Fourier filters of the original formulation, lifting its restriction to rectangular periodic domains. We first evaluate the closure on two-dimensional Kolmogorov flow, where TO-LRS yields stable, statistically accurate online LES. However, bounded high-frequency oscillations are observed in the solution fields. The decisive test is three-dimensional turbulent channel flow, simulated on a grid five times coarser in every direction than the high-fidelity reference. Here the plain BGK solver is unstable, and even calibrated Smagorinsky and WALE models over-dissipate the near-wall flow. TO-LRS, applied on top of an eddy-viscosity substrate and with the QoI set augmented by mean-profile QoIs, reproduces the reference distributions and holds the DNS mean velocity profile, at 40× lower online cost per simulated time unit than the high-fidelity simulation. These results establish reduced, QoI-based closures as an interpretable and inexpensive alternative to high-dimensional neural SGS models for LBM.
ER -