{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T05:00:30Z","timestamp":1773550830718,"version":"3.50.1"},"reference-count":26,"publisher":"University of Zielona G\u00f3ra, Poland","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2007,10,1]]},"abstract":"<jats:title>Finite-Volume Solvers for a Multilayer Saint-Venant System<\/jats:title><jats:p>We consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.<\/jats:p>","DOI":"10.2478\/v10006-007-0025-0","type":"journal-article","created":{"date-parts":[[2007,10,12]],"date-time":"2007-10-12T14:22:52Z","timestamp":1192198972000},"page":"311-320","source":"Crossref","is-referenced-by-count":37,"title":["Finite-Volume Solvers for a Multilayer Saint-Venant System"],"prefix":"10.61822","volume":"17","author":[{"given":"Emmanuel","family":"Audusse","sequence":"first","affiliation":[]},{"given":"Marie-Odile","family":"Bristeau","sequence":"additional","affiliation":[]}],"member":"37438","reference":[{"key":"1","doi-asserted-by":"crossref","first-page":"189","DOI":"10.3934\/dcdsb.2005.5.189","article-title":"A multilayer Saint-Venant model","volume":"2","author":"E Audusse","year":"2005","journal-title":"Discrete and Continuous Dynamical Systems, Series B"},{"key":"2","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.jcp.2004.12.016","article-title":"A well-balanced positivity preserving second order scheme for shallow water flows on unstructured meshes","volume":"206","author":"E. Audusse","year":"2005","journal-title":"Journal of Computational Physics"},{"key":"3","first-page":"181","article-title":"3D free surface flows simulations using a multilayer Saint-Venant model - Comparisons with Navier-Stokes solutions","author":"E. Audusse","year":"2006a"},{"key":"4","article-title":"Conservative and well-balanced discretizations for shallow water flows on rotational domains","author":"E. Audusse","year":"2006b"},{"key":"5","doi-asserted-by":"crossref","unstructured":"Audusse E., Bristeau M.O. and Decoene A. (2007): <i>Numerical simulations of 3D free surface flows by a multilayer Saint-Venant model.<\/i> (submitted).","DOI":"10.1002\/fld.1534"},{"key":"6","doi-asserted-by":"crossref","first-page":"1049","DOI":"10.1016\/0045-7930(94)90004-3","article-title":"Upwind methods for hyperbolic conservation laws with source terms","volume":"8","author":"A. Bermudez","year":"1994","journal-title":"Computers and Fluids"},{"key":"7","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1016\/S0045-7825(99)00015-8","article-title":"Positivity preserving finite volume Roe schemes for transportdiffusion equations","volume":"178","author":"F. Benkhaldoun","year":"1999","journal-title":"Computer Methods in Applied Mechanics and Engineering"},{"key":"8","unstructured":"Bouchut F. (2002): <i>An introduction to finite volume methods for hyperbolic systems of conservation laws with source.<\/i> Ecole CEA - EDF - INRIA Ecoulements peu profonds \u00e0 surface libre, Octobre 2002, INRIA Rocquencourt <a target=\"_blank\" href='http:\/\/www.dma.ens.fr\/~fbouchut\/publications\/fvcours.ps.gz'>http:\/\/www.dma.ens.fr\/~fbouchut\/publications\/fvcours.ps.gz<\/a>"},{"key":"9","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1017\/S0022112004009991","article-title":"Frontal geostrophic adjustment and nonlinear wave phenomena in one dimensional rotating shallow water. Part 2: Highresolution numerical simulations","volume":"513","author":"F. Bouchut","year":"2004","journal-title":"Journal of Fluid Mechanics"},{"key":"10","article-title":"Boundary Conditions for the Shallow Water Equations solved by Kinetic Schemes","volume":"4282","author":"M. Bristeau","year":"2001","journal-title":"INRIA Report"},{"key":"11","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1051\/m2an:2001108","article-title":"A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system","volume":"35","author":"M. Castro","year":"2001","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"12","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0021-9991(91)90211-3","article-title":"On Godunov type methods for near low densities","volume":"92","author":"B. Einfeldt","year":"1991","journal-title":"Journal of Computational Physics"},{"key":"13","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1051\/m2an:2004010","article-title":"A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography","volume":"2","author":"S. Ferrari","year":"2004","journal-title":"ESAIM: Mathematical Modelling and Numerical Analysis"},{"key":"14","unstructured":"George D. (2004): <i>Numerical Approximation of the Nonlinear Shallow Water Equations with Topography and Dry Beds: A Godunov-Type Scheme.