Document Zbl 1380.65301

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Comput. Phys.</a> <a href="/?q=in%3A372616" title="Articles in this Issue">351, 478-510 (2017)</a>. </div> <div class="abstract">Summary: The main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one- and two-dimensional cases. The mentioned equation has been classified in category of advection equations. The solutions of advection equations have some shock, thus, especial numerical methods should be employed for example discontinuous Galerkin and finite volume methods. Here, based on the proper orthogonal decomposition approach we want to construct a fast meshless method. To this end, we consider shallow water models and obtain a suitable time-discrete scheme based on the predictor-corrector technique. Then, by applying the proper orthogonal decomposition technique, a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem. Thus, by employing the new bases the CPU time will be reduced. Some examples have been studied to show the efficiency of the present numerical technique.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6817939">Cited in <strong>41</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M70" title="MSC2020">65M70</a> </td> <td class="space"> Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65D05" title="MSC2020">65D05</a> </td> <td class="space"> Numerical interpolation </td> </tr><tr> <td class="mono"> 76M25 </td> <td class="space"> Other numerical methods (fluid mechanics) (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A35Q35" title="MSC2020">35Q35</a> </td> <td class="space"> PDEs in connection with fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ameshless+method">meshless method</a>; <a href="/?q=ut%3Aproper+orthogonal+decomposition+procedure">proper orthogonal decomposition procedure</a>; <a href="/?q=ut%3Ashallow+water+equations">shallow water equations</a>; <a href="/?q=ut%3Aradial+basis+functions">radial basis functions</a>; <a href="/?q=ut%3Alocal+collocation+methods">local collocation methods</a>; <a href="/?q=ut%3Afinite+difference+methods">finite difference methods</a>; <a href="/?q=ut%3Alocal+moving+Kriging+interpolation">local moving Kriging interpolation</a></div> <div class="software"> <h3>Software:</h3><a href="/software/558">Matlab</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 1380.65301" data-ciurl="/ci/06817939" data-biburl="/bibtex/06817939.bib" data-amsurl="/amsrefs/06817939.bib" data-xmlurl="/xml/06817939.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06817939.pdf" title="Zbl 1380.65301 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.2017.09.007" aria-label="DOI for “The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations”" title="10.1016/j.jcp.2017.09.007">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">Alcrudoa, F.; Benkhaldoun, F., Exact solutions to the Riemann problem of the shallow water equations with a bottom step, Comput. 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