<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-03215358</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-15T11:38:29+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">A 3D cell-centered ADER MOOD Finite Volume method for solving updated Lagrangian hyperelasticity on unstructured grids</title>
            <author role="aut">
              <persName>
                <forename type="first">Walter</forename>
                <surname>Boscheri</surname>
              </persName>
              <email type="md5">50e7262027171a2e41ae2e41cb00965d</email>
              <email type="domain">univ-smb.fr</email>
              <idno type="idhal" notation="string">walterboscheri</idno>
              <idno type="idhal" notation="numeric">1420377</idno>
              <idno type="halauthorid" notation="string">1493272-1420377</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1467-1679</idno>
              <idno type="IDREF">https://www.idref.fr/282723218</idno>
              <affiliation ref="#struct-17555"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Raphaël</forename>
                <surname>Loubère</surname>
              </persName>
              <email type="md5">eb0f097476eb4b83790532e0fb73436f</email>
              <email type="domain">u-bordeaux.fr</email>
              <idno type="idhal" notation="string">raphael-loubere</idno>
              <idno type="idhal" notation="numeric">12020</idno>
              <idno type="halauthorid" notation="string">28668-12020</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-1249-1578</idno>
              <idno type="IDREF">https://www.idref.fr/069269858</idno>
              <affiliation ref="#struct-27730"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Pierre-Henri</forename>
                <surname>Maire</surname>
              </persName>
              <idno type="halauthorid">2200341-0</idno>
              <affiliation ref="#struct-21150"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Raphaël</forename>
                <surname>Loubère</surname>
              </persName>
              <email type="md5">eb0f097476eb4b83790532e0fb73436f</email>
              <email type="domain">u-bordeaux.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1" type="current">
              <date type="whenSubmitted">2021-05-03 12:05:47</date>
              <date type="whenModified">2025-04-01 14:41:04</date>
              <date type="whenReleased">2021-05-04 08:41:02</date>
              <date type="whenProduced">2022</date>
              <date type="whenEndEmbargoed">2021-05-03</date>
              <ref type="file" target="https://hal.science/hal-03215358v1/document">
                <date notBefore="2021-05-03"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-03215358v1/file/article_blm.pdf" id="file-3215358-2823140">
                <date notBefore="2021-05-03"/>
              </ref>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="104656">
                <persName>
                  <forename>Raphaël</forename>
                  <surname>Loubère</surname>
                </persName>
                <email type="md5">eb0f097476eb4b83790532e0fb73436f</email>
                <email type="domain">u-bordeaux.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-03215358</idno>
            <idno type="halUri">https://hal.science/hal-03215358</idno>
            <idno type="halBibtex">boscheri:hal-03215358</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Computational Physics&lt;/i&gt;, 2022, 449</idno>
            <idno type="halRef">Journal of Computational Physics, 2022, 449</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-3215358-2823140"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CEA">CEA - Commissariat à l'énergie atomique</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="IMB">Institut de Mathématiques de Bordeaux</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="DAM" corresp="CEA">Direction des applications militaires</idno>
            <idno type="stamp" n="UNIVERSITE-BORDEAUX">Université de Bordeaux</idno>
          </seriesStmt>
          <notesStmt>
            <note type="audience" n="2">International</note>
            <note type="popular" n="0">No</note>
            <note type="peer" n="1">Yes</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">A 3D cell-centered ADER MOOD Finite Volume method for solving updated Lagrangian hyperelasticity on unstructured grids</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Walter</forename>
                    <surname>Boscheri</surname>
                  </persName>
                  <email type="md5">50e7262027171a2e41ae2e41cb00965d</email>
                  <email type="domain">univ-smb.fr</email>
                  <idno type="idhal" notation="string">walterboscheri</idno>
                  <idno type="idhal" notation="numeric">1420377</idno>
                  <idno type="halauthorid" notation="string">1493272-1420377</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1467-1679</idno>
                  <idno type="IDREF">https://www.idref.fr/282723218</idno>
                  <affiliation ref="#struct-17555"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Raphaël</forename>
                    <surname>Loubère</surname>
                  </persName>
                  <email type="md5">eb0f097476eb4b83790532e0fb73436f</email>
                  <email type="domain">u-bordeaux.fr</email>
                  <idno type="idhal" notation="string">raphael-loubere</idno>
                  <idno type="idhal" notation="numeric">12020</idno>
                  <idno type="halauthorid" notation="string">28668-12020</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-1249-1578</idno>
                  <idno type="IDREF">https://www.idref.fr/069269858</idno>
                  <affiliation ref="#struct-27730"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Pierre-Henri</forename>
                    <surname>Maire</surname>
                  </persName>
                  <idno type="halauthorid">2200341-0</idno>
                  <affiliation ref="#struct-21150"/>
                </author>
              </analytic>
              <monogr>
                <idno type="halJournalId" status="VALID">15275</idno>
                <idno type="issn">0021-9991</idno>
                <idno type="eissn">1090-2716</idno>
                <title level="j">Journal of Computational Physics</title>
                <imprint>
                  <publisher>Elsevier</publisher>
                  <biblScope unit="volume">449</biblScope>
