Simulations of Shallow Water Equations with Finite Difference Lax-Wendroff Weighted Essentially Non-oscillatory Schemes |
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Authors: | Changna Lu Jianxian Qiu |
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Affiliation: | 1.College of Mathematics & Physics,Nanjing University of Information Science & Technology,Nanjing,P.R. China;2.Department of Mathematics,Nanjing University,Nanjing,P.R. China;3.School of Mathematical Sciences,Xiamen University,Xiamen,P.R. China |
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Abstract: | In this paper we study a Lax-Wendroff-type time discretization procedure for the finite difference weighted essentially non-oscillatory (WENO) schemes to solve one-dimensional and two-dimensional shallow water equations with source terms. In order to maintain genuinely high order accuracy and suit to problems with a rapidly varying bottom topography we use WENO reconstruction not only to the flux but also to the source terms of algebraical modified shallow water equations. Extensive simulations are performed, as a result, the WENO schemes with Lax-Wendroff-type time discretization can maintain nonoscillatory properties and more cost effective than that with Runge-Kutta time discretization. |
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