{
  "abstract": "This paper proposes a novel second-order prediction--filter--projection framework for incompressible flows with variable density and viscosity. In this framework, a constrained $L^2$-projection is enforced to unconditionally preserve the prescribed density bounds and discrete mass conservation, while a generalized-Laplacian reformulation combined with the D-CSAV approach is used to discretize the variable-viscosity momentum equation. In particular, a density-weighted second-order time filter is proposed, which eliminates the additional uniform-in-time bound restriction imposed on the time difference quotient of the discrete density in existing stability analyses. The resulting scheme is shown to satisfy an unconditional modified-energy dissipation law, without the viscosity-related restrictions imposed in earlier work. Then, an additional scalar auxiliary variable and its compatible temporal discretization are introduced to construct a variable-step prediction--filter--projection scheme. This scheme is also bound-preserving and mass-conserving, and satisfies an unconditional modified-energy dissipation law. Moreover, the modified energy is much closer to the ``original'' kinetic energy, differing from it only through the auxiliary-variable corrections. Based on the variable-step scheme, a reliable energy-based adaptive time-stepping strategy is developed. Finally, numerical experiments demonstrate the accuracy, physics-preserving properties, and efficiency of the proposed schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.00834",
  "author_total": 4,
  "authors": [
    {
      "name": "Baolin Kuang"
    },
    {
      "name": "Lanxin Sun"
    },
    {
      "name": "Rihui Lan"
    },
    {
      "name": "Hongfei Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/70gtq5cek2rxe.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.00834",
  "fulltext_url": null,
  "id": "70gtq5cek2rxe",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.00834",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.00834",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/70gtq5cek2rxe.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.00834",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.00834"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Efficient second-order physics-preserving schemes for incompressible flows with variable density and viscosity",
  "title_text": "Efficient second-order physics-preserving schemes for incompressible flows with variable density and viscosity",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/70gtq5cek2rxe",
  "venue": "arXiv",
  "versions": []
}