                  <date type="datePub">2022</date>
                </imprint>
              </monogr>
              <relatedItem target="https://doi.org/10.1016/j.jcp.2021.110779" type="Cites" subtype="http://purl.org/coar/resource_type/c_1843"/>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math">Mathematics [math]</classCode>
              <classCode scheme="halTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halOldTypology" n="ART">Journal articles</classCode>
              <classCode scheme="halTreeTypology" n="ART">Journal articles</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>In this paper, we present a conservative cell-centered Lagrangian Finite Volume scheme for solving the hyperelasticity equations on unstructured multidimensional grids. The starting point of the present approach is the cell-centered FV discretization named EUCCLHYD and introduced in the context of Lagrangian hydrodynamics. Here, it is combined with the a posteriori Multidimensional Optimal Order Detection (MOOD) limiting strategy to ensure robustness and stability at shock waves with piecewise linear spatial reconstruction. The ADER (Arbitrary high order schemes using DERivatives) approach is adopted to obtain second-order of accuracy in time. This strategy has been successfully tested in an hydrodynamics context and the present work aims at extending it to the case of hyperelasticity. Here, the hyperelasticty equations are written in the updated Lagrangian framework and the dedicated Lagrangian numerical scheme is derived in terms of nodal solver, Geometrical Conservation Law (GCL) compliance, subcell forces and compatible discretization. The Lagrangian numerical method is implemented in 3D under MPI parallelization framework allowing to handle genuinely large meshes. A relatively large set of numerical test cases is presented to assess the ability of the method to achieve effective second order of accuracy on smooth flows, maintaining an essentially non-oscillatory behavior and general robustness across discontinuities and ensuring at least physical admissibility of the solution where appropriate. Pure elastic neo-Hookean and non-linear materials are considered for our benchmark test problems in 2D and 3D. These test cases feature material bending, impact, compression, non-linear deformation and further bouncing/detaching motions.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-17555" status="VALID">
          <orgName>Department of Mathematics [Ferrara]</orgName>
          <desc>
            <address>
              <addrLine>Via Ludovico Ariosto, 35 - 44121 Ferrara</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">http://www.dm.unife.it/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-304516" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-27730" status="VALID">
          <idno type="IdRef">155051342</idno>
          <idno type="ISNI">0000000123024783</idno>
          <idno type="RNSR">200711916B</idno>
          <idno type="ROR">https://ror.org/05m3r1b84</idno>
          <orgName>Institut de Mathématiques de Bordeaux</orgName>
          <orgName type="acronym">IMB</orgName>
          <date type="start">2003-01-01</date>
          <desc>
            <address>
              <addrLine>351 cours de la Libération 33405 TALENCE CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.math.u-bordeaux.fr/IMB/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-259761" type="direct"/>
            <relation active="#struct-409745" type="direct"/>
            <relation name="UMR5251" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="laboratory" xml:id="struct-21150" status="VALID">
          <orgName>Centre d'études scientifiques et techniques d'Aquitaine (CESTA-CEA)</orgName>
          <orgName type="acronym">CESTA</orgName>
          <desc>
            <address>
              <addrLine>BP 2 33114 Le Barp</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation name="DAM/CESTA" active="#struct-5981" type="direct"/>
            <relation name="DAM" active="#struct-300016" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-304516" status="VALID">
          <orgName>Università degli Studi di Ferrara = University of Ferrara</orgName>
          <orgName type="acronym">UniFE</orgName>
          <desc>
            <address>
              <addrLine>via Ludovico Ariosto, 35, 44121 Ferrara</addrLine>
              <country key="IT"/>
            </address>
            <ref type="url">http://www.unife.it</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-259761" status="VALID">
          <idno type="IdRef">175206562</idno>
          <idno type="ROR">https://ror.org/057qpr032</idno>
          <orgName>Université de Bordeaux</orgName>
          <orgName type="acronym">UB</orgName>
          <desc>
            <address>
              <addrLine>35, place Pey Berland - 33076 Bordeaux</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.u-bordeaux.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-409745" status="VALID">
          <orgName>Institut Polytechnique de Bordeaux</orgName>
          <orgName type="acronym">Bordeaux INP</orgName>
          <desc>
            <address>
              <addrLine>Avenue des facultés33405 Talence</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.bordeaux-inp.fr/fr</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="regrouplaboratory" xml:id="struct-5981" status="VALID">
          <idno type="IdRef">026372096</idno>
          <idno type="ISNI">0000000119569481</idno>
          <idno type="ROR">https://ror.org/00kn4eb29</idno>
          <idno type="Wikidata">Q2931222</idno>
          <orgName>Direction des Applications Militaires</orgName>
          <orgName type="acronym">DAM</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">http://www-dam.cea.fr/</ref>
          </desc>
          <listRelation>
            <relation name="DAM" active="#struct-300016" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-300016" status="VALID">
          <idno type="IdRef">026372061</idno>
          <idno type="ISNI">0000000122998025</idno>
          <idno type="ROR">https://ror.org/00jjx8s55</idno>
          <idno type="Wikidata">Q868550</idno>
          <orgName>Commissariat à l'énergie atomique et aux énergies alternatives</orgName>
          <orgName type="acronym">CEA</orgName>
          <desc>
            <address>
              <addrLine>Centre de SaclayCentre de GrenobleCentre de Cadaracheetc</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.cea.fr/</ref>
          </desc>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>