{
  "abstract": "In computational fluid dynamics, the numerical simulation of free-surface flows using interface capturing approaches (level set, pseudo-concentration) requires accurate resolution of a transport equation. In the present work, this equation is solved using a new formulation of the Lesaint--Raviart discontinuous Galerkin method, which is particularly suitable for problems without inflow boundaries. The motion is described by the incompressible Navier--Stokes equations with surface tension, discretized using the standard $P2-P1$ Taylor--Hood finite element method in space. Surface tension effects are represented using the so-called Continuum Surface Force model. Finally, the proposed approach is implemented and tested on several benchmarks, including the single rising bubble and the Rayleigh--Taylor instability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07327",
  "author_total": 4,
  "authors": [
    {
      "name": "W. Herri"
    },
    {
      "name": "K. Benmoussa"
    },
    {
      "name": "R. Bouydou"
    },
    {
      "name": "D. Yakoubi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9sjwggr5kq8qw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07327",
  "fulltext_url": null,
  "id": "9sjwggr5kq8qw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07327",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "physics.flu-dyn"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7212033892",
  "pdf_url": "https://arxiv.org/pdf/2609.07327",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9sjwggr5kq8qw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.07327",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07327"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.flu-dyn",
      "subfield": "fluid-dynamics"
    }
  ],
  "title": "A new formulation of Discontinuous Galerkin method for interface capturing approaches",
  "title_text": "A new formulation of Discontinuous Galerkin method for interface capturing approaches",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/9sjwggr5kq8qw",
  "venue": "arXiv",
  "versions": []
}