{
  "abstract": "Multicomponent reacting-flow discretizations must conserve total species mass, preserve positive mass fractions, and dissipate a convex mixing potential. These properties are controlled at different stages of a solver, however, and a certificate established at one stage need not survive the next. We study this compatibility problem for mixture-averaged diffusion, non-orthogonal finite-volume reconstruction, and positivity-preserving Patankar time integration. The analysis is isothermal, uses prescribed density, and uses synthetic detailed-balance reaction networks for the chemistry tests. At the face level, the entropy-variable jump is shown to equal a log-mean Gibbs Hessian applied exactly to the mass-fraction jump. Requiring conservation and entropy neutrality of the mass-correction term on the simplex tangent space then yields a unique componentwise-positive face composition and an exact two-point entropy certificate. The arithmetic-weight face criterion is also satisfied by production neutral-air/carbon data and a quasi-neutral ambipolar-air control, but a face-level certificate does not automatically extend to subsequent discretization layers. A weighted least-squares non-orthogonal correction can, in the tested prototype, convert a dissipative two-point operator into an anti-dissipative multipoint operator. Likewise, Patankar rescaling can preserve positivity and conservation while increasing the free energy; an explicit finite-step rational counterexample establishes this failure independently of ensemble statistics. A fully discrete two-cell example further shows that a positive face entropy margin does not guarantee positivity of the fully discrete update. Thus conservation, positivity, and free-energy dissipation are layer-specific properties and require distinct discrete certificates.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.27272",
  "author_total": 1,
  "authors": [
    {
      "name": "Jingchao Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0493sez1yy49g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.27272",
  "fulltext_url": null,
  "id": "0493sez1yy49g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.27272",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7214183780",
  "pdf_url": "https://arxiv.org/pdf/2609.27272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0493sez1yy49g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.27272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.27272"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Layer-wise discrete certificates in multicomponent reacting-flow discretizations",
  "title_text": "Layer-wise discrete certificates in multicomponent reacting-flow discretizations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/0493sez1yy49g",
  "venue": "arXiv",
  "versions": []
}