{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T04:33:56Z","timestamp":1781152436131,"version":"3.54.1"},"reference-count":163,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2018,5,4]],"date-time":"2018-05-04T00:00:00Z","timestamp":1525392000000},"content-version":"unspecified","delay-in-days":3,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Acta Numerica"],"published-print":{"date-parts":[[2018,5,1]]},"abstract":"<jats:p>Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, finite-volume schemes are among the most popular tools. In this paper, we review such schemes and focus on one of the simplest (yet highly accurate and robust) methods: central-upwind schemes. These schemes belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes. Besides the classical one- and two-dimensional Saint-Venant systems, we will consider the shallow-water equations with friction terms, models with moving bottom topography, the two-layer shallow-water system as well as general non-conservative hyperbolic systems.<\/jats:p>","DOI":"10.1017\/s0962492918000028","type":"journal-article","created":{"date-parts":[[2018,5,4]],"date-time":"2018-05-04T12:25:54Z","timestamp":1525436754000},"page":"289-351","source":"Crossref","is-referenced-by-count":90,"title":["Finite-volume schemes for shallow-water equations"],"prefix":"10.1017","volume":"27","author":[{"given":"Alexander","family":"Kurganov","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2018,5,4]]},"reference":[{"key":"S0962492918000028_r162","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-012-9578-7"},{"key":"S0962492918000028_r161","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9377-y"},{"key":"S0962492918000028_r160","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2009.11.004"},{"key":"S0962492918000028_r158","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-950X(2000)126:3(144)"},{"key":"S0962492918000028_r157","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(79)90145-1"},{"key":"S0962492918000028_r143","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2001.6892"},{"key":"S0962492918000028_r12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.01.044"},{"key":"S0962492918000028_r74","doi-asserted-by":"crossref","first-page":"2016","DOI":"10.1016\/j.jcp.2007.03.003","article-title":"IMEX extensions of linear multistep methods with general monotonicity and boundedness properties","volume":"225","author":"Hundsdorfer","year":"2007","journal-title":"J. Comput. Phys."},{"key":"S0962492918000028_r55","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.08.007"},{"key":"S0962492918000028_r113","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1187"},{"key":"S0962492918000028_r121","unstructured":"M. Mignotte \u00a0and D. Stefanescu (2002), \u2018On an estimation of polynomial roots by Lagrange\u2019. Technical report 025\/2002, IRMA Strasbourg. http:\/\/hal.archives-ouvertes.fr\/hal-00129675\/en\/"},{"key":"S0962492918000028_r124","doi-asserted-by":"publisher","DOI":"10.1142\/9789814417099_0061"},{"key":"S0962492918000028_r20","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2008019"},{"key":"S0962492918000028_r45","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0096351","volume-title":"Advanced Numerical Approximation of Nonlinear Hyperbolic Equations","author":"Cockburn","year":"1998"},{"key":"S0962492918000028_r19","doi-asserted-by":"crossref","first-page":"371","DOI":"10.4208\/cicp.220210.020710a","article-title":"Finite volume evolution Galerkin methods for the shallow water equations with dry beds","volume":"10","author":"Bollermann","year":"2011","journal-title":"Commun. Comput. Phys."},{"key":"S0962492918000028_r21","doi-asserted-by":"crossref","first-page":"739","DOI":"10.3934\/dcdsb.2010.13.739","article-title":"A robust well-balanced scheme for multi-layer shallow water equations","volume":"13","author":"Bouchut","year":"2010","journal-title":"Discrete Contin. Dyn. Syst. Ser.