{
  "abstract": "We study rotational invariance, hyperbolicity, and well-balanced discretization of shallow water linearized moment equations in two horizontal dimensions. Although the direct extension has real characteristic speeds, its directional matrices can lack a complete eigenbasis. We construct a rotationally invariant modification and prove its global hyperbolicity for all states with positive water depth. For quasi-two-dimensional flows over non-flat topography with Navier-slip friction, we develop first- and second-order path-conservative finite-volume schemes that exactly preserve a discrete moving equilibrium constructed by midpoint collocation. Numerical tests confirm equilibrium preservation to roundoff, second-order approximation of smooth stationary branches, and near-second-order accuracy of the second-order scheme for the tested perturbations. Comparisons with three-dimensional two-phase OpenFOAM simulations illustrate the invariant shallow-water limit and show that retaining moments improves the reconstruction of curved rotational velocity profiles, while differences remain in radial motion.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28800",
  "author_total": 3,
  "authors": [
    {
      "name": "Shiping Zhou"
    },
    {
      "name": "Juntao Huang"
    },
    {
      "name": "Andrew Christlieb"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5yzc2cz8z655t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28800",
  "fulltext_url": null,
  "id": "5yzc2cz8z655t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28800",
  "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": "W7214360539",
  "pdf_url": "https://arxiv.org/pdf/2609.28800",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5yzc2cz8z655t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.28800",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28800"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Two-Dimensional Shallow Water Linearized Moment Equations: Hyperbolicity and Well-Balanced Schemes",
  "title_text": "Two-Dimensional Shallow Water Linearized Moment Equations: Hyperbolicity and Well-Balanced Schemes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/5yzc2cz8z655t",
  "venue": "arXiv",
  "versions": []
}