{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T05:24:50Z","timestamp":1773379490964,"version":"3.50.1"},"reference-count":41,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2016,12,8]],"date-time":"2016-12-08T00:00:00Z","timestamp":1481155200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2017,6]]},"DOI":"10.1007\/s10915-016-0329-z","type":"journal-article","created":{"date-parts":[[2016,12,8]],"date-time":"2016-12-08T10:45:06Z","timestamp":1481193906000},"page":"994-1034","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":39,"title":["A Positivity-Preserving Well-Balanced Central Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations"],"prefix":"10.1007","volume":"71","author":[{"given":"Maojun","family":"Li","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Philippe","family":"Guyenne","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengyan","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Liwei","family":"Xu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,12,8]]},"reference":[{"key":"329_CR1","doi-asserted-by":"publisher","first-page":"1049","DOI":"10.1016\/0045-7930(94)90004-3","volume":"23","author":"A Bermudez","year":"1994","unstructured":"Bermudez, A., Vazquez, M.E.: Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23, 1049\u20131071 (1994)","journal-title":"Comput. Fluids"},{"key":"329_CR2","doi-asserted-by":"publisher","first-page":"2587","DOI":"10.1137\/070686147","volume":"30","author":"C Berthon","year":"2008","unstructured":"Berthon, C., Marche, F.: A positive preserving high order VFRoe scheme for shallow water equations: a class of relaxation schemes. SIAM J. Sci. Comput. 30, 2587\u20132612 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"329_CR3","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s10915-004-4136-6","volume":"22","author":"O Bokhove","year":"2005","unstructured":"Bokhove, O.: Flooding and drying in discontinuous Galerkin finite-element discretizations of shallow-water equations. Part 1: one dimension. J. Sci. Comput. 22, 47\u201382 (2005)","journal-title":"J. Sci. Comput."},{"key":"329_CR4","doi-asserted-by":"publisher","first-page":"1548","DOI":"10.1016\/j.cma.2009.01.008","volume":"198","author":"S Bunya","year":"2009","unstructured":"Bunya, S., Kubatko, E.J., Westerink, J.J., Dawson, C.: A wetting and drying treatment for the Runge\u2013Kutta discontinuous Galerkin solution to the shallow water equations. Comput. Methods Appl. Mech. Eng. 198, 1548\u20131562 (2009)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"329_CR5","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1002\/fld.285","volume":"39","author":"P Brufau","year":"2002","unstructured":"Brufau, P., Vazquez-Cendon, M.E., Garcia-Navarro, P.: A numerical model for the flooding and drying of irregular domains. Int. J. Numer. Methods Fluids 39, 247\u2013275 (2002)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"329_CR6","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1051\/m2an\/2010060","volume":"45","author":"S Bryson","year":"2011","unstructured":"Bryson, S., Epshteyn, Y., Kurganov, A., Petrova, G.: Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-venant system. Math. Model. Numer. Anal. 45, 423\u2013446 (2011)","journal-title":"Math. Model. Numer. Anal."},{"key":"329_CR7","doi-asserted-by":"publisher","first-page":"897","DOI":"10.1142\/S021820250600139X","volume":"16","author":"MJ Castro","year":"2006","unstructured":"Castro, M.J., Gonzalez-Vida, J.M., Pares, C.: Numerical treatment of wet\/dry fronts in shallow flows with a modified Roe scheme. Math. Models Methods Appl. Sci. 16, 897\u2013931 (2006)","journal-title":"Math. Models Methods Appl. Sci."},{"key":"329_CR8","doi-asserted-by":"publisher","first-page":"255","DOI":"10.1016\/j.jcp.2012.12.019","volume":"238","author":"Y Cheng","year":"2013","unstructured":"Cheng, Y., Li, F., Qiu, J., Xu, L.: Positivity-preserving DG and central DG methods for ideal MHD equations. J. Comput. Phys. 238, 255\u2013280 (2013)","journal-title":"J. Comput. Phys."