{
  "abstract": "Entropy-stable boundary conditions are critical for ensuring that the corresponding numerical scheme satisfies the discrete entropy inequality, thus mimicking the second law of thermodynamics for the compressible Navier-Stokes equations discretely. Provably entropy-stable adiabatic wall boundary conditions were introduced in Parsani 2014~\\cite{parsani2014entropy}. These discrete wall boundary conditions were further generalized in Dalcin 2019~\\cite{dalcin2019conservative} to a moving adiabatic solid wall or a wall with a prescribed heat flux for the compressible Navier--Stokes equations discretized by using summation-by-parts (SBP) and simultaneous-approximation-term (SAT) operators. Currently, no entropy-stable formulation using SBP-SAT operators for isothermal wall boundary conditions is available in the literature. This paper presents new isothermal no-slip wall boundary conditions that: 1) enforce the $T|_{y=0}=T^{wall}$ and $\\vec{v}|_{y=0}=\\vec{v}^{wall}$ conditions with the design order of accuracy while maintaining stability, 2) provide the correct sign of entropy production at the wall, and 3) mimic the entropy balance of the Navier-Stokes equations at the discrete level. The structure-preserving and design-order properties of the proposed methodology are demonstrated and verified on standard benchmark problems for compressible flows.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.09249",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohammed Sayyari"
    },
    {
      "name": "Nail K. Yamaleev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/003evh8ysf2br.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.09249",
  "fulltext_url": null,
  "id": "003evh8ysf2br",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.09249",
  "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"
    ]
  ],
  "openalex": "W7221051900",
  "pdf_url": "https://arxiv.org/pdf/2610.09249",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/003evh8ysf2br.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.09249",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.09249"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "High-order entropy-stable isothermal wall boundary condition for the compressible Navier--Stokes equations",
  "title_text": "High-order entropy-stable isothermal wall boundary condition for the compressible Navier--Stokes equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/003evh8ysf2br",
  "venue": "arXiv",
  "versions": []
}