{
  "abstract": "We introduce a second-order approximation to the compressible atmospheric Euler equations with gravity that is invariant domain preserving and well-balanced with respect to stratified rest states, including isentropic and isothermal equilibria. The approximation is built upon discrete auxiliary states derived from a hydrostatic reconstruction of the density and potential temperature. These auxiliary states, together with an affine shift of the numerical state, provide local bounds needed for maintaining well-balancing and invariant domain preserving properties of the method. The numerical method is then verified and validated with analytic solutions, well-balancing tests, and typical benchmark problems for atmospheric flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.19764",
  "author_total": 3,
  "authors": [
    {
      "name": "Crystal Farris"
    },
    {
      "name": "Matthias Maier"
    },
    {
      "name": "Eric J. Tovar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jwyfsqdhxs4z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.19764",
  "fulltext_url": null,
  "id": "2jwyfsqdhxs4z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.19764",
  "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|Computational Fluid Dynamics and Aerodynamics"
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  ],
  "openalex": "W7165398329",
  "pdf_url": "https://arxiv.org/pdf/2606.19764",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jwyfsqdhxs4z.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:09Z",
      "native_id": "2606.19764",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.19764"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Well-balanced second-order approximation of the compressible atmospheric Euler equations",
  "title_text": "Well-balanced second-order approximation of the compressible atmospheric Euler equations",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:21Z",
  "url": "https://research.draconitic.com/paper/2jwyfsqdhxs4z",
  "venue": "arXiv",
  "versions": []
}