},{"key":"329_CR9","doi-asserted-by":"publisher","first-page":"199","DOI":"10.1006\/jcph.1998.5892","volume":"141","author":"B Cockburn","year":"1998","unstructured":"Cockburn, B., Shu, C.-W.: The Runge\u2013Kutta discontinuous Galerkin method for conservation laws V multidimensional systems. J. Comput. Phys. 141, 199\u2013224 (1998)","journal-title":"J. Comput. Phys."},{"key":"329_CR10","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.apnum.2016.08.008","volume":"110","author":"H Dong","year":"2016","unstructured":"Dong, H., Li, M.: A reconstructed central discontinuous Galerkin-finite element method for the fully nonlinear weakly dispersive Green-Naghdi model. Appl. Numer. Math. 110, 110\u2013127 (2016)","journal-title":"Appl. Numer. Math."},{"key":"329_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1002\/fld.1674","volume":"58","author":"A Ern","year":"2008","unstructured":"Ern, A., Piperno, S., Djadel, K.: A well-balanced Runge\u2013Kutta discontinuous Galerkin method for the shallow-water equations with flooding and drying. Int. J. Numer. Methods Fluids 58, 1\u201325 (2008)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"329_CR12","doi-asserted-by":"publisher","first-page":"574","DOI":"10.1016\/j.jcp.2007.08.007","volume":"227","author":"JM Gallardo","year":"2007","unstructured":"Gallardo, J.M., Pares, C., Castro, M.: On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. J. Comput. Phys. 227, 574\u2013601 (2007)","journal-title":"J. Comput. Phys."},{"key":"329_CR13","doi-asserted-by":"publisher","first-page":"3089","DOI":"10.1016\/j.jcp.2007.10.027","volume":"227","author":"DL George","year":"2008","unstructured":"George, D.L.: Augmented Riemann solvers for the shallow water equations over variable topography with steady states inundation. J. Comput. Phys. 227, 3089\u20133113 (2008)","journal-title":"J. Comput. Phys."},{"key":"329_CR14","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1137\/S003614450036757X","volume":"43","author":"S Gottlieb","year":"2001","unstructured":"Gottlieb, S., Shu, C.-W., Tadmor, E.: Strong stability preserving high order time discretization methods. SIAM Rev. 43, 89\u2013112 (2001)","journal-title":"SIAM Rev."},{"key":"329_CR15","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1137\/0733001","volume":"33","author":"JM Greenberg","year":"1996","unstructured":"Greenberg, J.M., LeRoux, A.Y.: A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33, 1\u201316 (1996)","journal-title":"SIAM J. Numer. Anal."},{"key":"329_CR16","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1137\/060666214","volume":"30","author":"P Guyenne","year":"2007","unstructured":"Guyenne, P., Nicholls, D.P.: A high-order spectral method for nonlinear water waves over moving bottom topography. SIAM J. Sci. Comput. 30, 81\u2013101 (2007)","journal-title":"SIAM J. Sci. Comput."},{"key":"329_CR17","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1006\/jcph.2000.6603","volume":"165","author":"ME Hubbard","year":"2000","unstructured":"Hubbard, M.E., Garcia-Navarro, P.: Flux difference splitting and the balancing of source terms and flux gradients. J. Comput. Phys. 165, 89\u2013125 (2000)","journal-title":"J. Comput. Phys."},{"key":"329_CR18","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1051\/m2an:2002019","volume":"36","author":"A Kurganov","year":"2002","unstructured":"Kurganov, A., Levy, D.: Central-upwind schemes for the Saint-Venant system. ESAIM Math. Mod. Numer. Anal. 36, 397\u2013425 (2002)","journal-title":"ESAIM Math. Mod. Numer. Anal."},{"key":"329_CR19","doi-asserted-by":"publisher","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 scheme for the Saint-Venant system. Commun. Math. Sci. 5, 133\u2013160 (2007)","journal-title":"Commun. Math. Sci."},{"key":"329_CR20","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1006\/jcph.1998.6058","volume":"146","author":"RJ LeVeque","year":"1998","unstructured":"LeVeque, R.J.: Balancing source terms and flux gradients on high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146, 346\u2013365 (1998)","journal-title":"J. Comput. Phys."