{
  "abstract": "We consider the fluid subsystem of a variationally derived hyperbolic thermodynamically compatible (HTC) model of compressible multiphase flows. Its total energy is in general not convex in the natural state variables, so a scalar numerical viscosity acting on them need not produce non-negative entropy. Reformulating the equations in terms of the volume fractions separates changes in the amount of each phase from changes in its intrinsic state. This guides the construction of a configurational numerical viscosity in phase variables, in which the energy is convex, while the scheme retains the structure of the HTC model. At the semi-discrete level, the new schemes satisfy: I) local conservation of the phase masses, the mixture momentum and the total energy; II) a cell entropy inequality whose production is non-negative face by face and phase by phase, with no convexity assumption in the evolved variables and no clipping; III) positivity of the partial densities and volume fractions under explicit time-step conditions; IV) exact preservation of contact equilibria; V) equivalence with a scheme for the density-weighted volume fractions. The key ingredients are: i) an exact decomposition of the jump of each phase across a face into a configurational part, dissipated with the material speed, and an intrinsic part, dissipated with the acoustic speed; ii) an exchange form of this dissipation between neighbouring cells, with non-negative weights; iii) a side-wise transfer of the dissipation to the evolved variables through the chain rule of each cell, which turns the energy defects into Bregman divergences of the single-fluid energies; iv) a thermodynamic correction of the reversible part built in the phase variables. Properties I)-V) are proved and verified numerically, including a shock tube in which the Rusanov viscosity produces negative entropy and a shock-water column interaction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23247",
  "author_total": 3,
  "authors": [
    {
      "name": "Davide Ferrari"
    },
    {
      "name": "Ilya Peshkov"
    },
    {
      "name": "Michael Dumbser"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jz615tw8x82c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23247",
  "fulltext_url": null,
  "id": "1jz615tw8x82c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23247",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Computational Fluid Dynamics and Aerodynamics"
    ]
  ],
  "openalex": "W7222982616",
  "pdf_url": "https://arxiv.org/pdf/2610.23247",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1jz615tw8x82c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2610.23247",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23247"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "A configurational numerical viscosity for thermodynamically compatible finite volume schemes of compressible multiphase flows",
  "title_text": "A configurational numerical viscosity for thermodynamically compatible finite volume schemes of compressible multiphase flows",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/1jz615tw8x82c",
  "venue": "arXiv",
  "versions": []
}