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A simple algorithm to improve the performance of the WENO scheme on non-uniform grids

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Abstract

This paper presents a simple approach for improving the performance of the weighted essentially non-oscillatory (WENO) finite volume scheme on non-uniform grids. This technique relies on the reformulation of the fifth-order WENO-JS (WENO scheme presented by Jiang and Shu in J. Comput. Phys. 126:202–228, 1995) scheme designed on uniform grids in terms of one cell-averaged value and its left and/or right interfacial values of the dependent variable. The effect of grid non-uniformity is taken into consideration by a proper interpolation of the interfacial values. On non-uniform grids, the proposed scheme is much more accurate than the original WENO-JS scheme, which was designed for uniform grids. When the grid is uniform, the resulting scheme reduces to the original WENO-JS scheme. In the meantime, the proposed scheme is computationally much more efficient than the fifth-order WENO scheme designed specifically for the non-uniform grids. A number of numerical test cases are simulated to verify the performance of the present scheme.

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Acknowledgements

The project was supported by the National Natural Science Foundation of China (Grant 11672160) and the National Key Research and Development Program of China (Grant 2016YF A0401200).

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Authors and Affiliations

  1. Tsinghua University, Beijing, 100084, China

    Wen-Feng Huang & Yu-Xin Ren

  2. China Aerodynamics Research and Development Center, Mianyang, 621000, China

    Wen-Feng Huang & Xiong Jiang

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  1. Wen-Feng Huang
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  2. Yu-Xin Ren
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  3. Xiong Jiang
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Correspondence to Yu-Xin Ren.

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Huang, WF., Ren, YX. & Jiang, X. A simple algorithm to improve the performance of the WENO scheme on non-uniform grids. Acta Mech. Sin. 34, 37–47 (2018). https://doi.org/10.1007/s10409-017-0715-2

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  • DOI: https://doi.org/10.1007/s10409-017-0715-2

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