<\/i> M.Sc. Thesis, University of Washington."},{"key":"15","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":"J.-F. Gerbeau","year":"2001","journal-title":"Discrete and Continuous Dynamical Systems, Ser. B"},{"key":"16","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-0713-9","author":"E. Godlewski","year":"1996","journal-title":"Numerical Approximation of Hyperbolic Systems of Conservation Laws"},{"key":"17","first-page":"271","author":"S Godunov","year":"1959","journal-title":"A difference method for numerical calculation of discontinuous equations of hydrodynamics"},{"key":"18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/1025002","article-title":"On upstream differencing and Godunov-type schemes for hyperbolic conservation laws","volume":"25","author":"A. Harten","year":"1983","journal-title":"SIAM Review"},{"key":"19","author":"J Hervouet","year":"2003","journal-title":"Hydrodynamique des \u00e9coulements \u00e0 surface libre; Mod\u00e9lisation num\u00e9rique avec la m\u00e9thode des \u00e9l\u00e9ments finis"},{"key":"20","unstructured":"Khobalatte B. (1993): <i>R\u00e9solution num\u00e9rique des \u00e9quations de la m\u00e9canique des fluides par des m\u00e9thides cin\u00e9tiques.<\/i> Ph.D. Thesis, Universit\u00e9 P. & M. Curie (Paris 6), (in French)."},{"key":"21","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-8629-1","author":"R LeVeque","year":"1992","journal-title":"Numerical Methods for Conservation Laws"},{"key":"22","first-page":"599","article-title":"Existence of entropy solutions for the hyperbolic systems of isentropic gas dynamics in Eulerian and Lagrangian coordinates","volume":"6","author":"P. Lions","year":"1996","journal-title":"Communications on Pure and Applied Mathematics"},{"key":"23","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198509134.001.0001","author":"B Perthame","year":"2002","journal-title":"Kinetic Formulations of Conservation Laws"},{"key":"24","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1007\/s10092-001-8181-3","article-title":"A kinetic scheme for the Saint-Venant system with a source term","volume":"4","author":"B. Perthame","year":"2001","journal-title":"Calcolo"},{"key":"25","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0021-9991(81)90128-5","article-title":"Approximate Riemann solvers, parameter vectors and difference schemes","volume":"43","author":"P Roe","year":"1981","journal-title":"Journal of Computational Physics"},{"key":"26","first-page":"147","article-title":"Th\u00e9orie du mouvement nonpermanent des eaux, avec application aux crues des rivi\u00e8res et \u00e0 l'introduction des mar\u00e9es dans leur lit (in French)","volume":"73","author":"A. de Saint-Venant","year":"1971","journal-title":"Comptes Rendus de l'Acad\u00e9mie des Sciences, Paris"}],"container-title":["International Journal of Applied Mathematics and Computer Science"],"original-title":[],"link":[{"URL":"http:\/\/content.sciendo.com\/view\/journals\/amcs\/17\/3\/article-p311.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/view\/j\/amcs.2007.17.issue-3\/v10006-007-0025-0\/v10006-007-0025-0.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T10:26:22Z","timestamp":1709202382000},"score":1,"resource":{"primary":{"URL":"https:\/\/content.sciendo.com\/doi\/10.2478\/v10006-007-0025-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,10,1]]},"references-count":26,"journal-issue":{"issue":"3"},"URL":"https:\/\/doi.org\/10.2478\/v10006-007-0025-0","relation":{},"ISSN":["1641-876X"],"issn-type":[{"value":"1641-876X","type":"print"}],"subject":[],"published":{"date-parts":[[2007,10,1]]}}}