{
  "abstract": "We present a hybridizable discontinuous Galerkin (HDG) method for one-dimensional blood flow in arterial networks with Windkessel boundary conditions. The scheme uses a Harten--Lax--van Leer (HLL) numerical flux and implicit time integration. After spatial discretization, the complete network---including cell states, hybrid traces, junction conditions, and dynamic $\\mathrm{RCR}$ terminal pressures---is written as a residual index-one differential--algebraic equation (DAE) and integrated with variable-step, variable-order backward differentiation formulas. The implicit formulation removes the CFL stability restriction of explicit schemes and allows variable-order, variable-step solvers. The resulting single global residual and Jacobian for the network and its terminal dynamics also provide a natural interface for monolithic coupling with external nonlinear models. We establish local solvability and a semi-discrete energy balance, and show numerically optimal convergence rates for both solution variables in the $L^2$ norm and the broken $H^1$ seminorm. The solver is validated against established benchmarks, including an aortic bifurcation and a $37$-artery network, and is further applied to a cerebral arterial network. Mass conservation is observed in a synthetically generated anatomical liver network of $8\\,\\mathrm{k}$ vessels, and strong-scaling studies are performed on synthetic networks of $50\\,\\mathrm{k}$ and $100\\,\\mathrm{k}$ vessels.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40080",
  "author_total": 3,
  "authors": [
    {
      "name": "Raksha Devi"
    },
    {
      "name": "Luca Heltai"
    },
    {
      "name": "Lucas O. Müller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4davmzwskq05d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40080",
  "fulltext_url": null,
  "id": "4davmzwskq05d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40080",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40080",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4davmzwskq05d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40080",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40080"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    }
  ],
  "title": "An HDG-type discretization of 1D embedded blood flow in complex networks with Riemann-coupled junctions",
  "title_text": "An HDG-type discretization of 1D embedded blood flow in complex networks with Riemann-coupled junctions",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/4davmzwskq05d",
  "venue": "arXiv",
  "versions": []
}