{
  "abstract": "In the Navier--Stokes equations, incompressibility allows rewriting the viscous term in various forms leading to distinct numerical properties and flow descriptions. Furthermore, models accounting for non-Newtonian, thermal or turbulent effects often break the constant-viscosity assumption, thereby producing additional consistency terms. In this context, the present work compares the classical symmetric-gradient diffusion term with more recent variable-viscosity generalizations of the Laplacian and rotational forms. We discuss, analyze and test their differences with respect to implementation, efficiency, numerical stability and outflow boundary conditions. With a focus on time-dependent flows, we consider second-order implicit-explicit (IMEX) temporal discretizations aimed at improving efficiency and numerical stability. Through a rigorous stability analysis, we show how selected explicit treatments can bypass algorithmic nonlinearities without inducing CFL conditions. Our numerical results highlight important differences between the three viscous formulations---especially in the presence of outflow boundaries, for which the generalized Laplacian form proves more suitable in diffusion-dominated regimes. %(as widely known for constant viscosity).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10919",
  "author_total": 4,
  "authors": [
    {
      "name": "Benjamin Cisternas"
    },
    {
      "name": "Douglas R. Q. Pacheco"
    },
    {
      "name": "Felipe Galarce"
    },
    {
      "name": "Ernesto Castillo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/53b1enr0b4x8h.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10919",
  "fulltext_url": null,
  "id": "53b1enr0b4x8h",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10919",
  "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|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7212313910",
  "pdf_url": "https://arxiv.org/pdf/2609.10919",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/53b1enr0b4x8h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10919",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10919"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Stress-divergence, Laplacian, and rotational forms of the incompressible Navier--Stokes equations with variable viscosity",
  "title_text": "Stress-divergence, Laplacian, and rotational forms of the incompressible Navier--Stokes equations with variable viscosity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/53b1enr0b4x8h",
  "venue": "arXiv",
  "versions": []
}