{
  "abstract": "We develop a high-order, fully explicit operator-splitting method for 2.5D ideal magnetohydrodynamics on Cartesian meshes. The hydrodynamic subflow is advanced by an entropy-stable discontinuous Galerkin spectral element method equipped with stagewise oscillation elimination and a positivity-preserving limiter. The magnetic--velocity subflow uses compatible finite elements and mass-lumped reconstructions of electric field and current density. Its discrete-curl update exactly preserves the global $H(\\mathrm{div})$ divergence-free subspace, while the ideal semidiscretization balances kinetic, magnetic, and internal energy. Curl-form artificial resistivity and a direction-resolved velocity filter return removed magnetic and kinetic energy to internal energy; consequently, the stabilized magnetic stage preserves positive internal energy and satisfies a discrete entropy inequality. The two solvers are composed by a second-order hydrodynamic--magnetic--hydrodynamic Strang splitting, yielding a matrix-free scheme that retains global mass, nodal admissibility, and magnetic divergence on accepted steps. Smooth Alfvén-wave and advected-vortex tests reveal an even--odd convergence pattern in the magnetic polynomial degree, verify second-order temporal accuracy, and show that stabilization preserves high-order accuracy. Field-loop, Orszag--Tang, rotor, MHD blast-wave, and Kelvin--Helmholtz calculations demonstrate robust performance for nonsmooth multidimensional flows and show that artificial resistivity suppresses grid-scale magnetic oscillations while retaining the resolved structures.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10849",
  "author_total": 2,
  "authors": [
    {
      "name": "Siyuan Fan"
    },
    {
      "name": "Guosheng Fu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/978svhnr78n5e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10849",
  "fulltext_url": null,
  "id": "978svhnr78n5e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10849",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7212263281",
  "pdf_url": "https://arxiv.org/pdf/2609.10849",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/978svhnr78n5e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.10849",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10849"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements",
  "title_text": "Structure-preserving operator splitting for 2.5D ideal MHD with an entropy-stable DGSEM and exactly divergence-free compatible finite elements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/978svhnr78n5e",
  "venue": "arXiv",
  "versions": []
}