\u00a0B"},{"key":"S0962492918000028_r156","volume-title":"Additive Operator-Difference Schemes: Splitting Schemes","author":"Vabishchevich","year":"2014"},{"key":"S0962492918000028_r117","first-page":"161","article-title":"On the flow of water in open channel and pipes","volume":"20","author":"Manning","year":"1891","journal-title":"Transactions of the Institution of Civil Engineers of Ireland"},{"key":"S0962492918000028_r57","volume-title":"Etudes Th\u00e9oriques et Pratiques sur l\u2019Ecoulement et le Mouvement des Eaux","author":"Gauckler","year":"1867"},{"key":"S0962492918000028_r32","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2012.01.007"},{"key":"S0962492918000028_r76","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1996.0130"},{"key":"S0962492918000028_r94","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827500373413"},{"key":"S0962492918000028_r132","first-page":"129","article-title":"Implicit\u2013Explicit Runge\u2013Kutta schemes and applications to hyperbolic systems with relaxation","volume":"25","author":"Pareschi","year":"2005","journal-title":"J. Sci. Comput."},{"key":"S0962492918000028_r152","doi-asserted-by":"publisher","DOI":"10.1137\/0721062"},{"key":"S0962492918000028_r137","volume-title":"Difference Methods for Initial-Value Problems","author":"Richtmyer","year":"1994"},{"key":"S0962492918000028_r163","doi-asserted-by":"publisher","DOI":"10.1007\/s11433-008-0135-1"},{"key":"S0962492918000028_r116","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(19991215)31:7<1037::AID-FLD909>3.0.CO;2-V"},{"key":"S0962492918000028_r52","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2011.03.042"},{"key":"S0962492918000028_r140","doi-asserted-by":"publisher","DOI":"10.1007\/88-470-0354-7_18"},{"key":"S0962492918000028_r107","doi-asserted-by":"publisher","DOI":"10.1029\/2010WR009751"},{"key":"S0962492918000028_r25","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.4208\/cicp.180513.230514a","article-title":"Solving two-mode shallow water equations using finite volume methods","volume":"16","author":"Castro D\u00edaz","year":"2014","journal-title":"Commun. Comput. Phys."},{"key":"S0962492918000028_r43","doi-asserted-by":"publisher","DOI":"10.1002\/fld.1355"},{"key":"S0962492918000028_r110","doi-asserted-by":"crossref","unstructured":"X. Liu , J. Albright , Y. Epshteyn \u00a0and A. Kurganov (2018), \u2018Well-balanced positivity preserving central-upwind scheme with a novel wet\/dry reconstruction on triangular grids for the Saint-Venant system\u2019. Submitted.","DOI":"10.1016\/j.jcp.2018.07.038"},{"key":"S0962492918000028_r66","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1007\/978-1-4612-2708-3_17","volume-title":"Algorithmic Trends in Computational Fluid Dynamics","author":"Harten","year":"1993"},{"key":"S0962492918000028_r26","doi-asserted-by":"crossref","unstructured":"M. J. Castro D\u00edaz , A. Kurganov \u00a0and T. Morales de Luna (2018), \u2018Path-conservative central-upwind schemes for nonconservative hyperbolic systems\u2019. Preprint.","DOI":"10.1051\/m2an\/2018077"},{"key":"S0962492918000028_r98","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160070112"},{"key":"S0962492918000028_r89","doi-asserted-by":"publisher","DOI":"10.1002\/num.20049"},{"key":"S0962492918000028_r91","doi-asserted-by":"publisher","DOI":"10.1137\/080719091"},{"key":"S0962492918000028_r151","doi-asserted-by":"publisher","DOI":"10.1137\/0705041"},{"key":"S0962492918000028_r16","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2011.04.011"},{"key":"S0962492918000028_r33","doi-asserted-by":"publisher","DOI":"10.1016\/j.jhydrol.2009.12.020"},{"key":"S0962492918000028_r155","doi-asserted-by":"publisher","DOI":"10.1007\/b79761"},{"key":"S0962492918000028_r108","first-page":"1539","article-title":"An improved quadrature rule for the flux-computation in staggered central difference schemes in multidimensions","volume":"63","author":"Lie","year":"2003a","journal-title":"J. Sci. Comput."