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Journal of Scientific Computing

, Volume 51, Issue 3, pp 527–559 | Cite as

Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations

  • Gang Li
  • Changna Lu
  • Jianxian QiuEmail author
Article

Abstract

In (J. Comput. Phys. 229: 8105–8129, 2010), Li and Qiu investigated the hybrid weighted essentially non-oscillatory (WENO) schemes with different indicators for Euler equations of gas dynamics. In this continuation paper, we extend the method to solve the one- and two-dimensional shallow water equations with source term due to the non-flat bottom topography, with a goal of obtaining the same advantages of the schemes for the Euler equations, such as the saving computational cost, essentially non-oscillatory property for general solution with discontinuities, and the sharp shock transition. Extensive simulations in one- and two-dimensions are provided to illustrate the behavior of this procedure.

Keywords

WENO approximation Up-wind linear approximation Troubled-cell indicator Shallow water equations Hybrid schemes Source term 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

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

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