Document Zbl 0945.76058

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Comput. Appl. Math.</a> <a href="/?q=in%3A59476" title="Articles in this Issue">109, No. 1-2, 153-171 (1999)</a>. </div> <div class="abstract">Summary: A numerical method is reviewed and described in detail which allows an accurate solution of the equations of radiation hydrodynamics for one-dimensional spherical configurations. Such problems occur in a large variety of astrophysical situations, where the interaction of matter with radiation (and vice versa) plays an important role (e.g. stellar structure, stellar pulsations, star and planet formation, radiation driven winds, stellar explosions, etc.). The method relies on a conservative formulation of the physical equations and uses an adaptive grid to resolve and trace any steep features developing within the flow. Due to the wide temporal as well as spatial range of physical time scales, the solution is advanced in time by an implicit discretization scheme resulting in a nonlinear system of algebraic equations which has to be solved by a Newton-Raphson procedure. A few examples concerning stellar pulsations of a class of luminous blue stars closes this article.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A76M20" title="MSC2020">76M20</a> </td> <td class="space"> Finite difference methods applied to problems in fluid mechanics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A76N15" title="MSC2020">76N15</a> </td> <td class="space"> Gas dynamics (general theory) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A85-08" title="MSC2020">85-08</a> </td> <td class="space"> Computational methods for problems pertaining to astronomy and astrophysics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A85A30" title="MSC2020">85A30</a> </td> <td class="space"> Hydrodynamic and hydromagnetic problems in astronomy and astrophysics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A78A40" title="MSC2020">78A40</a> </td> <td class="space"> Waves and radiation in optics and electromagnetic theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aradiation+hydrodynamics">radiation hydrodynamics</a>; <a href="/?q=ut%3Aone-dimensional+spherical+configurations">one-dimensional spherical configurations</a>; <a href="/?q=ut%3Aconservative+formulation">conservative formulation</a>; <a href="/?q=ut%3Aadaptive+grid">adaptive grid</a>; <a href="/?q=ut%3Aimplicit+discretization+scheme">implicit discretization scheme</a>; <a href="/?q=ut%3ANewton-Raphson+procedure">Newton-Raphson procedure</a>; <a href="/?q=ut%3Astellar+pulsations">stellar pulsations</a>; <a href="/?q=ut%3Aluminous+blue+stars">luminous blue stars</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 0945.76058" data-ciurl="/ci/01367802" data-biburl="/bibtex/01367802.bib" data-amsurl="/amsrefs/01367802.bib" data-xmlurl="/xml/01367802.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/01367802.pdf" title="Zbl 0945.76058 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/S0377-0427(99)00157-0" aria-label="DOI for “Implicit radiation hydrodynamics for 1D-problems”" title="10.1016/S0377-0427(99)00157-0">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">Balluch, M., Protostellar evolution I, Astron. 