{
  "abstract": "Deterministic micro--macro simulation of polymer solutions requires the coupled evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker--Planck/lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and polymer stress are approximately $0.0309\\%$ and $3.84\\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro--macro method to viscoelastic flows under different boundary constraints.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.32147",
  "author_total": 6,
  "authors": [
    {
      "name": "Xueqin Liu"
    },
    {
      "name": "Shi Shu"
    },
    {
      "name": "Yaolong Yu"
    },
    {
      "name": "Yuan Yu"
    },
    {
      "name": "Hao Zhang"
    },
    {
      "name": "Yuting Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5kcg3xgwnv2fq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.32147",
  "fulltext_url": null,
  "id": "5kcg3xgwnv2fq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.32147",
  "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.flu-dyn"
    ],
    [
      "openalex",
      "2206|Lattice Boltzmann Simulation Studies"
    ]
  ],
  "openalex": "W7214764441",
  "pdf_url": "https://arxiv.org/pdf/2609.32147",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5kcg3xgwnv2fq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.32147",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.32147"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A deterministic Fokker--Planck/lattice-Boltzmann micro--macro solver for dilute Hookean polymer solutions",
  "title_text": "A deterministic Fokker--Planck/lattice-Boltzmann micro--macro solver for dilute Hookean polymer solutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:12Z",
  "url": "https://research.draconitic.com/paper/5kcg3xgwnv2fq",
  "venue": "arXiv",
  "versions": []
}