{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,18]],"date-time":"2026-06-18T05:04:43Z","timestamp":1781759083540,"version":"3.54.5"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,9,14]],"date-time":"2016-09-14T00:00:00Z","timestamp":1473811200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["NO 361\/3-3"],"award-info":[{"award-number":["NO 361\/3-3"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,3]]},"DOI":"10.1007\/s10915-016-0286-6","type":"journal-article","created":{"date-parts":[[2016,9,14]],"date-time":"2016-09-14T09:21:25Z","timestamp":1473844885000},"page":"1390-1407","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["A New Stable Splitting for the Isentropic Euler Equations"],"prefix":"10.1007","volume":"70","author":[{"given":"Klaus","family":"Kaiser","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jochen","family":"Sch\u00fctz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ruth","family":"Sch\u00f6bel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sebastian","family":"Noelle","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2016,9,14]]},"reference":[{"key":"286_CR1","volume-title":"Fundamentals of Aerodynamics, $$3^{rd}$$","author":"JD Anderson","year":"2001","unstructured":"Anderson, J.D.: Fundamentals of Aerodynamics, $$3^{rd}$$ 3 rd edn. McGraw-Hill, New York (2001)"},{"key":"286_CR2","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/S0168-9274(97)00056-1","volume":"25","author":"UM Ascher","year":"1997","unstructured":"Ascher, U.M., Ruuth, S., Spiteri, R.: Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Math. 25, 151\u2013167 (1997)","journal-title":"Appl. Numer. Math."},{"key":"286_CR3","doi-asserted-by":"crossref","first-page":"797","DOI":"10.1137\/0732037","volume":"32","author":"UM Ascher","year":"1995","unstructured":"Ascher, U.M., Ruuth, S., Wetton, B.: Implicit-explicit methods for time-dependent partial differential equations. SIAM J. Numer. Anal. 32, 797\u2013823 (1995)","journal-title":"SIAM J. Numer. Anal."},{"key":"286_CR4","unstructured":"Balay, S., Brown, J., Buschelman, K., Eijkhout, V., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc users manual. Tech. Rep. ANL-95\/11 - Revision 3.1, Argonne National Laboratory (2010)"},{"key":"286_CR5","unstructured":"Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page. http:\/\/www.mcs.anl.gov\/petsc (2011)"},{"key":"286_CR6","doi-asserted-by":"crossref","unstructured":"Balay, S., Gropp, W.D., McInnes, L.C., Smith, B.F.: Efficient management of parallelism in object oriented numerical software libraries. In: E.\u00a0Arge, A.M. Bruaset, H.P. Langtangen (eds.) Modern Software Tools in Scientific Computing, pp. 163\u2013202. Birkh\u00e4user Press Boston (1997)","DOI":"10.1007\/978-1-4612-1986-6_8"},{"key":"286_CR7","unstructured":"Bispen, G.: IMEX finite volume methods for the shallow water equations. Ph.D. thesis, Johannes Gutenberg-Universit\u00e4t (2015)"},{"key":"286_CR8","doi-asserted-by":"crossref","first-page":"307","DOI":"10.4208\/cicp.040413.160114a","volume":"16","author":"G Bispen","year":"2014","unstructured":"Bispen, G., Arun, K., Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1, M., Noelle, S.: IMEX large time step finite volume methods for low froude number shallow water flows. Commun. Comput. Phys. 16, 307\u2013347 (2014)","journal-title":"Commun. Comput. Phys."},{"key":"286_CR9","doi-asserted-by":"crossref","first-page":"1600","DOI":"10.1137\/060656929","volume":"45","author":"S Boscarino","year":"2007","unstructured":"Boscarino, S.: Error analysis of IMEX Runge-Kutta methods derived from differential-algebraic systems. SIAM J.Numer. Anal. 45, 1600\u20131621 (2007)","journal-title":"SIAM J.Numer. Anal."},{"key":"286_CR10","doi-asserted-by":"crossref","first-page":"1515","DOI":"10.1016\/j.apnum.2008.10.003","volume":"59","author":"S Boscarino","year":"2009","unstructured":"Boscarino, S.: On an accurate third order implicit-explicit Runge-Kutta method for stiff problems. Appl. Numer. Math. 59, 1515\u20131528 (2009)","journal-title":"Appl. Numer. Math."},{"issue":"1","key":"286_CR11","doi-asserted-by":"crossref","first-page":"A22","DOI":"10.1137\/110842855","volume":"35","author":"S Boscarino","year":"2013","unstructured":"Boscarino, S., Pareschi, L., Russo, G.: Implicit-explicit Runge-Kutta schemes for hyperbolic systems and kinetic equations in the diffusion limit. SIAM J. Sci. Comput. 