<?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-00545843v2</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="2026-05-20T05:01:28+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Numerical modeling of transient two-dimensional viscoelastic waves</title>
            <author role="aut">
              <persName>
                <forename type="first">Bruno</forename>
                <surname>Lombard</surname>
              </persName>
              <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
              <email type="domain">lma.cnrs-mrs.fr</email>
              <idno type="idhal" notation="numeric">830034</idno>
              <idno type="halauthorid" notation="string">104987-830034</idno>
              <affiliation ref="#struct-136844"/>
            </author>
            <author role="aut">
              <persName>
                <forename type="first">Joël</forename>
                <surname>Piraux</surname>
              </persName>
              <email type="md5">9175a63654b6bb667b429c82e2808b47</email>
              <email type="domain">lma.cnrs-mrs.fr</email>
              <idno type="idhal" notation="numeric">830033</idno>
              <idno type="halauthorid" notation="string">104986-830033</idno>
              <affiliation ref="#struct-136844"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Bruno</forename>
                <surname>Lombard</surname>
              </persName>
              <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
              <email type="domain">lma.cnrs-mrs.fr</email>
            </editor>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2010-12-13 09:57:27</date>
            </edition>
            <edition n="v2" type="current">
              <date type="whenSubmitted">2011-03-31 15:13:54</date>
              <date type="whenWritten">2011-04-11</date>
              <date type="whenModified">2025-08-12 17:05:20</date>
              <date type="whenReleased">2011-04-04 09:33:59</date>
              <date type="whenProduced">2011</date>
              <date type="whenEndEmbargoed">2011-03-31</date>
              <ref type="file" target="https://hal.science/hal-00545843v2/document">
                <date notBefore="2011-03-31"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-00545843v2/file/Jcp3V2.pdf" id="file-581672-732774">
                <date notBefore="2011-03-31"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/1012.2669"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102242">
                <persName>
                  <forename>Bruno</forename>
                  <surname>Lombard</surname>
                </persName>
                <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
                <email type="domain">lma.cnrs-mrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-00545843</idno>
            <idno type="halUri">https://hal.science/hal-00545843</idno>
            <idno type="halBibtex">lombard:hal-00545843</idno>
            <idno type="halRefHtml">&lt;i&gt;Journal of Computational Physics&lt;/i&gt;, 2011, 230, pp.6099-6114</idno>
            <idno type="halRef">Journal of Computational Physics, 2011, 230, pp.6099-6114</idno>
            <availability status="restricted">
              <licence target="https://about.hal.science/hal-authorisation-v1/">HAL Authorization<ref corresp="#file-581672-732774"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="UNIV-AMU">Aix Marseille Université</idno>
            <idno type="stamp" n="LMA_UPR7051">Laboratoire de Mécanique et d'Acoustique</idno>
            <idno type="stamp" n="EC-MARSEILLE">Ecole Centrale de Marseille</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="PEIRESC">Fédération Fabri de Peiresc</idno>
            <idno type="stamp" n="IMI-AMU">Institut Mécanique et Ingénierie</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">Numerical modeling of transient two-dimensional viscoelastic waves</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Bruno</forename>
                    <surname>Lombard</surname>
                  </persName>
                  <email type="md5">7297d2c66b4a3e887d6bf9b028d53d8e</email>
                  <email type="domain">lma.cnrs-mrs.fr</email>
                  <idno type="idhal" notation="numeric">830034</idno>
                  <idno type="halauthorid" notation="string">104987-830034</idno>
                  <affiliation ref="#struct-136844"/>
                </author>
                <author role="aut">
                  <persName>
                    <forename type="first">Joël</forename>
                    <surname>Piraux</surname>
                  </persName>
                  <email type="md5">9175a63654b6bb667b429c82e2808b47</email>
                  <email type="domain">lma.cnrs-mrs.fr</email>
                  <idno type="idhal" notation="numeric">830033</idno>
                  <idno type="halauthorid" notation="string">104986-830033</idno>
                  <affiliation ref="#struct-136844"/>
                </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">230</biblScope>
                  <biblScope unit="pp">6099-6114</biblScope>
                  <date type="datePub">2011</date>
                </imprint>
              </monogr>
              <idno type="arxiv">1012.2669</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <keywords scheme="author">
                <term xml:lang="en">wave propagation</term>
                <term xml:lang="en">generalized Zener model</term>
                <term xml:lang="en">memory variables</term>
                <term xml:lang="en">ADER schemes</term>
                <term xml:lang="en">Cartesian grid methods</term>
                <term xml:lang="en">immersed interface method</term>
              </keywords>
              <classCode scheme="halDomain" n="spi.acou">Engineering Sciences [physics]/Acoustics [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="phys.meca.acou">Physics [physics]/Mechanics [physics]/Acoustics [physics.class-ph]</classCode>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</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>This paper deals with the numerical modeling of transient mechanical waves in linear viscoelastic solids. Dissipation mechanisms are described using the generalized Zener model. No time convolutions are required thanks to the introduction of memory variables that satisfy local-in-time differential equations. By appropriately choosing the relaxation parameters, it is possible to accurately describe a large range of materials, such as solids with constant quality factors. The evolution equations satisfied by the velocity, the stress, and the memory variables are written in the form of a first-order system of PDEs with a source term. This system is solved by splitting it into two parts: the propagative part is discretized explicitly, using a fourth-order ADER scheme on a Cartesian grid, and the diffusive part is then solved exactly. Jump conditions along the interfaces are discretized by applying an immersed interface method. Numerical experiments of wave propagation in viscoelastic and fluid media show the efficiency of this numerical modeling for dealing with challenging problems, such as multiple scattering configurations.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-136844" status="VALID">
          <idno type="IdRef">026390604</idno>
          <idno type="RNSR">199617659S</idno>
          <idno type="ROR">https://ror.org/03787ar02</idno>
          <orgName>Laboratoire de Mécanique et d'Acoustique [Marseille]</orgName>
          <orgName type="acronym">LMA</orgName>
          <date type="start">1941-01-01</date>
          <desc>
            <address>
              <addrLine>4 impasse Nikola TeslaCS 4000613453 Marseille Cedex 13</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.lma.cnrs-mrs.fr/</ref>
          </desc>
          <listRelation>
            <relation name="UMR7031" active="#struct-198056" type="direct"/>
            <relation name="UMR7031" active="#struct-300415" type="direct"/>
            <relation name="UMR7031" active="#struct-441569" type="direct"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-198056" status="VALID">
          <idno type="IdRef">15863621X</idno>
          <idno type="ISNI">0000 0001 2176 4817</idno>
          <idno type="ROR">https://ror.org/035xkbk20</idno>
          <orgName>Aix Marseille Université</orgName>
          <orgName type="acronym">AMU</orgName>
          <date type="start">2012-01-01</date>
          <desc>
            <address>
              <addrLine>Aix-Marseille UniversitéJardins du Pharo58 Boulevard Charles Livon13284 Marseille cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-amu.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-300415" status="VALID">
          <idno type="ISNI">0000 0004 1762 2703</idno>
          <idno type="ROR">https://ror.org/040baw385</idno>
          <orgName>École Centrale de Marseille</orgName>
          <orgName type="acronym">ECM</orgName>
          <date type="start">2006-09-27</date>
          <desc>
            <address>
              <addrLine>Pôle de l'étoile - Technopole de Château-Gombert - 38 rue Frédéric Joliot-Curie - 13013 Marseille</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.centrale-marseille.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>
      </listOrg>
    </back>
  </text>
</TEI>