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Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids

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Abstract

A novel class of weighted essentially nonoscillatory (WENO) schemes based on Hermite polynomials, termed as HWENO schemes, is developed and applied as limiters for high order discontinuous Galerkin (DG) method on triangular grids. The developed HWENO methodology utilizes high-order derivative information to keep WENO reconstruction stencils in the von Neumann neighborhood. A simple and efficient technique is also proposed to enhance the smoothness of the existing stencils, making higher-order scheme stable and simplifying the reconstruction process at the same time. The resulting HWENO-based limiters are as compact as the underlying DG schemes and therefore easy to implement. Numerical results for a wide range of flow conditions demonstrate that for DG schemes of up to fourth order of accuracy, the designed HWENO limiters can simultaneously obtain uniform high order accuracy and sharp, essentially non-oscillatory shock transition.

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Authors and Affiliations

  1. College of Aeronautics Science and Engineering, Beihang University, 100191, Beijing, China

    Zhen-Hua Jiang, Chao Yan, Jian Yu & Wu Yuan

Authors
  1. Zhen-Hua Jiang
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  2. Chao Yan
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  3. Jian Yu
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  4. Wu Yuan
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Correspondence to Zhen-Hua Jiang.

Additional information

The project was supported by the National Basic Research Program of China (2009CB724104) and the National Natural Science Foundation of China (90716010).

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Jiang, ZH., Yan, C., Yu, J. et al. Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids. Acta Mech Sin 28, 241–252 (2012). https://doi.org/10.1007/s10409-012-0062-2

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  • DOI: https://doi.org/10.1007/s10409-012-0062-2

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