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U., Adaptive radiation hydrodynamics of pulsating stars, Comput. Phys. Commun., 89, 69-90 (1995) · <a href="/0923.76249" class="nowrap">Zbl 0923.76249</a></td> </tr><tr> <td>[10]</td> <td class="space">Feuchtinger, M. U.; Dorfi, E. A., Properties of theoretical RRab light curves, Astron. Astrophys., 291, 817-824 (1997)</td> </tr><tr> <td>[11]</td> <td class="space">Gautschy, A.; Saio, H., Stellar pulsation across the HR diagram: part I, Ann. Rev. Astron. Astrophys., 33, 75-113 (1995)</td> </tr><tr> <td>[12]</td> <td class="space">Gautschy, A.; Saio, H., Stellar pulsation across the HR diagram: part II, Ann. Rev. Astron. Astrophys., 34, 551-606 (1996)</td> </tr><tr> <td>[13]</td> <td class="space">Höfner, S.; Dorfi, E. A., Dust formation in winds of long period variables VI, Astron. Astrophys., 319, 648-654 (1997)</td> </tr><tr> <td>[14]</td> <td class="space">R. Kippenhahn, A. Weigert, Stellar Structure and Evolution, Springer, Berlin, 1990.; R. Kippenhahn, A. 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(Suppl.), 79, 507-568 (1992)</td> </tr><tr> <td>[18]</td> <td class="space">Seaton, M. J.; Yan, Yu; Mihalas, D.; Prandhan, A. K., Opacities for stellar envelopes, Mon. Not. Roy. Astron. Soc., 266, 805-828 (1994)</td> </tr><tr> <td>[19]</td> <td class="space">Sod, G. A., A survey of several finite difference methods of systems of nonlinear hyperbolic conservation laws, J. Comput. Phys., 27, 1-31 (1978) · <a href="/0387.76063" class="nowrap">Zbl 0387.76063</a></td> </tr><tr> <td>[20]</td> <td class="space">H. Späth, Spline Algorithmen zur Konstruktion glatter Kurven und Flächen, Oldenburg, München, 1986.; H. Späth, Spline Algorithmen zur Konstruktion glatter Kurven und Flächen, Oldenburg, München, 1986.</td> </tr><tr> <td>[21]</td> <td class="space">Tscharnuter, W. M., A collapse model of the turbulent presolar nebula, Astron. Astrophys., 188, 55-73 (1987)</td> </tr><tr> <td>[22]</td> <td class="space">Tscharnuter, W. M.; Winkler, K.-H. A., A method for computing selfgravitating gas flows with radiation, Comput. Phys. Commun., 18, 171 (1979)</td> </tr><tr> <td>[23]</td> <td class="space">van Leer, B., Towards the ultimate conservative difference scheme, IV, J. Comput. Phys., 23, 276-299 (1977) · <a href="/0339.76056" class="nowrap">Zbl 0339.76056</a></td> </tr><tr> <td>[24]</td> <td class="space">von Neumann, J.; Richtmyer, R. D., A method for the numerical calculation of hydrodynamic shocks, J. Appl. Phys., 21, 232-237 (1950) · <a href="/0037.12002" class="nowrap">Zbl 0037.12002</a></td> </tr><tr> <td>[25]</td> <td class="space">K.-H.A. Winkler, Über ein numerisches Verfahren zur Berechnung instationärer sphärischer Stoßfronten mit Strahlung, Ph.D. Thesis, Univ. Göttingen, 1975, also preprint Max-Planck-Institut für Astrophysik, MPA90, Garching, engl. translation: Lawrence Livermore Lab. Rep. UCLR-Trans 11206, Univ. of. California, 1977.; K.-H.A. Winkler, Über ein numerisches Verfahren zur Berechnung instationärer sphärischer Stoßfronten mit Strahlung, Ph.D. Thesis, Univ. Göttingen, 1975, also preprint Max-Planck-Institut für Astrophysik, MPA90, Garching, engl. translation: Lawrence Livermore Lab. Rep. UCLR-Trans 11206, Univ. of. California, 1977.</td> </tr><tr> <td>[26]</td> <td class="space">Winkler, K.-H. A.; Norman, M. L.; Mihalas, D., Adaptive mesh radiation hydrodynamics I, J. Quant. Spectrosc. Radiat. Transfer, 31, 473-478 (1984)</td> </tr><tr> <td>[27]</td> <td class="space">K.-H.A. Winkler, M.L. Norman, Wh80s: Numerical radiation hydrodynamics, in: K.-H. Winkler, M.L. Norman (Eds.), Astrophysical Radiation Hydrodynamics, Vol. 188, NATO-ASI Series C, D. Reidel, Dordrecht, p. 223.; K.-H.A. Winkler, M.L. Norman, Wh80s: Numerical radiation hydrodynamics, in: K.-H. Winkler, M.L. Norman (Eds.), Astrophysical Radiation Hydrodynamics, Vol. 188, NATO-ASI Series C, D. Reidel, Dordrecht, p. 223.</td> </tr><tr> <td>[28]</td> <td class="space">Yorke, H. W., Numerical solution of the equation of radiation transfer in spherical geometry, Astron. Astrophys., 86, 286-294 (1980) · <a href="/0426.65077" class="nowrap">Zbl 0426.65077</a></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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