{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T05:00:31Z","timestamp":1773550831384,"version":"3.50.1"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2013,11,17]],"date-time":"2013-11-17T00:00:00Z","timestamp":1384646400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2014,8]]},"DOI":"10.1007\/s10915-013-9802-0","type":"journal-article","created":{"date-parts":[[2013,11,16]],"date-time":"2013-11-16T03:32:27Z","timestamp":1384572747000},"page":"408-437","source":"Crossref","is-referenced-by-count":38,"title":["A Multilayer Method for the Hydrostatic Navier-Stokes Equations: A Particular Weak Solution"],"prefix":"10.1007","volume":"60","author":[{"given":"E. D.","family":"Fern\u00e1ndez-Nieto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"E. H.","family":"Kon\u00e9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"T.","family":"Chac\u00f3n Rebollo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2013,11,17]]},"reference":[{"key":"9802_CR1","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1007\/s10915-012-9591-x","volume":"53","author":"C Acary-Robert","year":"2012","unstructured":"Acary-Robert, C., Fern\u00e1ndez-Nieto, E., Narbona-Reina, G., Vigneaux, P.: A well-balanced finite volume-augmented Lagrangian method for an integrated Herschel\u2013Bulkley model. J. Sci. Comput. 53, 608\u2013641 (2012)","journal-title":"J. Sci. Comput."},{"key":"9802_CR2","unstructured":"Amara, M., Capatina, D., Trujillo, D.: Variational Approach for the Multiscale Modeling of an Estuarian River. Part1: Derivation and Numerical Approximation of a 2D Horizontal Model. Report, INRIA, RR-6742 (2008)"},{"issue":"2","key":"9802_CR3","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3934\/dcdsb.2005.5.189","volume":"5","author":"E Audusse","year":"2005","unstructured":"Audusse, E.: A multilayer Saint-Venant model: derivation and numerical validation. Discret. Contin. Dyn. Syst. Ser. B 5(2), 189\u2013214 (2005)","journal-title":"Discret. Contin. Dyn. Syst. Ser. B"},{"issue":"1","key":"9802_CR4","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.jcp.2004.12.016","volume":"206","author":"E Audusse","year":"2005","unstructured":"Audusse, E., Bristeau, M.-O.: A well-balanced positivity preserving \u201csecond-order\u201d scheme for shallow water flows on unstructured meshes. J. Comput. Phys. 206(1), 311\u2013333 (2005)","journal-title":"J. Comput. Phys."},{"issue":"3","key":"9802_CR5","doi-asserted-by":"crossref","first-page":"311","DOI":"10.2478\/v10006-007-0025-0","volume":"17","author":"E Audusse","year":"2007","unstructured":"Audusse, E., Bristeau, M.-O.: Finite-volume solvers for a multilayer Saint-Venant system. Int. J. Appl. Math. Comput. Sci. 17(3), 311\u2013319 (2007)","journal-title":"Int. J. Appl. Math. Comput. Sci."},{"issue":"3","key":"9802_CR6","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1002\/fld.1534","volume":"56","author":"E Audusse","year":"2008","unstructured":"Audusse, E., Bristeau, M.-O., Decoene, A.: Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model. Intern. J. Numer. Methods Fluids 56(3), 331\u2013350 (2008)","journal-title":"Intern. J. Numer. Methods Fluids"},{"issue":"9","key":"9802_CR7","doi-asserted-by":"crossref","first-page":"3453","DOI":"10.1016\/j.jcp.2011.01.042","volume":"230","author":"E Audusse","year":"2011","unstructured":"Audusse, E., Bristeau, M.-O., Pelanti, M., Sainte-Marie, J.: Approximation of the hydrostatic Navier\u2013Stokes system for density stratified flows by a multilayer model: kinetic interpretation and numerical solution. J. Comput. Phys. 230(9), 3453\u20133478 (2011)","journal-title":"J. Comput. Phys."},{"issue":"1","key":"9802_CR8","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1051\/m2an\/2010036","volume":"45","author":"E Audusse","year":"2011","unstructured":"Audusse, E., Bristeau, M.-O., Perthame, B., Sainte-Marie, J.: A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation. ESAIM Math. Model. Numer. Anal. 45(1), 169\u2013200 (2011)","journal-title":"ESAIM Math. Model. Numer. Anal."