{
  "abstract": "The aim of this work is to design well-balanced semi-implicit relaxed finite volume methods for one-dimensional systems of hyperbolic balance laws with several time scales, in which the fast waves impose a severe time step restriction of fully explicit time discretizations. The strategy is based on the semi-implicit relaxation approach in which the flux is split into a slow and a fast part and the latter is linearised by means of Jin-Xin relaxation, such that the implicit contributions reduce to linear decoupled systems. The main difficulty with respect to well-balancing is the generation of implicit viscosity in these schemes which does not vanish on non-constant steady states. This is circumvented by rewriting the scheme in terms of fluctuations with respect to local steady states, and the resulting implicit operator is driven by equilibrium-corrected jumps that vanish identically at equilibrium. A second order extension of the first order well-balanced relaxed scheme is given in the framework of implicit-explicit Runge-Kutta schemes. Therein, to achieve the desired accuracy, the projection to the equilibrium manifold on each stage is exploited. The well-balanced properties of the first-and second-order schemes are proven and numerical results for the shallow water system and the Ripa model are given to assess the performance of the novel well-balanced schemes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Irene Gómez-Bueno"
    },
    {
      "name": "Manuel J Castro"
    },
    {
      "name": "Andrea Thomann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2cqpj80225nc9.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "2cqpj80225nc9",
  "issns": [],
  "landing_url": "https://hal.science/hal-05835613v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05835613/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2cqpj80225nc9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:01Z",
      "native_id": "hal-05835613",
      "source": "hal",
      "url": "https://hal.science/hal-05835613v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Well-balanced semi-implicit relaxed finite volume schemes for hyperbolic balance laws",
  "title_text": "Well-balanced semi-implicit relaxed finite volume schemes for hyperbolic balance laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:01Z",
  "url": "https://research.draconitic.com/paper/2cqpj80225nc9",
  "venue": "HAL",
  "versions": []
}