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Journal of Numerical Mathematics

Editor-in-Chief: Hoppe, Ronald H. W. / Kuznetsov, Yuri

Managing Editor: Olshanskii, Maxim

Editorial Board: Benzi, Michele / Brenner, Susanne C. / Carstensen, Carsten / Dryja, M. / Feistauer, Miloslav / Glowinski, R. / Lazarov, Raytcho / Nataf, Frédéric / Neittaanmaki, P. / Bonito, Andrea / Quarteroni, Alfio / Guzman, Johnny / Rannacher, Rolf / Repin, Sergey I. / Shi, Zhong-ci / Tyrtyshnikov, Eugene E. / Zou, Jun / Simoncini, Valeria / Reusken, Arnold

IMPACT FACTOR 2017: 0.951
5-year IMPACT FACTOR: 3.128

CiteScore 2017: 0.96

SCImago Journal Rank (SJR) 2017: 0.494
Source Normalized Impact per Paper (SNIP) 2017: 0.772

Mathematical Citation Quotient (MCQ) 2017: 1.68

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Volume 23, Issue 2


A well-balanced solver for the Saint Venant equations with variable cross-section

Raul Borsche
Published Online: 2015-08-07 | DOI: https://doi.org/10.1515/jnma-2015-0008


In this paper we construct a numerical solver for the Saint Venant equations. Special attention is given to the balancing of the source terms, including the bottom slope and variable cross-sectional profiles. Therefore a special discretization of the pressure law is used, in order to transfer analytical properties to the numerical method. Based on this approximation awell-balanced solver is developed, assuring the C-property and depth positivity. The performance of this method is studied in several test cases focusing on accurate capturing of steady states.

Keywords: Saint Venant equation,well-balanced; augmented Riemann solver; variable cross section; shallow water

About the article

Received: 2013-08-07

Accepted: 2014-04-03

Published Online: 2015-08-07

Published in Print: 2015-06-01

Citation Information: Journal of Numerical Mathematics, Volume 23, Issue 2, Pages 99–115, ISSN (Online) 1569-3953, ISSN (Print) 1570-2820, DOI: https://doi.org/10.1515/jnma-2015-0008.

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