Document Zbl 1149.74351

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Numer. Methods Eng.</a> <a href="/?q=in%3A189320" title="Articles in this Issue">23, No. 1, 71-84 (2007)</a>. </div> <div class="abstract">Summary: This paper proposes a new lattice Boltzmann (LB) method for the study of shock wave propagation in elastic solids. The method, which implements a flux-corrected transport (FCT) algorithm, contains three stages: collision, streaming, and correction. In the collision stage, distribution functions are updated. In the streaming stage, the distribution functions are shifted between lattice points. Generally, a partial differential equation (PDE) is solved in the streaming stage, and finite element methods are employed to support the use of unstructured meshes in the LB method. The FCT algorithm is used in the correction stage to revise the distribution functions at lattice points, so fluctuations behind shock wave fronts can be eliminated efficiently. In this method, schemes for shock wave reflection at fixed and free boundaries are developed based on the bounce-back technique. A similar technique is used to treat wave reflection and transmission at material interfaces of composites. Several one-dimensional examples show that this LB-FCT method can provide ideal depictions of shock wave propagation in structures, especially composite structures.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5121268">Cited in <strong>9</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A74J40" title="MSC2020">74J40</a> </td> <td class="space"> Shocks and related discontinuities in solid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A74H15" title="MSC2020">74H15</a> </td> <td class="space"> Numerical approximation of solutions of dynamical problems in solid mechanics </td> </tr><tr> <td class="mono"> 74S30 </td> <td class="space"> Other numerical methods in solid mechanics (MSC2010) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alattice+Boltzmann+method+flux-corrected+transport+shock+waves">lattice Boltzmann method flux-corrected transport shock waves</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 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method for shock wave propagation in solids”" title="10.1002/cnm.883">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">Batkov, Shear-strength of solids and its effect on plane shock-wave propagation, Combustion Explosion and Shock Waves 22 pp 238– (1986)</td> </tr><tr> <td>[2]</td> <td class="space">Shen, Shock wave induced vaporization of porous solids, Journal of Applied Physics 93 pp 5167– (2003)</td> </tr><tr> <td>[3]</td> <td class="space">Mabssout, A Taylor-Galerkin algorithm for shock wave propagation and strain localization failure of viscoplastic continua, Computer Methods in Applied Mechanics and Engineering 192 pp 955– (2003) · <a href="/1025.74032" class="nowrap">Zbl 1025.74032</a></td> </tr><tr> <td>[4]</td> <td class="space">Lomov, Numerical simulation of damage using an elastic-viscoplastic model with directional tensile failure, Journal of Physics IV 110 pp 281– 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