Document Zbl 1101.82335

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Stat. Phys.</a> <a href="/?q=in%3A51948" title="Articles in this Issue">73, No. 1-2, 193-207 (1993)</a>. </div> <div class="abstract">Summary: In this paper a planar stationary shock-wave-like solution of the Enskog equation obtained via a Monte Carlo technique is studied; both the algorithm used to obtain the solution and the qualitative behavior of the macroscopic quantities are discussed in comparison with the corresponding solution of the Boltzmann equation.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A5048604">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%3A82C40" title="MSC2020">82C40</a> </td> <td class="space"> Kinetic theory of gases in time-dependent statistical mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A45K05" title="MSC2020">45K05</a> </td> <td class="space"> Integro-partial differential equations </td> </tr><tr> <td class="mono"> 82C80 </td> <td class="space"> Numerical methods of time-dependent statistical mechanics (MSC2010) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M35" title="MSC2020">76M35</a> </td> <td class="space"> Stochastic analysis applied to problems in fluid mechanics </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3AKinetic+theory">Kinetic theory</a>; <a href="/?q=ut%3Agas+dynamics">gas dynamics</a>; <a href="/?q=ut%3AEnskog+equation">Enskog equation</a>; <a href="/?q=ut%3Adense+gases">dense gases</a>; <a href="/?q=ut%3Ashock+wave+-+Monte+Carlo+methods">shock wave - Monte Carlo methods</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 1101.82335" data-ciurl="/ci/05048604" data-biburl="/bibtex/05048604.bib" data-amsurl="/amsrefs/05048604.bib" data-xmlurl="/xml/05048604.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/05048604.pdf" title="Zbl 1101.82335 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/10.1007/BF01052757" aria-label="DOI for “Numerical analysis of a shock-wave solution of the Enskog equation obtained via a Monte Carlo method”" title="10.1007/BF01052757">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">D. Enskog,Kinetische Theorie (Svenska Akad., 63, 1921).</td> </tr><tr> <td>[2]</td> <td class="space">S. Chapman and T. G. Cowling,The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1960). · <a href="/0098.39702" class="nowrap">Zbl 0098.39702</a></td> </tr><tr> <td>[3]</td> <td class="space">P. Resibois and M. De Leener,Classical Kinetic Theory of Fluids (Wiley, London, 1977).</td> </tr><tr> <td>[4]</td> <td class="space">N. Bellomo, M. Lachowicz, J. Polewczac, and G. Toscani,Mathematical Topics in Nonlinear Kinetic Theory II: The Enskog Equation (World Scientific, Singapore, 1991). · <a href="/0733.76061" class="nowrap">Zbl 0733.76061</a></td> </tr><tr> <td>[5]</td> <td class="space">L. Arkeryd and C. Cercignani, Global existence in L1 for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation,J. Stat. Phys. 59:845-867 (1990). · <a href="/0780.76066" class="nowrap">Zbl 0780.76066</a> · <a href="https://doi.org/10.1007/BF01025854" class="nowrap">doi:10.1007/BF01025854</a></td> </tr><tr> <td>[6]</td> <td class="space">B. L. Holian, W. G. Hoover, B. Moran, and G. K. Straub, Shock-wave structure via nonequilibrium molecular dynamics and Navier-Stokes continuum mechanics,Phys. Rev. 22A:2798-2808 (1980).</td> </tr><tr> <td>[7]</td> <td class="space">H. M. Mott-Smith, The solution of the Boltzmann equation for a shock-wave,Phys. Rev. 82:885-900 (1951). · <a href="/0043.40703" class="nowrap">Zbl 0043.40703</a> · <a href="https://doi.org/10.1103/PhysRev.82.885" class="nowrap">doi:10.1103/PhysRev.82.885</a></td> </tr><tr> <td>[8]</td> <td class="space">A. V. Orlov, Extension of the Mott-Smith method to denser gases,Phys. Fluids A 4(8):1856-1858 (1992). · <a href="/0754.76052" class="nowrap">Zbl 0754.76052</a> · <a href="https://doi.org/10.1063/1.858358" class="nowrap">doi:10.1063/1.858358</a></td> </tr><tr> <td>[9]</td> <td class="space">A. Nordsieck and B. Hicks, Monte Carlo evaluation of the Boltzmann collision integral, inRarefied Gas Dynamics, Vol. 2, C. L. Brundin, ed. (Academic Press, New York, 1967, pp. 695-710.