},{"key":"S0962492918000028_r2","doi-asserted-by":"publisher","DOI":"10.1137\/06067167X"},{"key":"S0962492918000028_r102","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511791253"},{"key":"S0962492918000028_r141","first-page":"230","volume-title":"WASCOM 2009: 15th Conference on Waves and Stability in Continuous Media","author":"Russo","year":"2010"},{"key":"S0962492918000028_r73","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.jhydrol.2012.06.032","article-title":"Numerical modelling of turbidity currents in the Xiaolangdi reservoir, Yellow River, China","volume":"464","author":"Hu","year":"2012","journal-title":"J. Hydrol."},{"key":"S0962492918000028_r136","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.10.020"},{"key":"S0962492918000028_r142","first-page":"321","volume-title":"Minnesota International Hydraulics Convention","author":"Schijf","year":"1953"},{"key":"S0962492918000028_r3","first-page":"85","article-title":"G\u00e9n\u00e9ralisation du sch\u00e9ma de Nessyahu\u2013Tadmor pour une \u00e9quation hyperbolique \u00e0 deux dimensions d\u2019espace","volume":"320","author":"Arminjon","year":"1995","journal-title":"CR Acad. Sci. Paris S\u00e9r. I Math."},{"key":"S0962492918000028_r59","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0713-9"},{"key":"S0962492918000028_r80","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1061\/JWHEAU.0000482","article-title":"Stable channels with gravel-paved beds","volume":"93","author":"Kellerhals","year":"1967","journal-title":"ASCE Journal of the Waterways and Harbors Division"},{"key":"S0962492918000028_r135","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2014.09.027"},{"key":"S0962492918000028_r39","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1016\/j.jcp.2017.12.026","article-title":"Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes","volume":"358","author":"Chertock","year":"2018","journal-title":"J. Comput. Phys."},{"key":"S0962492918000028_r11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546785"},{"key":"S0962492918000028_r104","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599359461"},{"key":"S0962492918000028_r27","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2008.05.012"},{"key":"S0962492918000028_r131","first-page":"269","volume-title":"Recent Trends in Numerical Analysis","author":"Pareschi","year":"2001"},{"key":"S0962492918000028_r120","doi-asserted-by":"publisher","DOI":"10.1080\/10618569908940819"},{"key":"S0962492918000028_r53","volume-title":"M\u00e9canique Appliqu\u00e9e: Hydraulique","author":"Flamant","year":"1891"},{"key":"S0962492918000028_r6","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827503431090"},{"key":"S0962492918000028_r159","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9429(2007)133:1(48)"},{"key":"S0962492918000028_r119","first-page":"197","volume-title":"Finite Difference Methods, I: Solution of Equations in \u211d N","author":"Marchuk","year":"1990"},{"key":"S0962492918000028_r150","doi-asserted-by":"publisher","DOI":"10.1016\/j.advwatres.2011.04.017"},{"key":"S0962492918000028_r85","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2002019"},{"key":"S0962492918000028_r15","doi-asserted-by":"publisher","DOI":"10.1137\/070686147"},{"key":"S0962492918000028_r147","doi-asserted-by":"publisher","DOI":"10.1137\/070679065"},{"key":"S0962492918000028_r10","doi-asserted-by":"publisher","DOI":"10.1137\/0907051"},{"key":"S0962492918000028_r36","first-page":"303","volume-title":"Numerical Methods for Balance Laws","author":"Chertock","year":"2009"},{"key":"S0962492918000028_r105","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501385852"},{"key":"S0962492918000028_r154","doi-asserted-by":"publisher","DOI":"10.1080\/02626660109492804"},{"key":"S0962492918000028_r133","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-001-8181-3"},{"key":"S0962492918000028_r96","doi-asserted-by":"crossref","first-page":"A947","DOI":"10.1137\/15M1038670","article-title":"Second-order fully discrete central-upwind scheme for two-dimensional hyperbolic systems of conservation laws","volume":"39","author":"Kurganov","year":"2017","journal-title":"SIAM J. Sci. Comput."