{
  "abstract": "We consider variable-density Cahn--Hilliard--Navier--Stokes (CHNS) discretizations on finite element meshes that may change between accepted time levels through fixed-topology motion or topology-changing remeshing. When the discrete spaces vary in time, the phase, kinetic, and pressure histories entering a multistep scheme are measured in different discrete structures and cannot, in general, be transferred by a single operator. We develop decoupled backward Euler (BE) and second-order backward differentiation formula (BDF2) schemes by combining exact physical cross-mesh pairings with history representations compatible with the corresponding phase-energy, kinetic-energy, and pressure-gradient storages. The phase update also determines an Abels--Garcke--Grün-consistent mass flux used in the momentum transport. A scalar capillary-exchange equation separates the phase and fluid solves while retaining the discrete energy exchange. The resulting field subproblems are linear, the scalar equation has a unique positive solution, and the schemes satisfy modified energy balances without a time-step restriction under the stated admissibility assumptions. Numerical experiments confirm second-order temporal convergence under both mesh updates, phase-mass conservation, modified-energy decay in the unforced tests, and comparable Rayleigh--Taylor and rising-bubble dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21328",
  "author_total": 4,
  "authors": [
    {
      "name": "Wenbin Wang"
    },
    {
      "name": "Yunqing Huang"
    },
    {
      "name": "Yin Yang"
    },
    {
      "name": "Huayi Wei"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a1zh8regz3bsn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21328",
  "fulltext_url": null,
  "id": "a1zh8regz3bsn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21328",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7213918769",
  "pdf_url": "https://arxiv.org/pdf/2609.21328",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a1zh8regz3bsn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21328",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21328"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "History-Compatible Energy-Stable Finite Element Schemes for Variable-Density Cahn--Hilliard--Navier--Stokes Flows on Evolving Meshes",
  "title_text": "History-Compatible Energy-Stable Finite Element Schemes for Variable-Density Cahn--Hilliard--Navier--Stokes Flows on Evolving Meshes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/a1zh8regz3bsn",
  "venue": "arXiv",
  "versions": []
}