Document Zbl 1443.65157

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C.</a></div> <h2 class="title"> <strong>On the inter-comparison of two tracer transport schemes on icosahedral grids.</strong> <i>(English)</i> <a class="label nowrap" href="/1443.65157">Zbl 1443.65157</a> </h2> <div class="source"> <a href="/serials/1551" title="Journal Profile">Appl. Math. Modelling</a> <a href="/?q=in%3A443669" title="Articles in this Issue">39, No. 16, 4828-4847 (2015)</a>. </div> <div class="abstract">Summary: Two simple finite volume advection schemes based on linear sub-grid reconstruction are implemented over spherical icosahedral-hexagonal grids. One of theses schemes is fully discrete in space and time, while the other one is a semi-discrete scheme with third order Runge-Kutta time integration. For the linear sub-grid reconstruction, we propose two possible candidates for consistent gradient discretization over general grids. These gradients are designed in a finite volume sense with an adequate modification to guarantee convergence in the absence of special grid optimization. To generate our computational mesh from triangular grid, we either use centroids (BT grid) or circumcenters (VT grid) of the spherical triangular mesh. A numerical convergence study is used to show that for a first order convergence of our discrete gradients grid modification is sufficient, whereas to achieve second order convergence grid optimization is mandatory. This study also implicates that BT grid offers a better rate of convergence than VT grid.<br class="zbmathjax-paragraph">Monotonicity of the advection schemes is enforced by a slope limiter as well as flux-corrected transport (FCT). We compared aforementioned space-time coupled and space-time decoupled advection schemes in terms of their performance for the recently proposed advection test cases. Our findings advocate that space-time coupled advection scheme is performing better than its counterpart. Furthermore, we used the fully discrete advection scheme to carried out a comparison of slope limitation and FCT approach to achieve monotonicity.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7148426">Cited in <strong>1</strong> Document</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M08" title="MSC2020">65M08</a> </td> <td class="space"> Finite volume methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A86-10" title="MSC2020">86-10</a> </td> <td class="space"> Mathematical modeling or simulation for problems pertaining to geophysics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aicosahedral">icosahedral</a>; <a href="/?q=ut%3Atracer+transport">tracer transport</a>; <a href="/?q=ut%3Afinite+volume+scheme">finite volume scheme</a>; <a href="/?q=ut%3Aflux+corrected+transport">flux corrected transport</a></div> <div class="software"> <h3>Software:</h3><a href="/software/11655">chammp</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 1443.65157" data-ciurl="/ci/07148426" data-biburl="/bibtex/07148426.bib" data-amsurl="/amsrefs/07148426.bib" data-xmlurl="/xml/07148426.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07148426.pdf" title="Zbl 1443.65157 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.apm.2015.04.015" aria-label="DOI for “On the inter-comparison of two tracer transport schemes on icosahedral grids”" title="10.1016/j.apm.2015.04.015">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">Rasch, P. 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