Balanced Central NT Schemes for the Shallow Water Equations

Nelida Črnjarić-Žic (), Senka Vuković () and Luka Sopta ()
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Nelida Črnjarić-Žic: University of Rijeka, Faculty of Engineering
Senka Vuković: University of Rijeka, Faculty of Engineering
Luka Sopta: University of Rijeka, Faculty of Engineering

A chapter in Proceedings of the Conference on Applied Mathematics and Scientific Computing, 2005, pp 171-185 from Springer

Abstract: Abstract The numerical method we consider is based on the nonstaggered central scheme proposed by Jiang, Levy, Lin, Osher, and Tadmor (SIAM J. Numer. Anal. 35, 2147(1998)) that was obtained by conversion of the standard central NT scheme to the nonstaggered mesh. The generalization we propose is connected with the numerical evaluation of the geometrical source term. The presented scheme is applied to the nonhomogeneous shallow water system. Including an appropriate numerical treatment for the source term evaluation we obtain the scheme that preserves quiescent steady-state for the shallow water equations exactly. We consider two different approaches that depend on the discretization of the riverbed bottom. The obtained schemes are well balanced and present accurate and robust results in both steady and unsteady flow simulations.

Keywords: balance law; central schemes; exact C-property; shallow water equations (search for similar items in EconPapers)
Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4020-3197-7_11

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DOI: 10.1007/1-4020-3197-1_11

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