{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T03:37:31Z","timestamp":1787542651208,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>The numerical approximation of combustion processes may lead to numerical difficulties, which are caused by different time scales of the transport part and the reactive part of the model equations. Here we consider a modified fractional step method that overcomes this difficulty on standard test problems and allows the use of a mesh width and time step determined by the nonreactive part, without precisely resolving the very small reaction zone. High-resolution Godunov methods are employed and the structure of the Riemann solution is used to determine where burning should occur in each time step. The modification is implemented in the software packageCLAWPACK. Numerical results for 1D and 2D detonation waves are shown, including a detonation wave diffracting around a corner.<\/jats:p>","DOI":"10.1137\/s1064827599357814","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1489-1510","source":"Crossref","is-referenced-by-count":60,"title":["A Modified Fractional Step Method for the Accurate Approximation of Detonation Waves"],"prefix":"10.1137","volume":"22","author":[{"given":"Christiane","family":"Helzel","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Randall J.","family":"Leveque","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gerald","family":"Warnecke","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2012,2,17]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1088\/1364-7830\/3\/1\/005"},{"key":"R2","unstructured":"W. Bao and S. Jin,\n                      The Random Projection Method for Stiff Detonation Waves\n                      , Technical Report, School of Mathematics, Georgia Institute of Technology, Atlanta, 1999."},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6572"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90065-X"},{"key":"R5","unstructured":"M. J. Berger and R. J. LeVeque,\n                      amrclaw software\n                      , http:\/\/www.amath.washington. edu\/\u02dcrjl\/amrclaw\/."},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997315974"},{"key":"R7","unstructured":"A. C. Berkenbosch,\n                      Capturing Detonation Waves for Reactive Euler Equations\n                      , Ph.D. thesis, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, 1995."},{"key":"R8","doi-asserted-by":"publisher","DOI":"10.1088\/1364-7830\/2\/3\/006"},{"key":"R9","unstructured":"A. Bourlioux,\n                      Numerical Study of Unstable Detonations\n                      , Ph.D. thesis, Princeton University, Princeton, NJ, 1991."},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(76)90047-4"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1137\/0907073"},{"key":"R12","unstructured":"R. Courant and K. O. Friedrichs,\n                      Supersonic Flow and Shock Waves\n                      , Springer\u2010Verlag, New York, 1985."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1299\/jsmeb.38.497"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160180408"},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0713-9"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050021"},{"key":"R17","volume-title":"Numerical schemes for conservation laws","author":"Kr\u00f6ner Dietmar","year":"1997"},{"key":"R18","unstructured":"R. J. 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Golovichev, Yu. E. Markachev and L. V. Shurshalov; Translation edited and with a preface by V. L. Zimont and P. I. Chushkin92b:76067"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1137\/0153062"},{"key":"R26","unstructured":"Bj\u00f6rn Sj\u00f6green, Bj\u00f6rn Engquist, Numerical approximation of hyperbolic conservation laws with stiff terms, Studentlitteratur, Lund, 1991, 848\u201386092b:35095"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0873-0"},{"key":"R28","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0206"},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(77)90095-X"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1088\/1364-7830\/1\/1\/010"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S1064827599357814","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:34:29Z","timestamp":1787333669000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S1064827599357814"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":30,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S1064827599357814"],"URL":"https:\/\/doi.org\/10.1137\/s1064827599357814","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}