Document Zbl 1349.76558

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Comput. Phys.</a> <a href="/?q=in%3A361119" title="Articles in this Issue">302, 114-154 (2015)</a>. </div> <div class="abstract">Summary: This paper presents an extensive review of most of the existing TVD schemes found in literature that are based on the One-step Time-space-coupled Unsteady TVD criterion (OTU-TVD), the Multi-step Time-space-separated Unsteady TVD criterion (MTU-TVD) and the Semi-discrete Steady-state TVD criterion (SS-TVD). The design principles of these schemes are examined in detail. It is found that the selection of appropriate flux-limiters is a key design element in developing these schemes. Different flux-limiter forms (CFL-dependent or CFL-independent, and various limiting criteria) are shown to lead to different performances in accuracy and convergence. Furthermore, a refined SS-TVD flux-limiter, referred to henceforth as TCDF (Third-order Continuously Differentiable Function), is proposed for steady-state calculations based on the review. To evaluate the performance of the newly proposed scheme, many existing classical SS-TVD limiters are compared with the TCDF in eight two-dimensional test cases. The numerical results clearly show that the TCDF results in an improved overall performance.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6660820">Cited in <strong>25</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M20" title="MSC2020">76M20</a> </td> <td class="space"> Finite difference methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M06" title="MSC2020">65M06</a> </td> <td class="space"> Finite difference methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M12" title="MSC2020">65M12</a> </td> <td class="space"> Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atotal+variation+diminishing">total variation diminishing</a>; <a href="/?q=ut%3Ahigh+resolution+scheme">high resolution scheme</a>; <a href="/?q=ut%3Anormalized+variable+diagram">normalized variable diagram</a>; <a href="/?q=ut%3Aconvection+boundedness+criterion">convection boundedness criterion</a>; <a href="/?q=ut%3Aconvection+discretization">convection discretization</a>; <a href="/?q=ut%3Aflux+limiter">flux limiter</a></div> <div class="software"> <h3>Software:</h3><a href="/software/18281">SHASTA</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 1349.76558" data-ciurl="/ci/06660820" data-biburl="/bibtex/06660820.bib" data-amsurl="/amsrefs/06660820.bib" data-xmlurl="/xml/06660820.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06660820.pdf" title="Zbl 1349.76558 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.2015.08.042" aria-label="DOI for “A review on TVD schemes and a refined flux-limiter for steady-state calculations”" title="10.1016/j.jcp.2015.08.042">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://www.repository.cam.ac.uk/handle/1810/250531" title="Full Text Link">Link</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Ubbink, O.; Issa, R. 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