},{"key":"329_CR21","doi-asserted-by":"publisher","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. ESAIM Math. Model. Numer. Anal. 33, 547\u2013571 (1999)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"329_CR22","doi-asserted-by":"publisher","first-page":"404","DOI":"10.1007\/s10915-009-9340-y","volume":"45","author":"F Li","year":"2010","unstructured":"Li, F., Yakovlev, S.: A central discontinuous Galerkin method for Hamilton\u2013Jacobi equations. J. Sci. Comput. 45, 404\u2013428 (2010)","journal-title":"J. Sci. Comput."},{"key":"329_CR23","doi-asserted-by":"publisher","first-page":"2655","DOI":"10.1016\/j.jcp.2011.12.016","volume":"231","author":"F Li","year":"2012","unstructured":"Li, F., Xu, L.: Arbitrary order exactly divergence-free central discontinuous Galerkin methods for ideal MHD equations. J. Comput. Phys. 231, 2655\u20132675 (2012)","journal-title":"J. Comput. Phys."},{"key":"329_CR24","doi-asserted-by":"publisher","first-page":"4828","DOI":"10.1016\/j.jcp.2011.03.006","volume":"230","author":"F Li","year":"2011","unstructured":"Li, F., Xu, L., Yakovlev, S.: Central discontinuous Galerkin methods for ideal MHD equations with exactly divergence-free magnetic field. J. Comput. Phys. 230, 4828\u20134847 (2011)","journal-title":"J. Comput. Phys."},{"key":"329_CR25","doi-asserted-by":"publisher","first-page":"169","DOI":"10.1016\/j.jcp.2013.09.050","volume":"257","author":"M Li","year":"2014","unstructured":"Li, M., Guyenne, P., Li, F., Xu, L.: High order well-balanced CDG-FE methods for shallow water waves by a Green\u2013Naghdi model. J. Comput. Phys. 257, 169\u2013192 (2014)","journal-title":"J. Comput. Phys."},{"key":"329_CR26","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1016\/j.advwatres.2009.02.010","volume":"32","author":"Q Liang","year":"2009","unstructured":"Liang, Q., Marche, F.: Numerical resolution of well-balanced shallow water equations with complex source terms. Adv. Water Resour. 32, 873\u2013884 (2009)","journal-title":"Adv. Water Resour."},{"key":"329_CR27","doi-asserted-by":"publisher","first-page":"2442","DOI":"10.1137\/060666974","volume":"45","author":"Y Liu","year":"2007","unstructured":"Liu, Y., Shu, C.-W., Tadmor, E., Zhang, M.: Central discontinuous Galerkin methods on overlapping cells with a nonoscillatary hierarchical reconstruction. SIAM J. Numer. Anal. 45, 2442\u20132467 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"329_CR28","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1051\/m2an:2008018","volume":"42","author":"Y Liu","year":"2008","unstructured":"Liu, Y., Shu, C.-W., Tadmor, E., Zhang, M.: \n                        $$L^2$$\n                        \n                            \n                                            \n                                \n                                    L\n                                    2\n                                \n                            \n                        \n                     stability analysis of the central discontinuous Galerkin method and a comparison between the central and regular discontinuous Galerkin methods. ESAIM Math. Model. Numer. Anal. 42, 593\u2013607 (2008)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"key":"329_CR29","doi-asserted-by":"publisher","first-page":"867","DOI":"10.1002\/fld.1311","volume":"53","author":"F Marche","year":"2007","unstructured":"Marche, F., Bonneton, P., Fabrie, P., Seguin, N.: Evaluation of well-balanced bore-capturing schemes for 2D wetting and drying processes. Int. J. Numer. Methods Fluids 53, 867\u2013894 (2007)","journal-title":"Int. J. Numer. Methods Fluids"},{"key":"329_CR30","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1016\/S0045-7825(02)00551-0","volume":"192","author":"TC Rebollo","year":"2003","unstructured":"Rebollo, T.C., Delgado, A.D., Nieto, E.D.F.: A family of stable numerical solvers for the shallow water equations with source terms. Comput. Methods Appl. Mech. Eng. 192, 203\u2013225 (2003)","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"329_CR31","doi-asserted-by":"publisher","first-page":"532","DOI":"10.1007\/s10915-014-9866-5","volume":"62","author":"MA Rena","year":"2015","unstructured":"Rena, M.A., Li, F.: Operator bounds and time step conditions for DG and central DG methods. J. Sci. Comput. 