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

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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.

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Authors and Affiliations

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

    Gang Li & Jianxian Qiu

  2. School of Mathematical Science, Qingdao University, Qingdao, Shandong, 266071, P.R. China

    Gang Li

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

    Changna Lu

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

    Jianxian Qiu

Authors
  1. Gang Li
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  2. Changna Lu
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  3. Jianxian Qiu
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Corresponding author

Correspondence to Jianxian Qiu.

Additional information

The research was partially supported by NSFC 10931004, 40906048 and Science research fund of Nanjing University of Information Science & Technology 20090203.

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Li, G., Lu, C. & Qiu, J. Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations. J Sci Comput 51, 527–559 (2012). https://doi.org/10.1007/s10915-011-9520-4

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  • DOI: https://doi.org/10.1007/s10915-011-9520-4

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