Title: Numerical solution to the shallow water equations using explicit and implicit schemes
Abstract: Shallow water flows can be modeled mathematically. One available model is the shallow water equations. Accurate solutions to the shallow water equations are desired. In this paper we solve the one-dimensional shallow water equations for flat topography. We present the performance of three numerical methods. The first is the implicit collocated finite difference method proposed by Crowhurst and Li (the Crowhurst-Li FDM). The second is the explicit collocated Lax-Friedrichs finite volume method (the Lax-Friedrichs FVM). The third is the explicit staggered finite volume method proposed by Stelling and Duinmeijer (the Stelling-Duinmeijer FVM). All three methods are stable. We find that the Lax-Friedrichs FVM is simplest in terms of computation. We also find that the Stelling-Duinmeijer FVM is more accurate in solving dam break problems than the other two methods.
Publication Year: 2016
Publication Date: 2016-01-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 3
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