{
  "abstract": "This paper concerns the design of a fully explicit, energy-stable numerical scheme for a onedimensional hyperbolic relaxation approximation of the Serre–Green–Naghdi equations over a variable bottom. The method relies on an operator splitting that decouples the model into two hyperbolic subsystems, each admitting its own exact energy balance. The first retains the shallow-water components of the equations and is referred to as the gravity part, while the second, referred to as the acoustic part, contains in particular the stiff source terms arising from the relaxation strategy. The proposed method is designed to preserve the energy balance specific to each substep at the discrete level. This yields a numerical method for strictly wet, fully nonlinear dispersive flows satisfying local discrete energy estimates for regular and possibly strongly varying topographies.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Arnaud Duran"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9p0t13md8vear.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "9p0t13md8vear",
  "issns": [],
  "landing_url": "https://hal.science/hal-05765698v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-na"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05765698/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9p0t13md8vear.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05765698",
      "source": "hal",
      "url": "https://hal.science/hal-05765698v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Fully discrete energy stability for a one-dimensional hyperbolic relaxation model with complete topography terms",
  "title_text": "Fully discrete energy stability for a one-dimensional hyperbolic relaxation model with complete topography terms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/9p0t13md8vear",
  "venue": "HAL",
  "versions": []
}