{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,10]],"date-time":"2026-02-10T06:25:06Z","timestamp":1770704706163,"version":"3.49.0"},"reference-count":45,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2015,6,27]],"date-time":"2015-06-27T00:00:00Z","timestamp":1435363200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"name":"GNCS-INDAM","award":["2014 Project"],"award-info":[{"award-number":["2014 Project"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2016,3]]},"DOI":"10.1007\/s10915-015-0056-x","type":"journal-article","created":{"date-parts":[[2015,6,26]],"date-time":"2015-06-26T00:22:06Z","timestamp":1435278126000},"page":"1052-1076","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["Well-Balanced High Order 1D Schemes on Non-uniform Grids and Entropy Residuals"],"prefix":"10.1007","volume":"66","author":[{"given":"G.","family":"Puppo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Semplice","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2015,6,27]]},"reference":[{"key":"56_CR1","doi-asserted-by":"crossref","first-page":"2050","DOI":"10.1137\/S1064827503431090","volume":"25","author":"E Audusse","year":"2004","unstructured":"Audusse, E., Bouchut, F., Bristeau, M., Klein, R., Perthame, B.: A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25, 2050\u20132065 (2004)","journal-title":"SIAM J. Sci. Comput."},{"issue":"4","key":"56_CR2","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1002\/fld.1191","volume":"52","author":"A Baeza","year":"2006","unstructured":"Baeza, A., Mulet, P.: Adaptive mesh refinement techniques for high-order shock capturing schemes for multi-dimensional hydrodynamic simulations. Int. J. Numer. Methods Fluids 52(4), 455\u2013471 (2006). doi: 10.1002\/fld.1191","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"8","key":"56_CR3","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1016\/0045-7930(94)90004-3","volume":"23","author":"A Bermudez","year":"1994","unstructured":"Bermudez, A., Vazquez, M.: Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23(8), 1049\u20131071 (1994)","journal-title":"Comput. Fluids"},{"key":"56_CR4","doi-asserted-by":"crossref","DOI":"10.1007\/b93802","volume-title":"Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in mathematics","author":"F Bouchut","year":"2004","unstructured":"Bouchut, F.: Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in mathematics. Birkh\u00e4user, Basel (2004). doi: 10.1007\/b93802"},{"key":"56_CR5","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/j.advwatres.2012.05.018","volume":"46","author":"V Caleffi","year":"2012","unstructured":"Caleffi, V., Valiani, A.: A well-balanced, third-order-accurate RKDG scheme for SWE on curved boundary domains. Adv. Water Resour. 46, 31\u201345 (2012)","journal-title":"Adv. Water Resour."},{"issue":"3","key":"56_CR6","doi-asserted-by":"crossref","first-page":"1505","DOI":"10.1111\/j.1365-246X.2012.05471.x","volume":"189","author":"C Castro","year":"2012","unstructured":"Castro, C., Toro, E., K\u00e4ser, M.: ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves. Geophys. J. Int. 189(3), 1505\u20131520 (2012)","journal-title":"Geophys. J. Int."},{"issue":"3","key":"56_CR7","doi-asserted-by":"crossref","first-page":"531","DOI":"10.4310\/CMS.2008.v6.n3.a1","volume":"6","author":"A Chertock","year":"2008","unstructured":"Chertock, A., Kurganov, A.: A simple eulerian finite-volume method for compressible fluids in domains with moving boundaries. Commun. Math. Sci. 6(3), 531\u2013556 (2008)","journal-title":"Commun. Math. Sci."},{"key":"56_CR8","unstructured":"ClawPack (and related software) homepage. http:\/\/www.clawpack.com"},{"key":"56_CR9","doi-asserted-by":"crossref","unstructured":"Coco, A., Russo, G., Semplice, M.: Adaptive mesh refinement for hyperbolic systems based on third-order Compact WENO reconstruction. J. Sci. Comput. (2015). doi: 10.1007\/s10915-015-0038-z","DOI":"10.1007\/s10915-015-0038-z"},{"key":"56_CR10","doi-asserted-by":"crossref","unstructured":"Dafermos, C.M.: Hyperbolic conservation laws in continuum physics Grundlehren der Mathematischen Wissenschaften, vol. 325, 3rd edn. Springer, Berlin (2010). doi: 10.1007\/978-3-642-04048-1","DOI":"10.1007\/978-3-642-04048-1"},{"key":"56_CR11","doi-asserted-by":"crossref","first-page":"937","DOI":"10.1016\/j.jcp.2013.09.032","volume":"257","author":"R Donat","year":"2014","unstructured":"Donat, R., Mart\u00ed, M.C., Mart\u00ednez-Gavara, A., Mulet, P.: Well-balanced adaptive mesh refinement for shallow water flows. J. Comput. Phys. 257, 937\u2013953 (2014). doi: 10.1016\/j.jcp.2013.09.032","journal-title":"J. Comput. Phys."