{
  "abstract": "We analyze the moment hierarchy of a Callaway lattice Boltzmann model for phonon hydrodynamics and derive exact steady-state solutions for a driven planar channel with diffuse walls. The collision operator decomposes the population space into conserved, heat-flux, and fast kinetic sectors, whose coupling through streaming determines the transport response. For the two-dimensional, eight-velocity (D2Q8) lattice Boltzmann model, we derive a fully discrete closure that relates the heat flux to transverse kinetic moments. The higher-order transverse kinetic moment contains both a second-difference term and an explicit contribution from the imposed energy drop. Diffuse-wall population constraints then determine the heat-flux and kinetic-moment profiles without fitted parameters. The resulting solution reproduces the numerical bulk moment amplitudes and wall slip, while an exact wall relation separates the contribution of the higher-order moment from deviations from the leading gradient approximation. Finite-wave-number analysis further resolves the collision-sector mixing associated with longitudinal propagation. These results provide a unified description of collision relaxation, the moment hierarchy, and boundary response within the specified discrete model.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36146",
  "author_total": 1,
  "authors": [
    {
      "name": "Shimpei Saito"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dywgffw9e096k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36146",
  "fulltext_url": null,
  "id": "dywgffw9e096k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36146",
  "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",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2206|Lattice Boltzmann Simulation Studies"
    ]
  ],
  "openalex": "W7214972949",
  "pdf_url": "https://arxiv.org/pdf/2609.36146",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dywgffw9e096k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36146",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36146"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Moment hierarchy and exact steady-state solutions in a Callaway lattice Boltzmann model for phonon hydrodynamics",
  "title_text": "Moment hierarchy and exact steady-state solutions in a Callaway lattice Boltzmann model for phonon hydrodynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/dywgffw9e096k",
  "venue": "arXiv",
  "versions": []
}