{
  "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 $40\\times$ 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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32892",
  "author_total": 4,
  "authors": [
    {
      "name": "Rik Hoekstra"
    },
    {
      "name": "Xiao Xue"
    },
    {
      "name": "Peter V. Coveney"
    },
    {
      "name": "Wouter Edeling"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/640kv8bjd54pk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32892",
  "fulltext_url": null,
  "id": "640kv8bjd54pk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32892",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DS"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Lattice Boltzmann Simulation Studies"
    ]
  ],
  "openalex": "W7214729700",
  "pdf_url": "https://arxiv.org/pdf/2609.32892",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/640kv8bjd54pk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.32892",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32892"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Reduced Subgrid-Scale Terms for Turbulence Simulations with the Lattice Boltzmann Method",
  "title_text": "Reduced Subgrid-Scale Terms for Turbulence Simulations with the Lattice Boltzmann Method",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/640kv8bjd54pk",
  "venue": "arXiv",
  "versions": []
}