{
  "abstract": "We develop a method for lossy compression of incompressible (i.e., divergence-free) velocity fields that preserves zero divergence and, on periodic domains, periodicity. We fit the nodal velocities with property-preserving matrix-valued kernels and compress their coefficients using standard lossy compressors. Every decompressed coefficient vector defines a field with the same constraints, independently of the compression tolerance. We present several fitting schemes designed around either low-rank representation of or sparsity in the interpolation matrix. More specifically, we show results for global Matérn interpolation, a two-level Nyström approximation, Nyström--Wendland residual interpolation, multilevel Wendland interpolation and a property-preserving (redundant) kernel frame. We derive nodal error bounds that relate the compressor tolerance to the additional velocity error. Experiments with four compressors on cavity, Taylor--Green, and species-transport flows verify the bounds under their coefficient-error assumptions and compare storage at matched velocity accuracy. The low-rank methods give compact representations when they resolve the velocity field sufficiently accurately; residual, multilevel, and frame interpolation extend the attainable accuracy when they do not. We also measure changes in turbulent velocity statistics. The resulting representations support an accuracy--compression tradeoff while preserving incompressibility and periodicity analytically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02776",
  "author_total": 4,
  "authors": [
    {
      "name": "Andrey Pluzhnik"
    },
    {
      "name": "Ramansh Sharma"
    },
    {
      "name": "Martin Burtscher"
    },
    {
      "name": "Varun Shankar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/67ny7am0fzzf0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02776",
  "fulltext_url": null,
  "id": "67ny7am0fzzf0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02776",
  "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",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7220459312",
  "pdf_url": "https://arxiv.org/pdf/2610.02776",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/67ny7am0fzzf0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:50Z",
      "native_id": "2610.02776",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02776"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Property-Preserving Data Compression for Incompressible Flows",
  "title_text": "Property-Preserving Data Compression for Incompressible Flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:50Z",
  "url": "https://research.draconitic.com/paper/67ny7am0fzzf0",
  "venue": "arXiv",
  "versions": []
}