{
  "abstract": "The CHQ model describes viscoelastic phase separation in a polymer--solvent mixture: a Cahn--Hilliard equation for the polymer volume fraction $ϕ$ is two-way coupled, through a phase-dependent cross-diffusion flux, to a damped relaxation equation for a scalar bulk elastic stress $q$. We propose a scalar-auxiliary-variable (SAV) time discretisation of this system, combining the SAV reformulation of the double-well potential with a second-order backward differentiation formula (BDF2) and a second-order extrapolation of all phase-dependent mobilities: a linear, computationally cheaper complement to the reference scheme's fully nonlinear Newton solve. The resulting method is (i) linear at every time step, with a coupling structure we prove has exactly one solution at every step, for every choice of time-step size; (ii) mass conserving, exactly, as an algebraic identity of the discrete equations themselves (the only drift ever seen numerically traces to the finite tolerance of the iterative linear solver, not a failure of the conservation property); and (iii) unconditionally stable for a modified discrete energy, via an exact one-step energy--dissipation identity. We show the energy identity extends to this filtered variant as well, with two explicit extra non-negative terms. Hence, the scheme actually producing the physics results is itself provably stable for the same energy. A Fourier--Galerkin implementation verifies that the energy identity holds at every time step to within floating-point round-off. It also confirms second-order temporal accuracy, including in the steep-interface regime, and agreement with an independently implemented nonlinear Newton--BDF2 solver. Compared with that independent nonlinear Newton--BDF2 solver, at equal grid resolution, the SAV method uses $2.5$--$3.0\\times$ fewer linear-solver iterations and $1.7$--$2.0\\times$ less wall-clock time.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.30077",
  "author_total": 2,
  "authors": [
    {
      "name": "Ritesh Bhola"
    },
    {
      "name": "Michael te Vrugt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2thw92p8p3hxs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.30077",
  "fulltext_url": null,
  "id": "2thw92p8p3hxs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.30077",
  "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",
      "cond-mat.soft"
    ],
    [
      "arxiv",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "openalex",
      "2206|Advanced Numerical Methods in Computational Mathematics"
    ]
  ],
  "openalex": "W7223216671",
  "pdf_url": "https://arxiv.org/pdf/2610.30077",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2thw92p8p3hxs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.30077",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.30077"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.soft",
      "subfield": "condensed-matter"
    }
  ],
  "title": "A linear, second-order, unconditionally energy-stable scalar-auxiliary-variable scheme for the CHQ viscoelastic phase-separation model",
  "title_text": "A linear, second-order, unconditionally energy-stable scalar-auxiliary-variable scheme for the CHQ viscoelastic phase-separation model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/2thw92p8p3hxs",
  "venue": "arXiv",
  "versions": []
}