Hermite WENO-based limiters for high order discontinuous Galerkin method on unstructured grids |
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Authors: | Zhen-Hua Jiang Chao Yan Jian Yu Wu Yuan |
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Institution: | Zhen-Hua Jiang · Chao Yan · Jian Yu · Wu Yuan College of Aeronautics Science and Engineering,Beihang University,100191 Beijing,China |
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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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Keywords: | Discontinuous Galerkin method · Limiters · WENO · High order accuracy · Unstructured grids |
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