35(1), A22\u2013A51 (2013)","journal-title":"SIAM J. Sci. Comput."},{"key":"286_CR12","first-page":"545","volume":"54","author":"B Cockburn","year":"1990","unstructured":"Cockburn, B., Hou, S., Shu, C.W.: The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws IV: The multidimensional case. Math. Comput. 54, 545\u2013581 (1990)","journal-title":"Math. Comput."},{"key":"286_CR13","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/0021-9991(89)90183-6","volume":"84","author":"B Cockburn","year":"1989","unstructured":"Cockburn, B., Lin, S.Y.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One dimensional systems. J. Comput. Phys. 84, 90\u2013113 (1989)","journal-title":"J. Comput. Phys."},{"key":"286_CR14","first-page":"411","volume":"52","author":"B Cockburn","year":"1988","unstructured":"Cockburn, B., Shu, C.W.: TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws II: General framework. Math. Comput. 52, 411\u2013435 (1988)","journal-title":"Math. Comput."},{"key":"286_CR15","doi-asserted-by":"crossref","first-page":"337","DOI":"10.1051\/m2an\/1991250303371","volume":"25","author":"B Cockburn","year":"1991","unstructured":"Cockburn, B., Shu, C.W.: The Runge-Kutta local projection $$p^1$$ p 1 -discontinuous Galerkin finite element method for scalar conservation laws. RAIRO Math. Model. Numer. Anal. 25, 337\u2013361 (1991)","journal-title":"RAIRO Math. Model. Numer. Anal."},{"key":"286_CR16","first-page":"199","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.W.: The Runge-Kutta discontinuous Galerkin method for conservation laws V: multidimensional systems. Math. Comput. 141, 199\u2013224 (1998)","journal-title":"Math. Comput."},{"key":"286_CR17","doi-asserted-by":"crossref","first-page":"5685","DOI":"10.1016\/j.jcp.2012.04.025","volume":"231","author":"F Cordier","year":"2012","unstructured":"Cordier, F., Degond, P., Kumbaro, A.: An asymptotic-preserving all-speed scheme for the Euler and Navier-Stokes equations. J. Comput. Phys. 231, 5685\u20135704 (2012)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"286_CR18","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF01396412","volume":"35","author":"M Crouzeix","year":"1980","unstructured":"Crouzeix, M.: Une m\u00e9thode multipas implicite-explicite pour l\u2019approximation des \u00e9quations d\u2019\u00e9volution paraboliques. Numerische Mathematik 35(3), 257\u2013276 (1980)","journal-title":"Numerische Mathematik"},{"issue":"4","key":"286_CR19","first-page":"851","volume":"2","author":"P Degond","year":"2007","unstructured":"Degond, P., Jin, S., Liu, J.G.: Mach-number uniform asymptotic-preserving gauge schemes for compressible flows. Bull. Inst. Math. Acad. Sinicia 2(4), 851 (2007)","journal-title":"Bull. Inst. Math. Acad. Sinicia"},{"key":"286_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.4208\/cicp.210709.210610a","volume":"10","author":"P Degond","year":"2011","unstructured":"Degond, P., Tang, M.: All speed scheme for the low mach number limit of the isentropic Euler equation. Commun. Comput. Phys. 10, 1\u201331 (2011)","journal-title":"Commun. Comput. Phys."},{"issue":"20","key":"286_CR21","doi-asserted-by":"crossref","first-page":"7625","DOI":"10.1016\/j.jcp.2010.06.017","volume":"229","author":"F Filbet","year":"2010","unstructured":"Filbet, F., Jin, S.: A class of asymptotic-preserving schemes for kinetic equations and related problems with stiff sources. J. Comput. Phys. 229(20), 7625\u20137648 (2010)","journal-title":"J. Comput. Phys."},{"issue":"6","key":"286_CR22","doi-asserted-by":"crossref","first-page":"3394","DOI":"10.1137\/090775889","volume":"32","author":"F Giraldo","year":"2010","unstructured":"Giraldo, F., Restelli, M., L\u00e4uter, M.: Semi-implicit formulations of the Navier-Stokes equations: application to nonhydrostatic atmospheric modeling. SIAM J. Sci. Comput. 32(6), 3394\u20133425 (2010)","journal-title":"SIAM J. Sci. Comput."