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Journal of Scientific Computing

, Volume 47, Issue 3, pp 281–302 | Cite as

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

  • Changna Lu
  • Jianxian Qiu
Article

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.

Keywords

Lax-Wendroff-type time discretization Weighted essentially non-oscillatory schemes Shallow water equations High order accuracy 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.College of Mathematics & PhysicsNanjing University of Information Science & TechnologyNanjingP.R. China
  2. 2.Department of MathematicsNanjing UniversityNanjingP.R. China
  3. 3.School of Mathematical SciencesXiamen UniversityXiamenP.R. China

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