{
  "abstract": "Positivity-preserving schemes for hyperbolic balance laws are typically built from the Zhang-Shu limiter and strong-stability-preserving Runge-Kutta (SSP-RK) time stepping, at the cost of a restrictive time-step condition. The modified Patankar deferred correction (mPDeC) method removes this restriction, offering high-order accuracy, conservation, and unconditional positivity. However, its solution-dependent Patankar weights make the time update nonlinear, so, unlike with RK methods, preserving (steady and moving) equilibria, i.e., well-balancing (WB), is no longer straightforward. In this paper, we construct high-order, WB, positivity-preserving mPDeC schemes by combining mPDeC with a flux-globalization approach. We demonstrate the idea on the one-dimensional shallow water equations, using a WB A-WENO spatial discretization, and introduce a modified local characteristic decomposition that remains stable in the presence of dry states. Numerical experiments on one-dimensional benchmarks confirm that the method satisfies the desired properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21857",
  "author_total": 3,
  "authors": [
    {
      "name": "Philipp Öffner"
    },
    {
      "name": "Michael Redle"
    },
    {
      "name": "Davide Torlo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78n5bjerzjcs6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21857",
  "fulltext_url": null,
  "id": "78n5bjerzjcs6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21857",
  "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"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7222626615",
  "pdf_url": "https://arxiv.org/pdf/2610.21857",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78n5bjerzjcs6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21857",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21857"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order positivity-preserving well-balanced schemes: combining flux globalization with modified Patankar deferred correction methods",
  "title_text": "High-order positivity-preserving well-balanced schemes: combining flux globalization with modified Patankar deferred correction methods",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/78n5bjerzjcs6",
  "venue": "arXiv",
  "versions": []
}