},{"key":"S0962492918000028_r90","doi-asserted-by":"publisher","DOI":"10.4310\/CMS.2007.v5.n1.a6"},{"key":"S0962492918000028_r77","doi-asserted-by":"publisher","DOI":"10.1137\/S106482759631041X"},{"key":"S0962492918000028_r112","doi-asserted-by":"publisher","DOI":"10.1007\/s002110050345"},{"key":"S0962492918000028_r126","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(90)90260-8"},{"key":"S0962492918000028_r28","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2001108"},{"key":"S0962492918000028_r146","doi-asserted-by":"publisher","DOI":"10.1080\/1061856031000104851"},{"key":"S0962492918000028_r139","first-page":"267","article-title":"The calculation of the interaction of non-stationary shock waves with barriers","volume":"1","author":"Rusanov","year":"1961","journal-title":"\u017d. Vy\u010disl. Mat. i Mat. Fiz."},{"key":"S0962492918000028_r60","first-page":"271","article-title":"A difference method for numerical calculation of discontinuous solutions of the equations of hydrodynamics","volume":"47","author":"Godunov","year":"1959","journal-title":"Mat. Sb. (N.S.)"},{"key":"S0962492918000028_r95","doi-asserted-by":"publisher","DOI":"10.1137\/040614189"},{"key":"S0962492918000028_r37","doi-asserted-by":"publisher","DOI":"10.1137\/151005798"},{"key":"S0962492918000028_r48","first-page":"147","article-title":"Th\u00e9orie du mouvement non permanent des eaux, avec application aux crues des rivi\u00e8res et \u00e0 l\u2019introduction des mar\u00e9es dans leur lits","volume":"73","author":"de Saint-Venant","year":"1871","journal-title":"CR Acad. Sci. Paris"},{"key":"S0962492918000028_r1","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1994.1148"},{"key":"S0962492918000028_r4","doi-asserted-by":"publisher","DOI":"10.1080\/10618569808940837"},{"key":"S0962492918000028_r5","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-9274(97)00056-1"},{"key":"S0962492918000028_r51","volume-title":"Zur Physik der D\u00fcnen","author":"Exner","year":"1920"},{"key":"S0962492918000028_r7","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/j.compfluid.2016.06.005","article-title":"Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows","volume":"136","author":"Beljadid","year":"2016","journal-title":"Comput. and Fluids"},{"key":"S0962492918000028_r8","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90065-X"},{"key":"S0962492918000028_r41","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-75712-2_33"},{"key":"S0962492918000028_r9","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(84)90013-5"},{"key":"S0962492918000028_r14","unstructured":"A. Bernstein , A. Chertock , A. Kurganov \u00a0and T. Wu (2018), \u2018Central-upwind scheme for shallow water equations with time-dependent bottom topography\u2019. Preprint."},{"key":"S0962492918000028_r17","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827597324998"},{"key":"S0962492918000028_r22","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2010060"},{"key":"S0962492918000028_r24","doi-asserted-by":"publisher","DOI":"10.1137\/040607642"},{"key":"S0962492918000028_r130","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2004041"},{"key":"S0962492918000028_r29","doi-asserted-by":"publisher","DOI":"10.1016\/S1007-5704(03)00115-1"},{"key":"S0962492918000028_r30","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-09-02317-5"},{"key":"S0962492918000028_r31","doi-asserted-by":"publisher","DOI":"10.1142\/S021820250700256X"},{"key":"S0962492918000028_r34","doi-asserted-by":"crossref","first-page":"1643","DOI":"10.4310\/CMS.2016.v14.n6.a9","article-title":"Moving-water equilibria preserving central-upwind schemes for the shallow water equations","volume":"14","author":"Cheng","year":"2016","journal-title":"Commun. Math. Sci."},{"key":"S0962492918000028_r35","doi-asserted-by":"crossref","unstructured":"Y. Cheng , A. Chertock , M. Herty , A. Kurganov \u00a0and T. Wu (2018), \u2018A new approach for designing moving-water equilibria preserving schemes for the shallow water equations\u2019. Preprint.","DOI":"10.1007\/s10915-019-00947-w"},{"key":"S0962492918000028_r38","doi-asserted-by":"publisher","DOI":"10.1002\/fld.4023"},{"key":"S0962492918000028_r40","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9381-2"},{"key":"S0962492918000028_r42","first-page":"63","volume-title":"Finite Volumes for Complex Applications