Document Zbl 07819061

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Comput. Phys.</a> <a href="/?q=in%3A509911" title="Articles in this Issue">499, Article ID 112714, 26 p. (2024)</a>. </div> <div class="abstract">Summary: The aim of this work is to construct efficient finite volume schemes for the numerical study of sediment transport in shallow water, in the framework of the Exner model [<span class="zbmathjax-textit">S. Boscarino</span> et al., SIAM J. Numer. Anal. 55, No. 4, 2085–2109 (2017; <a href="/1372.65261">Zbl 1372.65261</a>); <span class="zbmathjax-textit">M. J. Castro Díaz</span> et al., Comput. Fluids 37, No. 3, 299–316 (2008; <a href="/1237.76082">Zbl 1237.76082</a>)]. In most cases, the velocity related to the sediment is much lower that the fluid velocity, which, in turn, may be much lower that the free-surface wave speed. Explicit methods that resolve all waves require small time steps due to the CFL stability restriction because of fast surface waves. Furthermore, if Rusanov flux is adopted, slow sediment waves may be affected by the large numerical diffusion. The objective of the present work is to drastically improve the efficiency in the computation of the evolution of the sediment by treating water waves implicitly, thus allowing much larger time steps than the one required by fully explicit schemes. The goal is reached by suitably semi-implicit schemes obtained by the use of implicit-explicit Runge-Kutta methods.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A7819061">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A7819061">Cited in <strong>4</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><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><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%3A86Axx" title="MSC2020">86Axx</a> </td> <td class="space"> Geophysics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Asemi-implicit+scheme">semi-implicit scheme</a>; <a href="/?q=ut%3AExner+model">Exner model</a>; <a href="/?q=ut%3Asediment+transport">sediment transport</a>; <a href="/?q=ut%3Ahigh-order+scheme">high-order scheme</a>; <a href="/?q=ut%3Aasymptotic-preserving+scheme">asymptotic-preserving scheme</a>; <a href="/?q=ut%3AGrass+equation">Grass equation</a></div><div class="keywords"> <h3>Citations:</h3><a href="/1372.65261">Zbl 1372.65261</a>; <a href="/1237.76082">Zbl 1237.76082</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 07819061" data-ciurl="/ci/07819061" data-biburl="/bibtex/07819061.bib" data-amsurl="/amsrefs/07819061.bib" data-xmlurl="/xml/07819061.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07819061.pdf" title="Zbl 07819061 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.2023.112714" aria-label="DOI for “A semi-implicit finite volume method for the Exner model of sediment transport”" title="10.1016/j.jcp.2023.112714">DOI</a> <a class="btn btn-default btn-xs" type="button" href="https://arxiv.org/abs/2303.03801"title="Note: arXiv document may differ from published version">arXiv</a> </div> <div class="sfx" style="float: right;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" title="Open Access License" class="cc-license-link no-new-tab-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/cc.svg" alt="Creative Commons CC license icon" class="cc-license-icon"> <img src="https://static.zbmath.org/contrib/img/cc/svg/icons/by.svg" alt="Creative Commons BY license icon" class="cc-license-icon"> </a> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Audusse, E.; Berthon, C.; Chalons, C.; Delestre, O.; Goutal, N.; Jodeau, M.; Sainte-Marie, J.; Giesselmann, J.; Sadaka, G., Sediment transport modelling: relaxation schemes for Saint-Venant-Exner and three layer models. 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