62, 532\u2013554 (2015)","journal-title":"J. Sci. Comput."},{"key":"329_CR32","doi-asserted-by":"publisher","first-page":"523","DOI":"10.1017\/S002211208700329X","volume":"185","author":"CE Synolakis","year":"1987","unstructured":"Synolakis, C.E.: The runup of solitary waves. J. Fluid Mech. 185, 523\u2013545 (1987)","journal-title":"J. Fluid Mech."},{"key":"329_CR33","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1006\/jcph.2002.7076","volume":"179","author":"S Vukovic","year":"2002","unstructured":"Vukovic, S., Sopta, L.: ENO and WENO schemes with the exact conservation property for one-dimensional shallow water equations. J. Comput. Phys. 179, 593\u2013621 (2002)","journal-title":"J. Comput. Phys."},{"key":"329_CR34","doi-asserted-by":"publisher","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."},{"key":"329_CR35","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1007\/s10915-005-9027-y","volume":"27","author":"Y Xing","year":"2006","unstructured":"Xing, Y., Shu, C.-W.: High order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms. J. Sci. Comput. 27, 477\u2013494 (2006)","journal-title":"J. Sci. Comput."},{"key":"329_CR36","doi-asserted-by":"publisher","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, 567\u2013598 (2006)","journal-title":"J. Comput. Phys."},{"key":"329_CR37","first-page":"100","volume":"1","author":"Y Xing","year":"2006","unstructured":"Xing, Y., Shu, C.-W.: A new approach of high-order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms. Commun. Comput. Phys. 1, 100\u2013134 (2006)","journal-title":"Commun. Comput. Phys."},{"key":"329_CR38","doi-asserted-by":"publisher","first-page":"1476","DOI":"10.1016\/j.advwatres.2010.08.005","volume":"33","author":"Y Xing","year":"2010","unstructured":"Xing, Y., Zhang, X., Shu, C.-W.: Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations. Adv. Water Resour. 33, 1476\u20131493 (2010)","journal-title":"Adv. Water Resour."},{"key":"329_CR39","doi-asserted-by":"publisher","first-page":"533","DOI":"10.1006\/jcph.2002.7040","volume":"178","author":"K Xu","year":"2002","unstructured":"Xu, K.: A well-balanced gas-kinetic scheme for the shallow-water equations with source terms. J. Comput. Phys. 178, 533\u2013562 (2002)","journal-title":"J. Comput. Phys."},{"key":"329_CR40","doi-asserted-by":"publisher","first-page":"8446","DOI":"10.1016\/j.jcp.2009.08.015","volume":"228","author":"L Xu","year":"2009","unstructured":"Xu, L., Guyenne, P.: Numerical simulation of three-dimensional nonlinear water waves. J. Comput. Phys. 228, 8446\u20138466 (2009)","journal-title":"J. Comput. Phys."},{"key":"329_CR41","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jcph.2000.6670","volume":"168","author":"G Zhou","year":"2001","unstructured":"Zhou, G., Causon, D.M., Mingham, C.G., Ingram, D.M.: The surface gradient method for the treatment of source terms in the shallow-water equations. J. Comput. Phys. 168, 1\u201325 (2001)","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\/s10915-016-0329-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-016-0329-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-016-0329-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,4,26]],"date-time":"2017-04-26T09:27:18Z","timestamp":1493198838000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-016-0329-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,12,8]]},"references-count":41,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,6]]}},"alternative-id":["329"],"URL":"https:\/\/doi.org\/10.1007\/s10915-016-0329-z","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,12,8]]}}}