{
  "abstract": "We present a class of high-order well-balanced WENO finite-difference schemes for hyperbolic systems with source terms based on the local flux approach. The governing equations are reformulated in terms of a generalized flux that incorporates the source terms and nonconservative products, so that its variation vanishes at stationary states within the WENO reconstruction stencils. A path-conservative formulation with Roe linearization is employed to approximate the flux/nonconservative contribution and source contributions. The proposed approach does not require solving the ODE system associated with the equilibria or explicitly reconstructing equilibrium solutions. Upwind flux splitting and characteristic-wise WENO reconstruction are used to achieve high-order accuracy and nonoscillatory shock-capturing properties. Numerical experiments for Burgers' equations with source terms, the shallow water equations, and the two-layer shallow water equations demonstrate accurate preservation of moving equilibria, high-order convergence, resolution of small perturbations of steady states, and robust performance for Riemann problems.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Baifen Ren"
    },
    {
      "name": "Maria Kazolea"
    },
    {
      "name": "Carlos Parés-Madronal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7xrwk1398cm6b.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "7xrwk1398cm6b",
  "issns": [],
  "landing_url": "https://inria.hal.science/hal-05788823v1",
  "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"
    ],
    [
      "hal",
      "1.math.math-na"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://inria.hal.science/hal-05788823/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7xrwk1398cm6b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:52Z",
      "native_id": "hal-05788823",
      "source": "hal",
      "url": "https://inria.hal.science/hal-05788823v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-na",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Local flux high-order well-balanced WENO finite-difference methods for hyperbolic systems with source terms",
  "title_text": "Local flux high-order well-balanced WENO finite-difference methods for hyperbolic systems with source terms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:52Z",
  "url": "https://research.draconitic.com/paper/7xrwk1398cm6b",
  "venue": "HAL",
  "versions": []
}