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Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema

Author

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  • Lang Wu
  • Dazhi Zhang
  • Boying Wu
  • Xiong Meng

Abstract

Fifth-order mapped semi-Lagrangian weighted essentially nonoscillatory (WENO) methods at certain smooth extrema are developed in this study. The schemes contain the mapped semi-Lagrangian finite volume (M-SL-FV) WENO 5 method and the mapped compact semi-Lagrangian finite difference (M-C-SL-FD) WENO 5 method. The weights in the more common scheme lose accuracy at certain smooth extrema. We introduce mapped weighting to handle the problem. In general, a cell average is applied to construct the M-SL-FV WENO 5 reconstruction, and the M-C-SL-FD WENO 5 interpolation scheme is proposed based on an interpolation approach. An accuracy test and numerical examples are used to demonstrate that the two schemes reduce the loss of accuracy and improve the ability to capture discontinuities.

Suggested Citation

  • Lang Wu & Dazhi Zhang & Boying Wu & Xiong Meng, 2014. "Fifth-Order Mapped Semi-Lagrangian Weighted Essentially Nonoscillatory Methods Near Certain Smooth Extrema," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-14, July.
    • Handle: RePEc:hin:jnljam:127624
    DOI: 10.1155/2014/127624
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    Cited by:

    1. Barnosa Pola, Fernanda Paula & Venturini Pola, Ives Renê, 2019. "Optimizing computational high-order schemes in finite volume simulations using unstructured mesh and topological data structures," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 1-17.

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