{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,5]],"date-time":"2026-06-05T06:42:53Z","timestamp":1780641773033,"version":"3.54.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T00:00:00Z","timestamp":1175126400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T00:00:00Z","timestamp":1175126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2007,5]]},"DOI":"10.1007\/s00211-007-0069-y","type":"journal-article","created":{"date-parts":[[2007,3,29]],"date-time":"2007-03-29T18:06:35Z","timestamp":1175191595000},"page":"369-425","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":75,"title":["Hyperbolic balance laws: Riemann invariants and the generalized Riemann problem"],"prefix":"10.1007","volume":"106","author":[{"given":"Matania","family":"Ben-Artzi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jiequan","family":"Li","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,3,29]]},"reference":[{"issue":"1","key":"69_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/0021-9991(84)90013-5","volume":"55","author":"M. Ben-Artzi","year":"1984","unstructured":"Ben-Artzi M. and Falcovitz J. (1984). A second-order Godunov-type scheme for compressible fluid dynamics. J. Comput. Phys. 55(1): 1\u201332","journal-title":"J. Comput. Phys."},{"issue":"3","key":"69_CR2","doi-asserted-by":"publisher","first-page":"744","DOI":"10.1137\/0907051","volume":"7","author":"M. Ben-Artzi","year":"1986","unstructured":"Ben-Artzi M. and Falcovitz J. (1986). An upwind second-order scheme for compressible duct flows. SIAM J. Sci. Statist. Comput. 7(3): 744\u2013768","journal-title":"SIAM J. Sci. Statist. Comput."},{"issue":"1","key":"69_CR3","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/0021-9991(89)90065-X","volume":"81","author":"M. Ben-Artzi","year":"1989","unstructured":"Ben-Artzi M. (1989). The generalized Riemann problem for reactive flows. J. Comput. Phys. 81(1): 70\u2013101","journal-title":"J. Comput. Phys."},{"key":"69_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546785","volume-title":"Generalized Riemann Problems in Computational Gas Dynamics","author":"M. Ben-Artzi","year":"2003","unstructured":"Ben-Artzi M. and Falcovitz J. (2003). Generalized Riemann Problems in Computational Gas Dynamics. Cambridge University Press, Cambridge"},{"key":"69_CR5","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/j.jcp.2006.01.044","volume":"218","author":"M. Ben-Artzi","year":"2006","unstructured":"Ben-Artzi M., Li J. and Warnecke G. (2006). A direct Eulerian GRP scheme for compressible fluid flows. J. Comp. Phys. 218: 19\u201343","journal-title":"J. Comp. Phys."},{"key":"69_CR6","doi-asserted-by":"publisher","first-page":"35","DOI":"10.1017\/S0022112004009991","volume":"514","author":"F. Bouchut","year":"2004","unstructured":"Bouchut F., Le Sommer J. and Zeitlin V. (2004). Frontal geostrophic adjustment and nonlinear wave phenomena in one dimensional rotating shallow water. Part 2: High resolution numerical simulations. J. Fluid Mech. 514: 35\u201363","journal-title":"J. Fluid Mech."},{"issue":"6","key":"69_CR7","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/s0294-1449(16)30310-9","volume":"6","author":"A. Bourgeade","year":"1989","unstructured":"Bourgeade A., LeFloch Ph. and Raviart P.-A. (1989). An asymptotic expansion for the solution of the generalized Riemann problem. II. Application to the equations of gas dynamics. Ann. Inst. H. Poincar Anal. Non Linaire 6(6): 437\u2013480","journal-title":"Ann. Inst. H. Poincar Anal. Non Linaire"},{"key":"69_CR8","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-22019-1","volume-title":"Hyperbolic Conservation Laws in Continuum Physics","author":"C.M. Dafermos","year":"2000","unstructured":"Dafermos C.M. (2000). Hyperbolic Conservation Laws in Continuum Physics. Springer, Heidelberg"},{"key":"69_CR9","first-page":"271","volume":"47","author":"S.K. Godunov","year":"1959","unstructured":"Godunov S.K. (1959). A finite difference method for the numerical computation and disontinuous solutions of the equations of fluid dynamics. Mat. Sb. 47: 271\u2013295","journal-title":"Mat. Sb."