},{"key":"56_CR12","doi-asserted-by":"crossref","first-page":"8209","DOI":"10.1016\/j.jcp.2008.05.025","volume":"227","author":"M Dumbser","year":"2008","unstructured":"Dumbser, M., Balsara, D.S., Toro, E.F., Munz, C.D.: A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes. J. Comput. Phys. 227, 8209\u20138253 (2008)","journal-title":"J. Comput. Phys."},{"issue":"1\u20133","key":"56_CR13","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/S0898-1221(03)80019-6","volume":"45","author":"R Fazio","year":"2003","unstructured":"Fazio, R., LeVeque, R.: Moving-mesh methods for one-dimensional hyperbolic problems using ClawPack. Comput. Math. Appl. 45(1\u20133), 273\u2013298 (2003)","journal-title":"Comput. Math. Appl."},{"key":"56_CR14","unstructured":"Fluent homepage. http:\/\/www.ansys.com"},{"key":"56_CR15","unstructured":"GEOClaw HomePage. http:\/\/depts.washington.edu\/clawpack\/geoclaw\/"},{"issue":"8","key":"56_CR16","doi-asserted-by":"crossref","first-page":"1000","DOI":"10.1002\/fld.2298","volume":"66","author":"DL George","year":"2011","unstructured":"George, D.L.: Adaptive finite volume methods with well-balanced Riemann solvers for modeling floods in rugged terrain: application to the Malpasset dam-break flood (France, 1959). Int. J. Numer. Methods Fluids 66(8), 1000\u20131018 (2011). doi: 10.1002\/fld.2298","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"23","key":"56_CR17","doi-asserted-by":"crossref","first-page":"7780","DOI":"10.1016\/j.jcp.2012.07.014","volume":"231","author":"Y Gorsse","year":"2012","unstructured":"Gorsse, Y., Iollo, A., Telib, H., Weynans, L.: A simple second order Cartesian scheme for compressible Euler flows. J. Comput. Phys. 231(23), 7780\u20137794 (2012). doi: 10.1016\/j.jcp.2012.07.014","journal-title":"J. Comput. Phys."},{"issue":"2","key":"56_CR18","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1016\/0021-9991(83)90066-9","volume":"50","author":"A Harten","year":"1983","unstructured":"Harten, A., Hyman, J.: Self adjusting grid methods for one-dimensional hyperbolic conservation laws. J. Comput. Phys. 50(2), 235\u2013269 (1983)","journal-title":"J. Comput. Phys."},{"key":"56_CR19","doi-asserted-by":"crossref","first-page":"190","DOI":"10.1007\/s10915-010-9430-x","volume":"48","author":"G Hern\u00e0ndez-Due\u00f1as","year":"2011","unstructured":"Hern\u00e0ndez-Due\u00f1as, G., Smadar, K.: Shallow water flows in channels. J. Sci. Comput. 48, 190\u2013208 (2011). doi: 10.1007\/s10915-010-9430-x","journal-title":"J. Sci. Comput."},{"issue":"5","key":"56_CR20","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1002\/fld.325","volume":"39","author":"Z Hu","year":"2002","unstructured":"Hu, Z., Greaves, D., Wu, G.: Numerical simulation of fluid flows using an unstructured finite volume method with adaptive tri-tree grids. Int. J. Numer. Methods Fluids 39(5), 403\u2013440 (2002)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"56_CR21","doi-asserted-by":"crossref","first-page":"133","DOI":"10.4310\/CMS.2007.v5.n1.a6","volume":"5","author":"A Kurganov","year":"2007","unstructured":"Kurganov, A., Petrova, G.: A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Commun. Math. Sci. 5, 133\u2013160 (2007)","journal-title":"Commun. Math. Sci."},{"issue":"4","key":"56_CR22","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1002\/fld.1004","volume":"49","author":"P Lamby","year":"2005","unstructured":"Lamby, P., M\u00fcller, S., Stiriba, Y.: Solution of shallow water equations using fully adaptive multiscale schemes. Int. J. Numer. Methods Fluids 49(4), 417\u2013437 (2005)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"56_CR23","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1006\/jcph.1998.6058","volume":"146","author":"R LeVeque","year":"1998","unstructured":"LeVeque, R.: Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146, 346\u2013356 (1998)","journal-title":"J. Comput. Phys."