IV","author":"Chertock","year":"2005"},{"key":"S0962492918000028_r44","doi-asserted-by":"publisher","DOI":"10.3846\/13926292.2013.869269"},{"key":"S0962492918000028_r68","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(87)90031-3"},{"key":"S0962492918000028_r46","first-page":"483","article-title":"Definition and weak stability of nonconservative products","volume":"74","author":"Dal Maso","year":"1995","journal-title":"J. Math. Pures Appl. (9)"},{"key":"S0962492918000028_r47","volume-title":"Recherches Exp\u00e9rimentales Relatives au Mouvement de l\u2019Eau dans les Tuyaux","volume":"1","author":"Darcy","year":"1857"},{"key":"S0962492918000028_r49","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.01.006"},{"key":"S0962492918000028_r50","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2013.09.022"},{"key":"S0962492918000028_r54","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160070206"},{"key":"S0962492918000028_r56","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7930(02)00011-7"},{"key":"S0962492918000028_r58","doi-asserted-by":"crossref","first-page":"89","DOI":"10.3934\/dcdsb.2001.1.89","article-title":"Derivation of viscous Saint-Venant system for laminar shallow water: Numerical validation","volume":"1","author":"Gerbeau","year":"2001","journal-title":"Discrete Contin. Dyn. Syst. Ser.\u00a0B"},{"key":"S0962492918000028_r61","doi-asserted-by":"publisher","DOI":"10.1142\/7498"},{"key":"S0962492918000028_r62","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1137\/S003614450036757X","article-title":"Strong stability-preserving high-order time discretization methods","volume":"43","author":"Gottlieb","year":"2001","journal-title":"SIAM Rev."},{"key":"S0962492918000028_r63","unstructured":"A. J. Grass (1981), Sediment Transport by Waves and Currents, Department of Civil Engineering, University College, London."},{"key":"S0962492918000028_r64","doi-asserted-by":"crossref","first-page":"908","DOI":"10.1016\/j.jcp.2016.05.054","article-title":"Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations","volume":"321","author":"Guermond","year":"2016","journal-title":"J. Comput. Phys."},{"key":"S0962492918000028_r138","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(81)90128-5"},{"key":"S0962492918000028_r67","doi-asserted-by":"publisher","DOI":"10.1137\/0724022"},{"key":"S0962492918000028_r69","doi-asserted-by":"publisher","DOI":"10.1137\/1025002"},{"key":"S0962492918000028_r70","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-950X(1992)118:3(249)"},{"key":"S0962492918000028_r71","first-page":"129","volume-title":"Ninth International Conference Zaragoza\u2013Pau on Applied Mathematics and Statistics","author":"Higueras","year":"2006"},{"key":"S0962492918000028_r72","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.05.011"},{"key":"S0962492918000028_r65","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(89)90226-X"},{"key":"S0962492918000028_r75","doi-asserted-by":"publisher","DOI":"10.1016\/j.mcm.2010.09.005"},{"key":"S0962492918000028_r78","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142997317560"},{"key":"S0962492918000028_r79","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2001130"},{"key":"S0962492918000028_r81","volume-title":"Numerical Schemes for Conservation Laws","author":"Kr\u00f6ner","year":"1997"},{"key":"S0962492918000028_r82","volume-title":"European Conference on Computational Fluid Dynamics: ECCOMAS CFD 2006","author":"Kurganov","year":"2006"},{"key":"S0962492918000028_r83","first-page":"525","volume-title":"Handbook of Numerical Methods for Hyperbolic Problems","author":"Kurganov","year":"2016"},{"key":"S0962492918000028_r84","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827599360236"},{"key":"S0962492918000028_r86","first-page":"141","article-title":"On the reduction of numerical dissipation in central-upwind schemes","volume":"2","author":"Kurganov","year":"2007","journal-title":"Commun. Comput. Phys."},{"key":"S0962492918000028_r87","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1515\/cmam-2014-0003","article-title":"Central-upwind scheme for Savage\u2013Hutter type model of submarine landslides and generated tsunami waves","volume":"14","author":"Kurganov","year":"2014","journal-title":"Comput. Methods Appl. Math."