{
  "abstract": "The wave-particle decomposition is presented as a framework for multiscale kinetic transport, comprising a theory and an algorithm. Along the characteristics of the kinetic equation, the equilibrium integral of the solution over a local kinetic horizon defines a wave, which depends only on the conservative variables, and its exact complement defines a particle. Both obey kinetic equations whose moments are extended Navier-Stokes equations, and the conservation laws together with the particle equation form a closed system that is equivalent to the kinetic equation for every horizon. Parametrized by the ratio of the horizon to the relaxation time, these systems form a continuous spectrum from kinetic theory to Navier-Stokes hydrodynamics that adapts to the flow from cell to cell. The algorithm is a coupled wave-particle iteration for steady flows. It alternates a macroscopic iteration for the conservative variables, with the particle frozen, and a kinetic iteration for the particle, with the wave fixed. Its fixed point is the discrete kinetic solution, it is asymptotic preserving, and its near-continuum convergence factor is bounded by the share of the transport carried by the particle, a share that decays exponentially with the horizon-to-relaxation ratio. The collision model enters only through a conservative remainder, and the equations and the iteration are written out for the Bhatnagar-Gross-Krook, Shakhov and ellipsoidal statistical models, the Boltzmann and Landau equations, neutron transport and radiative transfer. The decomposition is related to the unified gas-kinetic wave-particle method, the micro-macro decomposition, penalization and synthetic acceleration. Computations of hypersonic flows past a cylinder and around the three-dimensional X38 vehicle illustrate how the division of the distribution adapts to the flow and how strongly the iteration is accelerated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33622",
  "author_total": 2,
  "authors": [
    {
      "name": "Chang Liu"
    },
    {
      "name": "Kun Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c1qht8my6vyth.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33622",
  "fulltext_url": null,
  "id": "c1qht8my6vyth",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33622",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7214783081",
  "pdf_url": "https://arxiv.org/pdf/2609.33622",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c1qht8my6vyth.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.33622",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33622"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A wave-particle decomposition framework for multiscale kinetic transport: continuous-spectrum equations and coupled wave-particle iteration",
  "title_text": "A wave-particle decomposition framework for multiscale kinetic transport: continuous-spectrum equations and coupled wave-particle iteration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/c1qht8my6vyth",
  "venue": "arXiv",
  "versions": []
}