{
  "abstract": "Explicit lattice Boltzmann simulations of slow transient flows are constrained by the acoustic time step. Dual-time stepping can remove this restriction, but slow inner convergence has limited reported wall-clock gains to roughly four- to tenfold, without a mechanism that strengthens under refinement. We present the macroscopic-shadow-corrected lattice Boltzmann method (MSC-LBM), which applies defect correction to the unsplit kinetic residual. At each Fourier wavenumber, a Stokes-like system is solved exactly for the conserved residual moments while preserving the second-order backward-differentiation formula (BDF2) fixed point and temporal accuracy. Along the two-relaxation-time axis $Λ=1/4$, $ω^+=ω^-=1$ makes one collision eliminate all non-hydrodynamic perturbations; $η(ν)=|6ν-1|/(6ν+1)$ vanishes at $ν=1/6$, leaving hydrodynamic slow modes whose long-wave shadow is inverted by the corrector. In completed timing campaigns, MSC-LBM achieves 27.95- and 52.71-fold wall-clock speedups at $N=256$, $\\mathrm{Re}=1$ under matched-accuracy and $1\\%$ gates. The matched speedup rises monotonically to 122.02 at $N=1024$, with gains persisting across $\\mathrm{Re}=10^{-4}$--$100$. The three-dimensional D3Q19 extension reaches 27.85 and 8.84 under the same gates at $N=128$, $\\mathrm{Re}=1$. A bounce-back-consistent kinetic coarse solver with adaptive relinearisation extends MSC-LBM to fully enclosed cavities, yielding setup-excluding physical-march speedups of 26.86 at $\\mathrm{Re}=10$ and 3.84 at $\\mathrm{Re}=100$ for $N=128$. An exact per-wavenumber symbol inverse establishes the attainable off-design contraction envelope. The contraction, parameter-sweep, and timing results jointly delimit the demonstrated operating regime: low-to-moderate-Reynolds-number transients for which acoustic stepping need not dictate computational cost.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39474",
  "author_total": 4,
  "authors": [
    {
      "name": "Yanhui Ding"
    },
    {
      "name": "Yaolong Yu"
    },
    {
      "name": "Yuan Yu"
    },
    {
      "name": "Hao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99ymxp9z17ktt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39474",
  "fulltext_url": null,
  "id": "99ymxp9z17ktt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39474",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Lattice Boltzmann Simulation Studies"
    ]
  ],
  "openalex": "W7215096612",
  "pdf_url": "https://arxiv.org/pdf/2609.39474",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99ymxp9z17ktt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39474",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39474"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows",
  "title_text": "A macroscopic-shadow-corrected lattice Boltzmann method for fast, time-accurate simulation of low-Reynolds-number transient flows",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/99ymxp9z17ktt",
  "venue": "arXiv",
  "versions": []
}