},{"key":"S0962492918000028_r106","doi-asserted-by":"publisher","DOI":"10.1002\/nme.1471"},{"key":"S0962492918000028_r23","doi-asserted-by":"publisher","DOI":"10.1137\/100795280"},{"key":"S0962492918000028_r88","doi-asserted-by":"publisher","DOI":"10.1007\/PL00005455"},{"key":"S0962492918000028_r92","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2000.6459"},{"key":"S0962492918000028_r101","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.1998.6058"},{"key":"S0962492918000028_r13","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s00574-016-0124-3","article-title":"Central-upwind scheme for shallow water equations with discontinuous bottom topography","volume":"47","author":"Bernstein","year":"2016","journal-title":"Bull. Braz. Math. Soc. (N.S.)"},{"key":"S0962492918000028_r93","doi-asserted-by":"publisher","DOI":"10.1002\/num.10025"},{"key":"S0962492918000028_r97","unstructured":"J. L. Lagrange (1798), Trait\u00e9 de la R\u00e9solution des \u00c9quations Num\u00e9riques. Reprinted in \u0152uvres (1879)."},{"key":"S0962492918000028_r99","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-0348-8150-0"},{"key":"S0962492918000028_r100","doi-asserted-by":"publisher","DOI":"10.1142\/S0219891604000287"},{"key":"S0962492918000028_r103","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:1999152"},{"key":"S0962492918000028_r18","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-012-9677-5"},{"key":"S0962492918000028_r109","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827501392880"},{"key":"S0962492918000028_r111","doi-asserted-by":"publisher","DOI":"10.1137\/0733038"},{"key":"S0962492918000028_r114","doi-asserted-by":"publisher","DOI":"10.1137\/S1064827502419439"},{"key":"S0962492918000028_r115","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2006.06.015"},{"key":"S0962492918000028_r118","unstructured":"G. I. Marchuk (1988), Metody Rasshchepleniya [Splitting Methods] (in Russian), Nauka."},{"key":"S0962492918000028_r122","doi-asserted-by":"publisher","DOI":"10.4208\/cicp.2009.v6.p848"},{"key":"S0962492918000028_r123","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-010-9425-7"},{"key":"S0962492918000028_r125","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2010.08.006"},{"key":"S0962492918000028_r127","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.08.019"},{"key":"S0962492918000028_r128","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2007.03.031"},{"key":"S0962492918000028_r129","first-page":"67","volume-title":"Numerical Methods for Balance Laws","author":"Par\u00e9s","year":"2009"},{"key":"S0962492918000028_r134","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112002002550"},{"key":"S0962492918000028_r144","doi-asserted-by":"publisher","DOI":"10.1016\/j.compfluid.2015.11.017"},{"key":"S0962492918000028_r145","doi-asserted-by":"crossref","first-page":"1073","DOI":"10.1137\/0909073","article-title":"Total-variation-diminishing time discretizations","volume":"6","author":"Shu","year":"1988","journal-title":"SIAM J. Sci. Comput."},{"key":"S0962492918000028_r148","doi-asserted-by":"publisher","DOI":"10.1016\/0021-9991(88)90177-5"},{"key":"S0962492918000028_r149","doi-asserted-by":"publisher","DOI":"10.1016\/j.cageo.2006.02.020"},{"key":"S0962492918000028_r153","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-003-1119-7"}],"container-title":["Acta Numerica"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0962492918000028","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,8,22]],"date-time":"2022-08-22T00:12:31Z","timestamp":1661127151000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0962492918000028\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,5,1]]},"references-count":163,"alternative-id":["S0962492918000028"],"URL":"https:\/\/doi.org\/10.1017\/s0962492918000028","relation":{},"ISSN":["0962-4929","1474-0508"],"issn-type":[{"value":"0962-4929","type":"print"},{"value":"1474-0508","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,5,1]]}}}