},{"key":"69_CR10","doi-asserted-by":"crossref","unstructured":"Godlewski, E., Raviart, P.-A.: Numerical approximation of hyperbolic systems of conservation laws. Appl. Math. Sci. 118, Springer, Heidelberg (1996)","DOI":"10.1007\/978-1-4612-0713-9"},{"issue":"4","key":"69_CR11","doi-asserted-by":"publisher","first-page":"631","DOI":"10.1051\/m2an:2001130","volume":"35","author":"S. Jin","year":"2001","unstructured":"Jin S. (2001). A steady-state capturing method for hyperbolic systems with geometrical source terms. M2 AN Math. Model. Numer. Anal. 35(4): 631\u2013645","journal-title":"M2 AN Math. Model. Numer. Anal."},{"issue":"1","key":"69_CR12","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/0021-9991(79)90145-1","volume":"32","author":"B. van Leer","year":"1979","unstructured":"Leer B. (1979). Towards the ultimate conservative difference scheme, V. A second-order sequel to Godunov\u2019s method. J. Comput. Phys. 32(1): 101\u2013136","journal-title":"J. Comput. Phys."},{"issue":"6","key":"69_CR13","doi-asserted-by":"publisher","first-page":"834","DOI":"10.1002\/nme.1471","volume":"65","author":"J. Li","year":"2006","unstructured":"Li J. and Chen G. (2006). The generalized Riemann problem method for the shallow water equations with bottom topography. Int. J. Numer. Methods Eng. 65(6): 834\u2013862","journal-title":"Int. J. Numer. Methods Eng."},{"key":"69_CR14","unstructured":"Li, T.T.: Global Classical Solutions for Quasilinear Hyperbolic Systems. Research in Applied Mathematics. Wiley, Chichester\/Masson, Paris (1994)"},{"issue":"2","key":"69_CR15","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1016\/s0294-1449(16)30350-x","volume":"5","author":"Ph. LeFloch","year":"1988","unstructured":"LeFloch Ph. and Raviart P.-A. (1988). An asymptotic expansion for the solution of the generalized Riemann problem. I. General theory. Ann. Inst. H. Poincar Anal. Non Linaire 5(2): 179\u2013207","journal-title":"Ann. Inst. H. Poincar Anal. Non Linaire"},{"key":"69_CR16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0873-0","volume-title":"Shock Waves and Reaction-Diffusion Equations","author":"J. Smoller","year":"1994","unstructured":"Smoller J. (1994) Shock Waves and Reaction-Diffusion Equations, 2nd edn, vol. 258. Springer, New York","edition":"2"},{"issue":"5","key":"69_CR17","doi-asserted-by":"publisher","first-page":"995","DOI":"10.1137\/0721062","volume":"21","author":"P.K. Sweby","year":"1984","unstructured":"Sweby P.K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21(5): 995\u20131011","journal-title":"SIAM J. Numer. Anal."},{"key":"69_CR18","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03490-3","volume-title":"Riemann solvers and numerical methods for fluid dynamics. A practical introduction","author":"E. Toro","year":"1997","unstructured":"Toro E. (1997). Riemann solvers and numerical methods for fluid dynamics. A practical introduction. Springer, Berlin"},{"key":"69_CR19","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1016\/j.jcp.2005.06.018","volume":"212","author":"E. Toro","year":"2006","unstructured":"Toro E. (2006). Derivative Riemann solvers for systems of conservation laws and ADER methods.  J. Comp. Phys. 212: 150\u2013165","journal-title":"J. Comp. Phys."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0069-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00211-007-0069-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0069-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0069-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T04:08:00Z","timestamp":1652846880000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00211-007-0069-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,3,29]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,5]]}},"alternative-id":["69"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0069-y","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,3,29]]},"assertion":[{"value":"15 June 2006","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 January 2007","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2007","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}