{
  "abstract": "We propose a Discrete Duality Finite Volume (DDFV) scheme for a phase-field model of surfactant dynamics during the phase separation of a two-phase flow. The model couples two Cahn-Hilliard equations, for the phase-field variable and for the surfactant concentration. We discretize the model in space via the DDFV method, well-suited to general meshes and nonlinear diffusion, and in time via a semi-implicit Euler scheme. The discrete scheme and the corresponding numerical analysis rely on two dedicated operators discretizing the nonlinear term coupling the surfactant concentration and the phase-field gradient consistently across the primal, dual and diamond meshes. We first prove the existence of a discrete solution at each time step, via a topological degree argument. We then prove that, as the mesh size and time step tend to zero, the approximate solutions converge to a weak solution of the continuous problem. The existence of a solution to the continuous problem then follows as a consequence. To our knowledge, the finite volume analysis, the convergence of the scheme and the existence of a continuous solution are all new for this model. We finally report numerical simulations illustrating the interface-driven surfactant dynamics, including a benchmark showing the stabilization of the interfaces under high surfactant concentration.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Margherita Castellano"
    },
    {
      "name": "Ludovic Goudenège"
    },
    {
      "name": "Flore Nabet"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5mtfdhx6nb3wh.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "5mtfdhx6nb3wh",
  "issns": [],
  "landing_url": "https://hal.science/hal-05747365v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "hal",
      "1.math.math-na"
    ],
    [
      "hal",
      "1.phys.meca"
    ],
    [
      "hal",
      "2.phys.meca.mefl"
    ]
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05747365/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5mtfdhx6nb3wh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:34Z",
      "native_id": "hal-05747365",
      "source": "hal",
      "url": "https://hal.science/hal-05747365v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "hal:2.phys.meca.mefl",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "CONVERGENCE ANALYSIS OF A DISCRETE DUALITY FINITE-VOLUME METHOD FOR CAHN-HILLIARD EQUATIONS WITH SURFACTANTS",
  "title_text": "CONVERGENCE ANALYSIS OF A DISCRETE DUALITY FINITE-VOLUME METHOD FOR CAHN-HILLIARD EQUATIONS WITH SURFACTANTS",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/5mtfdhx6nb3wh",
  "venue": "HAL",
  "versions": []
}