},{"key":"56_CR24","doi-asserted-by":"crossref","unstructured":"LeVeque, R.J.: Numerical methods for conservation laws, 2nd edn. Lectures in Mathematics ETH Z\u00fcrich. Birkh\u00e4user, Basel (1992). doi: 10.1007\/978-3-0348-8629-1","DOI":"10.1007\/978-3-0348-8629-1"},{"issue":"3","key":"56_CR25","doi-asserted-by":"crossref","first-page":"547","DOI":"10.1051\/m2an:1999152","volume":"33","author":"D Levy","year":"1999","unstructured":"Levy, D., Puppo, G., Russo, G.: Central WENO schemes for hyperbolic systems of conservation laws. M2AN Math. Model. Numer. Anal. 33(3), 547\u2013571 (1999)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"2","key":"56_CR26","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1137\/S1064827599359461","volume":"22","author":"D Levy","year":"2000","unstructured":"Levy, D., Puppo, G., Russo, G.: Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22(2), 656\u2013672 (2000)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"56_CR27","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1002\/fld.2266","volume":"66","author":"Q Liang","year":"2011","unstructured":"Liang, Q.: A structured but non-uniform Cartesian grid-based model for the shallow water equations. Int. J. Numer. Methods Fluids 66(5), 537\u2013554 (2011)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"2","key":"56_CR28","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1016\/j.compfluid.2008.02.008","volume":"38","author":"Q Liang","year":"2009","unstructured":"Liang, Q., Borthwick, A.: Adaptive quadtree simulation of shallow flows with wet-dry fronts over complex topography. Comput. Fluids 38(2), 221\u2013234 (2009)","journal-title":"Comput. Fluids"},{"issue":"2","key":"56_CR29","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.jcp.2005.08.019","volume":"213","author":"S Noelle","year":"2006","unstructured":"Noelle, S., Pankratz, N., Puppo, G., Natvig, J.R.: Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys. 213(2), 474\u2013499 (2006)","journal-title":"J. Comput. Phys."},{"key":"56_CR30","doi-asserted-by":"crossref","first-page":"474","DOI":"10.1016\/j.jcp.2005.08.019","volume":"213","author":"S Noelle","year":"2007","unstructured":"Noelle, S., Xing, Y., Shu, C.W.: High-order well-balanced finite volume WENO schemes for shallow water equation with moving water. J. Comput. Phys. 213, 474\u2013499 (2007)","journal-title":"J. Comput. Phys."},{"key":"56_CR31","doi-asserted-by":"crossref","unstructured":"Puppo, G.: Numerical entropy production for central schemes. SIAM J. Sci. Comput. 25(4), 1382\u20131415 (electronic) (2003\/04). doi: 10.1137\/S1064827502386712","DOI":"10.1137\/S1064827502386712"},{"issue":"5","key":"56_CR32","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.4208\/cicp.250909.210111a","volume":"10","author":"G Puppo","year":"2011","unstructured":"Puppo, G., Semplice, M.: Numerical entropy and adaptivity for finite volume schemes. Commun. Comput. Phys. 10(5), 1132\u20131160 (2011). doi: 10.4208\/cicp.250909.210111a","journal-title":"Commun. Comput. Phys."},{"key":"56_CR33","unstructured":"Puppo, G., Semplice, M.: Finite volume schemes on 2d non-uniform grids. In: AIMS (ed.) Proceedings of \u201cFourteenth International Conference devoted to Theory, Numerics and Applications of Hyperbolic Problems\u201d (HYP2012) (2014)"},{"issue":"10","key":"56_CR34","doi-asserted-by":"crossref","first-page":"3780","DOI":"10.1016\/j.jcp.2011.02.008","volume":"230","author":"C Shen","year":"2011","unstructured":"Shen, C., Qiu, J.M., Christlieb, A.: Adaptive mesh refinement based on high order finite difference WENO scheme for multi-scale simulations. J. Comput. Phys. 230(10), 3780\u20133802 (2011)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"56_CR35","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1006\/jcph.2001.6892","volume":"175","author":"J Shi","year":"2002","unstructured":"Shi, J., Hu, C., Shu, C.W.: A technique of treating negative weights in WENO schemes. J. Comput. Phys. 175(1), 108\u2013127 (2002)","journal-title":"J. Comput. Phys."