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Abstract
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
Received: 2013-8-7
Accepted: 2014-4-3
Published Online: 2015-8-7
Published in Print: 2015-6-1
© 2015 by Walter de Gruyter Berlin/Boston
