{
  "abstract": "This paper develops a compact fourth-order positivity-preserving active flux (AF) method for the one-and two-dimensional compressible Navier-Stokes equations on Cartesian meshes. The method retains the cell averages and shared point values of the standard third-order AF method as its degrees of freedom. To avoid the order reduction that can arise when diffusion is discretized using operators from the standard third-order AF method, while maintaining compactness, the divergence of the viscous flux is discretized directly using compact fourth-order operators. For the inviscid part, incorporating a downwind point value into the biased stencil yields fourth-order accuracy. A monolithic flux limiting blends high-order total numerical fluxes with loworder positivity-preserving counterparts, treating the inviscid and viscous fluxes jointly while maintaining local conservation. Together with a scaling limiter for point values, this procedure preserves density and pressure positivity for both cell averages and point values. Numerical experiments demonstrate fourth-order convergence, positivity preservation, and accurate resolution of shocks and viscous flow structures. For the two-dimensional viscous shock tube, a comparison with a discontinuous Galerkin method shows improved computational efficiency in resolving complex interaction of shock waves and boundary layers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29081",
  "author_total": 3,
  "authors": [
    {
      "name": "Junming Duan"
    },
    {
      "name": "Wasilij Barsukow"
    },
    {
      "name": "Christian Klingenberg"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a9txx8knfg5tb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29081",
  "fulltext_url": null,
  "id": "a9txx8knfg5tb",
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  "landing_url": "https://hal.science/hal-05794424v1",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
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  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05794424/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a9txx8knfg5tb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:54Z",
      "native_id": "hal-05794424",
      "source": "hal",
      "url": "https://hal.science/hal-05794424v1"
    },
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29081",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29081"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A compact high-order and positivity-preserving active flux method for compressible Navier--Stokes equations on Cartesian meshes",
  "title_text": "A compact high-order and positivity-preserving active flux method for compressible Navier--Stokes equations on Cartesian meshes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/a9txx8knfg5tb",
  "venue": "HAL",
  "versions": []
}