Document Zbl 1081.82619

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David</a></div> <h2 class="title"> <strong>Moment closure hierarchies for kinetic theories.</strong> <i>(English)</i> <a class="label nowrap" href="/1081.82619">Zbl 1081.82619</a> </h2> <div class="source"> <a href="/serials/140" title="Journal Profile">J. Stat. Phys.</a> <a href="/?q=in%3A54599" title="Articles in this Issue">83, No. 5-6, 1021-1065 (1996)</a>. </div> <div class="abstract">Summary: This paper presents a systematicnonperturbative derivation of a hierarchy of closed systems of moment equations corresponding to any classical kinetic theory. The first member of the hierarchy is the Euler system, which is based on Maxwellian velocity distributions, while the second member is based on nonisotropic Gaussian velocity distributions. The closure proceeds in two steps. The first ensures that every member of the hierarchy is hyperbolic, has an entropy, and formally recovers the Euler limit. The second involves modifying the collisional terms so that members of the hierarchy beyound the second also recover the correct Navier-Stokes behavior. This is achieved through the introduction of a generalization of the BGK collision operator. The simplest such system in three spatial dimensions is a 14-moment closure, which also recovers the behavior of the Grad 13-moment system when the velocity distributions lie near local Maxwellians. The closure procedure can be applied to a general class of kinetic theories.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A1554087">Cited in <strong>5</strong> Reviews</a></div><div class="clear"><a href="/?q=rf%3A1554087">Cited in <strong>384</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A82C40" title="MSC2020">82C40</a> </td> <td class="space"> Kinetic theory of gases in time-dependent statistical mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76P05" title="MSC2020">76P05</a> </td> <td class="space"> Rarefied gas flows, Boltzmann equation in fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Akinetic+theory">kinetic theory</a>; <a href="/?q=ut%3Amoment+closures">moment closures</a>; <a href="/?q=ut%3Ahyperbolic+systems">hyperbolic systems</a>; <a href="/?q=ut%3Aentropy%2C+BGK">entropy, BGK</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1081.82619" data-ciurl="/ci/01554087" data-biburl="/bibtex/01554087.bib" data-amsurl="/amsrefs/01554087.bib" data-xmlurl="/xml/01554087.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01554087.pdf" title="Zbl 1081.82619 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/BF02179552" aria-label="DOI for “Moment closure hierarchies for kinetic theories.”" title="10.1007/BF02179552">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">L. 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