},{"issue":"4","key":"9802_CR9","doi-asserted-by":"crossref","first-page":"2173","DOI":"10.1137\/100795280","volume":"34","author":"MJ Castro D\u00edaz","year":"2012","unstructured":"Castro D\u00edaz, M.J., Fern\u00e1ndez-Nieto, E.D.: A class of computationally fast first order finite volume solvers: PVM methods. SIAM J. Sci. Comput. 34(4), 2173\u20132196 (2012)","journal-title":"SIAM J. Sci. Comput."},{"issue":"5","key":"9802_CR10","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1051\/m2an:2003043","volume":"37","author":"T Chac\u00f3n Rebollo","year":"2003","unstructured":"Chac\u00f3n Rebollo, T., Dom\u00ednguez Delgado, A., Fern\u00e1ndez Nieto, E.D.: An entropy-correction free solver for non-homogeneous shallow water equations. M2AN Math. Model. Numer. Anal. 37(5), 755\u2013772 (2003)","journal-title":"M2AN Math. Model. Numer. Anal."},{"key":"9802_CR11","unstructured":"Dal Maso, G., Lefloch, P.G., Murat, F.: Definition and weak stability of nonconservative products. J. Math. Pures Appl. (9), 74(6), 483\u2013548 (1995)"},{"key":"9802_CR12","unstructured":"Fern\u00e1ndez-Nieto, E.D., Kon\u00e9, E.H., Morales de Luna, T., B\u00fcrger, R.: A multilayer shallow water system for polydisperse sedimentation. J. Comput. Phys. 238(1), 281\u2013314 (2013)"},{"issue":"2","key":"9802_CR13","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1007\/s10915-008-9185-9","volume":"36","author":"ED Fern\u00e1ndez-Nieto","year":"2008","unstructured":"Fern\u00e1ndez-Nieto, E.D., Narbona-Reina, G.: Extension of WAF type methods to non-homogeneous shallow water equations with pollutant. J. Sci. Comput. 36(2), 193\u2013217 (2008)","journal-title":"J. Sci. Comput."},{"key":"9802_CR14","unstructured":"Fr\u00e9d\u00e9ric, H.: Freefem++ home page. http:\/\/www.freefem.org\/ff++\/ (2012)"},{"key":"9802_CR15","doi-asserted-by":"crossref","unstructured":"Par\u00e9s, C.: Numerical methods for nonconservative hyperbolic systems: a theoretical framework. SIAM J. Numer. Anal. 44(1), 300\u2013321 (electronic) (2006)","DOI":"10.1137\/050628052"},{"issue":"5","key":"9802_CR16","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1051\/m2an:2004041","volume":"38","author":"C Par\u00e9s","year":"2004","unstructured":"Par\u00e9s, C., Castro, M.: On the well-balance property of Roe\u2019s method for nonconservative hyperbolic systems. Applications to shallow-water systems. M2AN Math. Model. Numer. Anal. 38(5), 821\u2013852 (2004)","journal-title":"M2AN Math. Model. Numer. Anal."},{"issue":"3","key":"9802_CR17","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1142\/S0218202511005118","volume":"21","author":"J Sainte-Marie","year":"2011","unstructured":"Sainte-Marie, J.: Vertically averaged models for the free surface non-hydrostatic Euler system: derivation and kinetic interpretation. Math. Models Methods Appl. Sci. 21(3), 459\u2013490 (2011)","journal-title":"Math. Models Methods Appl. Sci."},{"issue":"2","key":"9802_CR18","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1016\/0021-9991(92)90378-C","volume":"102","author":"I Toumi","year":"1992","unstructured":"Toumi, I.: A weak formulation of Roe\u2019s approximate Riemann solver. J. Comput. Phys. 102(2), 360\u2013373 (1992)","journal-title":"J. Comput. Phys."},{"issue":"2","key":"9802_CR19","doi-asserted-by":"crossref","first-page":"769","DOI":"10.1137\/S0036142901390378","volume":"40","author":"J Yan","year":"2002","unstructured":"Yan, J., Shu, C.-W.: A local discontinuous Galekin method for KdV type equations. Siam J. Numer. Anal. 40(2), 769\u2013791 (2002)","journal-title":"Siam J. Numer. Anal."}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9802-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10915-013-9802-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-013-9802-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,2]],"date-time":"2019-08-02T01:20:16Z","timestamp":1564708816000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10915-013-9802-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,17]]},"references-count":19,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2014,8]]}},"alternative-id":["9802"],"URL":"https:\/\/doi.org\/10.1007\/s10915-013-9802-0","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,17]]}}}