{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:33:41Z","timestamp":1787337221844,"version":"build-2736575974"},"reference-count":30,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2006,1]]},"abstract":"<jats:p>The Riemann problem is considered for the investigation of nonclassical wave phenomena in Bethe--Zel'dovich--Thompson (BZT)-fluids and fluids which undergo a phase transition, i.e., the isentropes suffer kinks at the saturation boundaries. These fluids are modeled by a general equation of state that also takes into account regions of negative nonlinearity where the isentropes are nonconvex in the pressure-volume plane. Here the physical model is based on thermodynamical equilibrium. Both nonsmoothness as well as nonconvexity significantly influence the composition of the wave curves which are crucial for determining the solution for the Riemann problem for the Euler equations. This work gives explicit criteria for the composition of these wave curves by elementary wave types such as shocks, simple waves, and composite waves. Numerous examples for different wave curve compositions are presented.<\/jats:p>","DOI":"10.1137\/040619909","type":"journal-article","created":{"date-parts":[[2008,2,6]],"date-time":"2008-02-06T16:45:19Z","timestamp":1202316319000},"page":"651-681","source":"Crossref","is-referenced-by-count":42,"title":["The Riemann Problem for the Euler Equations with Nonconvex and Nonsmooth Equation of State: Construction of Wave Curves"],"prefix":"10.1137","volume":"28","author":[{"given":"Siegfried","family":"M\u00fcller","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alexander","family":"Voss","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"H. D. Baehr,\n                      Thermodynamik\n                      , Springer\u2010Verlag, New York, 1988."},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1017\/S002211208300004X"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.12.005"},{"key":"R4","volume-title":"Optimization and nonsmooth analysis","author":"Clarke Frank","year":"1983"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01233668"},{"key":"R6","doi-asserted-by":"crossref","unstructured":"M. S. Cramer,\n                      Nonclassical dynamics of classical waves\n                      , in Nonlinear Waves in Real Fluids, A. 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Thompson,\n                      Liquid\u2010vapor adiabatic phase changes and related phenomena\n                      , in Nonlinear Waves in Real Fluids, A. Kluwick, ed., Springer\u2010Verlag, New York, 1991, pp. 147\u2013213.","DOI":"10.1007\/978-3-7091-2608-0_6"},{"key":"R25","doi-asserted-by":"publisher","DOI":"10.1063\/1.864093"},{"key":"R26","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-03915-1"},{"key":"R27","doi-asserted-by":"publisher","DOI":"10.1017\/S0022377803002186"},{"key":"R28","unstructured":"A. Vo\u00df,\n                      Exact Riemann Solutions for the Euler Equations with Nonconvex and Nonsmooth Equation of State\n                      , Ph.D. thesis, RWTH Aachen, Aachen, Germany, 2005, available online at http:\/\/darwin.bth.rwth\u2010aachen.de\/opus\/volltexte\/2005\/1210\/."},{"key":"R29","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(72)90103-5"},{"key":"R30","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(72)90075-3"}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/040619909","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:50:13Z","timestamp":1787334613000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/040619909"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,1]]},"references-count":30,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2006,1]]}},"alternative-id":["10.1137\/040619909"],"URL":"https:\/\/doi.org\/10.1137\/040619909","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,1]]}}}