},{"issue":"9","key":"286_CR23","doi-asserted-by":"crossref","first-page":"1077","DOI":"10.1002\/fld.2118","volume":"63","author":"FX Giraldo","year":"2010","unstructured":"Giraldo, F.X., Restelli, M.: High-order semi-implicit time-integrators for a triangular discontinuous Galerkin oceanic shallow water model. Int. J. Numer. Methods Fluids 63(9), 1077\u20131102 (2010)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"286_CR24","doi-asserted-by":"crossref","first-page":"955","DOI":"10.4208\/cicp.250910.131011a","volume":"12","author":"J Haack","year":"2012","unstructured":"Haack, J., Jin, S., Liu, J.G.: An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equations. Commun. Comput. Phys. 12, 955\u2013980 (2012)","journal-title":"Commun. Comput. Phys."},{"key":"286_CR25","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-09947-6","volume-title":"Solving Ordinary Differential Equations II","author":"E Hairer","year":"1991","unstructured":"Hairer, E., Wanner, G.: Solving Ordinary Differential Equations II. Springer Series in Computational Mathematics, Berlin (1991)"},{"issue":"2","key":"286_CR26","doi-asserted-by":"crossref","first-page":"2016","DOI":"10.1016\/j.jcp.2007.03.003","volume":"225","author":"W Hundsdorfer","year":"2007","unstructured":"Hundsdorfer, W., Ruuth, S.J.: IMEX extensions of linear multistep methods with general monotonicity and boundedness properties. J. Comput. Phys. 225(2), 2016\u20132042 (2007)","journal-title":"J. Comput. Phys."},{"key":"286_CR27","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1137\/S1064827598334599","volume":"21","author":"S Jin","year":"1999","unstructured":"Jin, S.: Efficient asymptotic-preserving (AP) schemes for some multiscale kinetic equations. SIAM J. Sci. Comput. 21, 441\u2013454 (1999)","journal-title":"SIAM J. Sci. Comput."},{"key":"286_CR28","unstructured":"Jin, S.: Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review. Rivista di Matematica della Universita Parma 3, 177\u2013216 (2012)"},{"key":"286_CR29","doi-asserted-by":"crossref","first-page":"2405","DOI":"10.1137\/S0036142997315962","volume":"35","author":"S Jin","year":"1998","unstructured":"Jin, S., Pareschi, L., Toscani, G.: Diffusive relaxation schemes for multiscale discrete-velocity kinetic equations. SIAM J. Numer. Anal. 35, 2405\u20132439 (1998)","journal-title":"SIAM J. Numer. Anal."},{"key":"286_CR30","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/S0168-9274(02)00138-1","volume":"44","author":"CA Kennedy","year":"2003","unstructured":"Kennedy, C.A., Carpenter, M.H.: Additive Runge-Kutta schemes for convection-diffusion-reaction equations. Appl. Numer. Math. 44, 139\u2013181 (2003)","journal-title":"Appl. Numer. Math."},{"key":"286_CR31","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1002\/cpa.3160340405","volume":"34","author":"S Klainerman","year":"1981","unstructured":"Klainerman, S., Majda, A.: Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Commun. Pure Appl. Math. 34, 481\u2013524 (1981)","journal-title":"Commun. Pure Appl. Math."},{"key":"286_CR32","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1016\/S0021-9991(95)90034-9","volume":"121","author":"R Klein","year":"1995","unstructured":"Klein, R.: Semi-implicit extension of a Godunov-type scheme based on low mach number asymptotics I: one-dimensional flow. J. Comput. Phys. 121, 213\u2013237 (1995)","journal-title":"J. Comput. Phys."},{"key":"286_CR33","unstructured":"Kr\u00f6ner, D.: Numerical Schemes for Conservation Laws. Wiley-Teubner Series Advances in Numerical Mathematics, viii+508 pp. John Wiley & Sons, Ltd., Chichester; B. G. Teubner, Stuttgart (1997)"},{"key":"286_CR34","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1137\/140999992","volume":"54","author":"K Kuepper","year":"2016","unstructured":"Kuepper, K., Frank, M., Jin, S.: An asymptotic preserving 2-d staggered grid method for multiscale transport equations. SIAM J. Numer. Anal. 54, 440\u2013461 (2016)","journal-title":"SIAM J. Numer. Anal."},{"key":"286_CR35","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/j.jcp.2012.10.038","volume":"235","author":"A M\u00fcller","year":"2013","unstructured":"M\u00fcller, A., Behrens, J., Giraldo, F., Wirth, V.: Comparison between adaptive and uniform discontinuous Galerkin simulations in dry 2d bubble experiments. J. Comput. Phys. 235, 371\u2013393 (2013)","journal-title":"J. Comput. Phys."},{"key":"286_CR36","doi-asserted-by":"crossref","first-page":"B989","DOI":"10.1137\/120895627","volume":"36","author":"S Noelle","year":"2014","unstructured":"Noelle, S., Bispen, G., Arun, K., Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1, M., Munz, C.D.: A weakly asymptotic preserving low mach number scheme for the Euler equations of gas dynamics. SIAM J. Sci. Comput. 