Document Zbl 07953994

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Comput. Phys.</a> <a href="/?q=in%3A521241" title="Articles in this Issue">520, Article ID 113501, 20 p. (2025)</a>. </div> <div class="abstract">Summary: The recently-developed general synthetic iterative scheme (GSIS), which is tailored for non-equilibrium dilute gas, has been extended to find the steady-state solutions of the non-equilibrium dense gas flows based on the Shakhov-Enskog model, resolving the problems of slow convergence and requirement of ultra-fine grids in near-continuum flows that exist in the conventional iterative scheme. The key ingredient of GSIS is the tight coupling of the mesoscopic kinetic equation and the macroscopic synthetic equations that are exactly derived from the kinetic equation. On the one hand, high-order terms computed from the velocity distribution function provide the higher-order constitutive relations describing the non-equilibrium effects for the macroscopic synthetic equations. On the other hand, the macroscopic quantities obtained from the macroscopic synthetic equations are used to guide the evolution of the velocity distribution function in the kinetic equation. The efficiency and accuracy of GSIS are demonstrated in several test cases, including the shock wave passing through a cylinder and the pressure-driven dense gas flows passing through parallel plates and porous media. The effects of denseness are analyzed in a wide range of gas rarefaction.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76Mxx" title="MSC2020">76Mxx</a> </td> <td class="space"> Basic methods in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76Pxx" title="MSC2020">76Pxx</a> </td> <td class="space"> Rarefied gas flows, Boltzmann equation in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65Mxx" title="MSC2020">65Mxx</a> </td> <td class="space"> Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Adense+gas">dense gas</a>; <a href="/?q=ut%3Ageneral+synthetic+iterative+scheme">general synthetic iterative scheme</a>; <a href="/?q=ut%3Aporous+media">porous media</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 07953994" data-ciurl="/ci/07953994" data-biburl="/bibtex/07953994.bib" data-amsurl="/amsrefs/07953994.bib" data-xmlurl="/xml/07953994.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07953994.pdf" title="Zbl 07953994 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/10.1016/j.jcp.2024.113501" aria-label="DOI for “General synthetic iterative scheme for non-equilibrium dense gas flows”" title="10.1016/j.jcp.2024.113501">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">Wu, K.; Chen, Z.; Li, X., Real gas transport through nanopores of varying cross-section type and shape in shale gas reservoirs, Chem. 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