{
  "abstract": "Standard convolutional neural networks for turbulence super-resolution are restricted to uniform structured grids, preventing their direct application to the non-uniform and non-orthogonal meshes commonly used in wall-bounded flows and complex geometries. We introduce a finite-volume convolution unit (FVCU) that removes this restriction. The key idea is to construct convolutional layers using finite-volume operators that are applicable to non-uniform and unstructured meshes. To this end, we use an exact representation of a 3D convolution as a linear combination of successive axis-wise convolutions. We adopt axis-wise gradient, averaging, and identity operators, as they can be evaluated on arbitrary polyhedral cells using finite-volume discretization. The resulting FVCU is well-defined on general meshes, serving as a drop-in replacement for conventional convolution layers. The FVCU is embedded in a super-resolution neural network and trained to reconstruct 3D velocity fields from $4\\times$ coarsened low-resolution fields in turbulent channel flow on a non-uniform mesh, and in circular-pipe flow on a non-orthogonal O-grid mesh. Inspired by the role of the Van Driest damping function in near-wall subgrid-scale modelling in large-eddy simulations, this function is supplied as a conditional input to encode wall proximity. An ablation study confirms that the network interprets this input in a physically consistent manner. In both configurations, the model accurately reconstructs instantaneous velocity fields, Reynolds-stresses and their anisotropy, and energy spectra beyond the Nyquist limit of the low-resolution mesh. On an elliptic pipe unseen during training, the model reproduces the main flow features and local statistics, with a modest overprediction of small-scale energy. These results demonstrate a framework for extending CNN-based super-resolution to general finite-volume grids.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12141",
  "author_total": 3,
  "authors": [
    {
      "name": "Hesam Tofighian"
    },
    {
      "name": "Jordan A. Denev"
    },
    {
      "name": "Nikolai Kornev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9hqk9pefwqv75.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12141",
  "fulltext_url": null,
  "id": "9hqk9pefwqv75",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12141",
  "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",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7221094014",
  "pdf_url": "https://arxiv.org/pdf/2610.12141",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hqk9pefwqv75.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:54Z",
      "native_id": "2610.12141",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12141"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "Extending convolutional neural networks to finite-volume meshes for fine-scale reconstruction of wall-bounded turbulence",
  "title_text": "Extending convolutional neural networks to finite-volume meshes for fine-scale reconstruction of wall-bounded turbulence",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:54Z",
  "url": "https://research.draconitic.com/paper/9hqk9pefwqv75",
  "venue": "arXiv",
  "versions": []
}