{
  "abstract": "Immersed-boundary methods avoid body-fitted meshes, but the energy or entropy stability of the underlying flow discretisation does not automatically extend to the immersed treatment. This manuscript analyses the volume-penalised compressible Navier--Stokes equations for both energy and entropy stability, on the continuous and semi-discrete levels, and integrates the isolated source exactly in time. The source is formulated as a one-parameter family indexed by $θ$, whose momentum component relaxes the fluid velocity towards the prescribed solid velocity; $θ$ sets how much of the resulting kinetic-energy loss leaves the domain rather than being converted to internal energy. The two stability requirements impose opposing bounds on $θ$, with dissipation of the relative total energy requiring $θ\\geq0$ and stability of the mathematical entropy requiring $θ\\leq1$. Where penalisation acts, both conditions are therefore satisfied if and only if $0\\leqθ\\leq1$, and the symmetric value $θ=1/2$ divides the kinetic-energy loss equally between the domain and the internal energy. We conclude that any entropy-stable split-form discontinuous Galerkin spectral element method remains semi-discretely entropy stable once the source is added at the collocation nodes, for stationary and prescribed moving bodies alike.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17973",
  "author_total": 4,
  "authors": [
    {
      "name": "Abbas Ballout"
    },
    {
      "name": "Albert Jiménez-Ramos"
    },
    {
      "name": "Gonzalo Rubio"
    },
    {
      "name": "Esteban Ferrer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p84nkra2mmv9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17973",
  "fulltext_url": null,
  "id": "9p84nkra2mmv9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17973",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7221769342",
  "pdf_url": "https://arxiv.org/pdf/2610.17973",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p84nkra2mmv9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:11Z",
      "native_id": "2610.17973",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17973"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Simultaneous energy and entropy stability of volume-penalisation immersed-boundary methods for the compressible Navier--Stokes equations",
  "title_text": "Simultaneous energy and entropy stability of volume-penalisation immersed-boundary methods for the compressible Navier--Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:19Z",
  "url": "https://research.draconitic.com/paper/9p84nkra2mmv9",
  "venue": "arXiv",
  "versions": []
}