{
  "abstract": "Topology optimization of fluid flows requires the computation of the cost function gradient. Based on the partial differential equations that govern the physics, the only efficient manner to do so is using the adjoint-state method. This article highlights the property that the cost gradient is naturally not well calculated when the cost function incorporates macroscopic data at the boundary, in a LBM framework. This is due to the advection nature of Boltzmann equations which are in terms of distribution functions at the mesoscopic scale, while the cost function incorporates variables at the macroscopic scale. Two methodologies are proposed to improve the accuracy of the gradient calculation: shifting the domain of integration of the cost function and a lumping strategy. This lumping strategy has proved to constitute a substantial improvement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "Yann Favennec"
    },
    {
      "name": "Mahmoud Assaf"
    },
    {
      "name": "Christophe Josset"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c7n44c14ryqjx.bib",
  "cited_by": 0,
  "doi": "10.1016/j.compfluid.2026.107231",
  "fulltext_url": null,
  "id": "c7n44c14ryqjx",
  "issns": [
    "0045-7930",
    "1879-0747"
  ],
  "landing_url": "https://hal.science/hal-05741095v1",
  "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-mp"
    ],
    [
      "hal",
      "1.math.math-oc"
    ],
    [
      "openalex",
      "2206|Lattice Boltzmann Simulation Studies"
    ]
  ],
  "openalex": "W7169009462",
  "pdf_url": "https://hal.science/hal-05741095/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": "Elsevier",
  "ris": "https://research.draconitic.com/paper/c7n44c14ryqjx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "hal-05741095",
      "source": "hal",
      "url": "https://hal.science/hal-05741095v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-mp",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oc",
      "subfield": "optimisation-control"
    }
  ],
  "title": "Adjoint-state Lattice Boltzmann Method: A necessary correction when cost function incorporates macroscopic quantities on boundaries",
  "title_text": "Adjoint-state Lattice Boltzmann Method: A necessary correction when cost function incorporates macroscopic quantities on boundaries",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:41Z",
  "url": "https://research.draconitic.com/paper/c7n44c14ryqjx",
  "venue": "Computers and Fluids",
  "versions": []
}