},{"key":"56_CR36","doi-asserted-by":"crossref","unstructured":"Shu, C.W.: Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. In: Advanced Numerical Approximation of Nonlinear Hyperbolic Equations (Cetraro, 1997), Lecture Notes in Math., vol. 1697, pp. 325\u2013432. Springer, Berlin (1998)","DOI":"10.1007\/BFb0096355"},{"issue":"7","key":"56_CR37","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1002\/fld.681","volume":"44","author":"H Tang","year":"2004","unstructured":"Tang, H.: Solution of the shallow-water equations using an adaptive moving mesh method. Int. J. Numer. Methods Fluids 44(7), 789\u2013810 (2004)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"2","key":"56_CR38","doi-asserted-by":"crossref","first-page":"487","DOI":"10.1137\/S003614290138437X","volume":"41","author":"H Tanq","year":"2003","unstructured":"Tanq, H., Tang, T.: Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAM J. Numer. Anal. 41(2), 487\u2013515 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"56_CR39","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1006\/jcph.1998.6127","volume":"148","author":"M V\u00e1squez-Cend\u00f3n","year":"1999","unstructured":"V\u00e1squez-Cend\u00f3n, M.: Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 148, 497\u2013526 (1999)","journal-title":"J. Comput. Phys."},{"issue":"4","key":"56_CR40","doi-asserted-by":"crossref","first-page":"2463","DOI":"10.1016\/j.jcp.2007.11.006","volume":"227","author":"G Vignoli","year":"2008","unstructured":"Vignoli, G., Titarev, V., Toro, E.: ADER schemes for the shallow water equations in channel with irregular bottom elevation. J. Comput. Phys. 227(4), 2463\u20132480 (2008)","journal-title":"J. Comput. Phys."},{"issue":"5","key":"56_CR41","doi-asserted-by":"crossref","first-page":"485","DOI":"10.1002\/fld.712","volume":"45","author":"J Wang","year":"2004","unstructured":"Wang, J., Borthwick, A., Taylor, R.: Finite-volume-type vof method on dynamically adaptive quadtree grids. Int. J. Numer. Methods Fluids 45(5), 485\u2013508 (2004)","journal-title":"Int. J. Numer. Methods Fluids"},{"issue":"1","key":"56_CR42","doi-asserted-by":"crossref","first-page":"433","DOI":"10.1016\/j.amc.2007.06.024","volume":"196","author":"R Wang","year":"2008","unstructured":"Wang, R., Feng, H., Spiteri, R.J.: Observations on the fifth-order WENO method with non-uniform meshes. Appl. Math. Comput. 196(1), 433\u2013447 (2008)","journal-title":"Appl. Math. Comput."},{"issue":"PA","key":"56_CR43","first-page":"536","volume":"257","author":"Y Xing","year":"2013","unstructured":"Xing, Y.: Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium. J. Comput. Phys. 257(PA), 536\u2013553 (2013)","journal-title":"J. Comput. Phys."},{"key":"56_CR44","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1016\/j.jcp.2005.02.006","volume":"208","author":"Y Xing","year":"2005","unstructured":"Xing, Y., Shu, C.W.: High order finite difference WENO schemes with the exact conservation property for the shallow water equations. J. Comput. Phys. 208, 206\u2013227 (2005)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"56_CR45","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1016\/j.jcp.2005.10.005","volume":"214","author":"Y Xing","year":"2006","unstructured":"Xing, Y., Shu, C.W.: High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. J. Comput. Phys. 214(2), 567\u2013598 (2006)","journal-title":"J. Comput. Phys."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0056-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-015-0056-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-015-0056-x","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,27]],"date-time":"2019-08-27T14:46:35Z","timestamp":1566917195000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-015-0056-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,6,27]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2016,3]]}},"alternative-id":["56"],"URL":"https:\/\/doi.org\/10.1007\/s10915-015-0056-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,6,27]]}}}