36, B989\u2013B1024 (2014)","journal-title":"SIAM J. Sci. Comput."},{"issue":"1\u20132","key":"286_CR37","first-page":"129","volume":"25","author":"L Pareschi","year":"2005","unstructured":"Pareschi, L., Russo, G.: Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation. J. Sci. Comput. 25(1\u20132), 129\u2013155 (2005)","journal-title":"J. Sci. Comput."},{"key":"286_CR38","unstructured":"Restelli, M.: Semi-lagrangian and semi-implicit discontinuous Galerkin methods for atmospheric modeling applications. PhD thesis Politecnico di Milano (2007)"},{"key":"286_CR39","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1007\/s007910050004","volume":"1","author":"J Sch\u00f6berl","year":"1997","unstructured":"Sch\u00f6berl, J.: Netgen - an advancing front 2d\/3d-mesh generator based on abstract rules. Comput. Visualization Sci. 1, 41\u201352 (1997)","journal-title":"Comput. Visualization Sci."},{"issue":"2","key":"286_CR40","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1006\/jdeq.1994.1157","volume":"114","author":"S Schochet","year":"1994","unstructured":"Schochet, S.: Fast singular limits of hyperbolic PDEs. J. Differ. Equ. 114(2), 476\u2013512 (1994)","journal-title":"J. Differ. Equ."},{"key":"286_CR41","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.apnum.2016.04.004","volume":"107","author":"J Sch\u00fctz","year":"2016","unstructured":"Sch\u00fctz, J., Kaiser, K.: A new stable splitting for singularly perturbed ODEs. Appl. Numer. Math. 107, 18\u201333 (2016)","journal-title":"Appl. Numer. Math."},{"key":"286_CR42","unstructured":"Sch\u00fctz, J., Kaiser, K., Noelle, S.: The RS-IMEX splitting for the isentropic Euler equations. In: S.\u00a0Elgeti, J.W. Simon (eds.) Conference Proceedings of the YIC GACM 2015. Publication Server of RWTH Aachen University. urn:nbn:de:hbz:82-rwth-2015-039806. https:\/\/publications.rwth-aachen.de\/record\/480970\/files\/ProceedingsYIC-GACM-ACCES.pdf (2015)"},{"issue":"2","key":"286_CR43","doi-asserted-by":"crossref","first-page":"522","DOI":"10.1007\/s10915-014-9942-x","volume":"64","author":"J Sch\u00fctz","year":"2015","unstructured":"Sch\u00fctz, J., Noelle, S.: Flux splitting for stiff equations: a notion on stability. J. Sci. Comput. 64(2), 522\u2013540 (2015)","journal-title":"J. Sci. Comput."},{"key":"286_CR44","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-05146-3","volume-title":"Principles of Computational Fluid Dynamics. Springer Series in Computational Mechanics","author":"P Wesseling","year":"2001","unstructured":"Wesseling, P.: Principles of Computational Fluid Dynamics. Springer Series in Computational Mechanics, vol. 29. Springer, Berlin (2001)"},{"key":"286_CR45","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1016\/j.jcp.2014.02.034","volume":"268","author":"L Yelash","year":"2014","unstructured":"Yelash, L., M\u00fcller, A., Luk\u00e1\u010dov\u00e1-Medvid\u2019ov\u00e1, M., Giraldo, F.X., Wirth, V.: Adaptive discontinuous evolution Galerkin method for dry atmospheric flow. J. Comput. Phys. 268, 106\u2013133 (2014)","journal-title":"J. Comput. Phys."},{"issue":"10","key":"286_CR46","doi-asserted-by":"crossref","first-page":"3079","DOI":"10.1090\/S0002-9939-05-08077-9","volume":"133","author":"WA Yong","year":"2005","unstructured":"Yong, W.A.: A note on the zero Mach number limit of compressible Euler equations. Proc American Math. Soc. 133(10), 3079\u20133085 (2005)","journal-title":"Proc American Math. Soc."},{"key":"286_CR47","unstructured":"Zakerzadeh, H., Noelle, S.: A note on the stability of implicit-explicit flux splittings for stiff hyperbolic systems. IGPM Preprint Nr. 449 (2016)"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0286-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0286-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0286-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,19]],"date-time":"2024-06-19T10:26:42Z","timestamp":1718792802000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0286-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,9,14]]},"references-count":47,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,3]]}},"alternative-id":["286"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0286-6","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,9,14]]}}}