Document Zbl 1349.76692

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Comput. Phys.</a> <a href="/?q=in%3A361117" title="Articles in this Issue">300, 70-91 (2015)</a>. </div> <div class="abstract">Summary: In this paper, we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice Boltzmann method for convection-diffusion equations with general Robin boundary conditions. One scheme is for straight boundaries, with the boundary points locating at any distance from the lattice nodes, and has second-order accuracy. The other is for curved boundaries, has only first-order accuracy and is much simpler than the existing schemes. Unlike those in the literature, our schemes involve only the current lattice node. Such a “single-node” boundary schemes are highly desirable for problems with complex geometries. The two schemes are validated numerically with a number of examples. The numerical results show the utility of the constructed schemes and very well support our theoretical predications.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6660751">Cited in <strong>21</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M28" title="MSC2020">76M28</a> </td> <td class="space"> Particle methods and lattice-gas methods </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A65M75" title="MSC2020">65M75</a> </td> <td class="space"> Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs </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><tr> <td> <a class="mono" href="/classification/?q=cc%3A35K57" title="MSC2020">35K57</a> </td> <td class="space"> Reaction-diffusion equations </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alattice+Boltzmann+method">lattice Boltzmann method</a>; <a href="/?q=ut%3Aconvection-diffusion+equations">convection-diffusion equations</a>; <a href="/?q=ut%3ARobin+boundary+conditions">Robin boundary conditions</a>; <a href="/?q=ut%3Acurved+boundaries">curved boundaries</a>; <a href="/?q=ut%3Aasymptotic+analysis">asymptotic analysis</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 1349.76692" data-ciurl="/ci/06660751" data-biburl="/bibtex/06660751.bib" data-amsurl="/amsrefs/06660751.bib" data-xmlurl="/xml/06660751.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06660751.pdf" title="Zbl 1349.76692 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.2015.07.045" aria-label="DOI for “Boundary conditions of the lattice Boltzmann method for convection-diffusion equations”" title="10.1016/j.jcp.2015.07.045">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">Wang, C.-W.; Sastry, A. 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