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Simulations of Shallow Water Equations with Finite Difference Lax-Wendroff Weighted Essentially Non-oscillatory Schemes

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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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Authors and Affiliations

  1. College of Mathematics & Physics, Nanjing University of Information Science & Technology, Nanjing, Jiangsu, 210044, P.R. China

    Changna Lu

  2. Department of Mathematics, Nanjing University, Nanjing, Jiangsu, 210093, P.R. China

    Jianxian Qiu

  3. School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, P.R. China

    Jianxian Qiu

Authors
  1. Changna Lu
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  2. Jianxian Qiu
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Correspondence to Jianxian Qiu.

Additional information

The research of C. Lu was supported by NSFC 40906048 and Science research fund of Nanjing University of Information Science & Technology 20090203. The research of J. Qiu was supported by NSFC 10931004.

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Lu, C., Qiu, J. Simulations of Shallow Water Equations with Finite Difference Lax-Wendroff Weighted Essentially Non-oscillatory Schemes. J Sci Comput 47, 281–302 (2011). https://doi.org/10.1007/s10915-010-9437-3

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  • DOI: https://doi.org/10.1007/s10915-010-9437-3

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