</td> </tr><tr> <td>[10]</td> <td class="space">F. G. Tcheremissine, Fast solutions of the Boltzmann equation, inRarefied Gas Dynamics, Vol. 1, A. E. Beylich, ed. (VCH, Aachen, 1991), pp. 273-284.</td> </tr><tr> <td>[11]</td> <td class="space">V. V. Aristov, Development of the regular method of the Boltzmann equation, inRarefied Gas Dynamics, Vol. 1, A. E. Beylich, ed. (VCH, Aachen, 1991), pp. 879-885.</td> </tr><tr> <td>[12]</td> <td class="space">G. A. Bird,Molecular Gas Dynamics (Clarendon Press, Oxford, 1976).</td> </tr><tr> <td>[13]</td> <td class="space">K. Nambu, Theoretical basis of the direct simulation Monte Carlo method, inRarefied Gas Dynamics, Vol. 2, V. Boffi and C. Cercignani, eds. (Teubner, Stuttgart, 1986), pp. 379-383.</td> </tr><tr> <td>[14]</td> <td class="space">K. Koura, Null collision technique in the direct simulation Monte-Carlo method,Phys. Fluids 29:3509-3511 (1986). · <a href="https://doi.org/10.1063/1.865826" class="nowrap">doi:10.1063/1.865826</a></td> </tr><tr> <td>[15]</td> <td class="space">V. V. Aristov and F. G. Tcheremissine, The conservative splitting method for solving the Boltzmann equation,USSR Comp. Math. Phys. 20:208 (1980). · <a href="/0458.76061" class="nowrap">Zbl 0458.76061</a> · <a href="https://doi.org/10.1016/0041-5553(80)90074-9" class="nowrap">doi:10.1016/0041-5553(80)90074-9</a></td> </tr><tr> <td>[16]</td> <td class="space">M. H. Kalos and P. A. Whitlock,Monte Carlo Methods (Wiley, New York, 1986).</td> </tr><tr> <td>[17]</td> <td class="space">A. Frezzotti and R. Pavani, Direct numerical solution of the Boltzmann equation for a relaxation problem of a binary mixture,Meccanica 24:139 (1989). · <a href="/0679.76088" class="nowrap">Zbl 0679.76088</a> · <a href="https://doi.org/10.1007/BF01559416" class="nowrap">doi:10.1007/BF01559416</a></td> </tr><tr> <td>[18]</td> <td class="space">M. N. Kogan,Rarefied Gas Dynamics (Plenum Press, New York, 1969).</td> </tr><tr> <td>[19]</td> <td class="space">H. Van Beijeren and M. H. Ernst, The modified Enskog equation,Physica 68:437-456 (1973). · <a href="https://doi.org/10.1016/0031-8914(73)90372-8" class="nowrap">doi:10.1016/0031-8914(73)90372-8</a></td> </tr><tr> <td>[20]</td> <td class="space">P. Resibois, H-theorem for the (modified) nonlinear Enskog equation,J. Stat. Phys. 19:593-609 (1978). · <a href="https://doi.org/10.1007/BF01011771" class="nowrap">doi:10.1007/BF01011771</a></td> </tr><tr> <td>[21]</td> <td class="space">K. A. Fiscko and D. R. Chapman, Comparison of Burnett, Super-Burnett and Monte Carlo solutions for hypersonic shock structure, inRarefied Gas Dynamics, Vol. 1, E. P. Muntz, D. P. Weaver, and D. H. Campbell, eds. (AIAA, Pasadena, California, 1988), pp. 374-395.</td> </tr><tr> <td>[22]</td> <td class="space">E. Salomons and M. Mareschal, Usefulness of the Burnett description of strong shock waves,Phys. Rev. Lett. 69(2):269-272 (1992). · <a href="https://doi.org/10.1103/PhysRevLett.69.269" class="nowrap">doi:10.1103/PhysRevLett.69.269</a></td> </tr><tr> <td>[23]</td> <td class="space">B. L. Holian, C. W. Patterson, M. Mareschal, and E. Salomons, Modeling shock waves in an ideal gas: Going beyond the Navier-Stokes level,Phys. Rev. E 47(1):R24-27 (1993). · <a href="https://doi.org/10.1103/PhysRevE.47.R24" class="nowrap">doi:10.1103/PhysRevE.47.R24</a></td> </tr><tr> <td>[24]</td> <td class="space">W. Marques and G. M. Kremer, On Enskog’s dense gas theory. II. The linearized Burnett equations for monatomic gases,Rev. Bras. Fis. 21(3):402-417 (1991).</td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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