{
  "abstract": "In this paper, we propose a linear and decoupled fully discrete scheme that preserves the entropy production property for the dynamic van der Waals model. This model provides a thermodynamically consistent diffuse-interface framework for describing non-isothermal phase transitions in single-component liquid-vapor systems, containing the coupled conservation laws of mass, momentum and energy. We first introduce an equivalent reformulation of the governing equations that avoids the use of chain-rule identities, which generally fail under discrete differentiation. Further, a component-wise convex-splitting method is employed to calculate the discrete chemical potential and temperature. This treatment provides a discrete entropy-stable inequality without a time step restriction. Based on the explicitly treated velocity, the scheme allows the three conservation equations to be solved linearly and sequentially in a decoupled manner. Since the momentum equation does not directly affect the entropy-stability analysis, we use a classical linear semi-implicit scheme to solve it. Numerical experiments verify the expected numerical accuracy. Simulations of droplet evaporation and two- and three-dimensional Leidenfrost effects further demonstrate the proposed method can capture complex non-isothermal phase-transition dynamics while numerically reproducing the discrete entropy production behavior.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13029",
  "author_total": 3,
  "authors": [
    {
      "name": "Yunzhuo Guo"
    },
    {
      "name": "Zhonghua Qiao"
    },
    {
      "name": "Xianmin Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/432bcf5v32jjq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13029",
  "fulltext_url": null,
  "id": "432bcf5v32jjq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13029",
  "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|Fluid Dynamics and Heat Transfer"
    ]
  ],
  "openalex": "W7221570581",
  "pdf_url": "https://arxiv.org/pdf/2610.13029",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/432bcf5v32jjq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13029",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13029"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Linear and entropy-stable scheme for the dynamic van der Waals model of non-isothermal liquid-vapor flows",
  "title_text": "Linear and entropy-stable scheme for the dynamic van der Waals model of non-isothermal liquid-vapor flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/432bcf5v32jjq",
  "venue": "arXiv",
  "versions": []
}