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An Efficient Adaptive Central-Upwind WENO-CU6 Numerical Scheme with a New Sensor

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Abstract

We present a novel efficient adaptive central-upwind WENO-CU6 scheme (named as EWENO-CU6) to maximize the order of accuracy, minimize dissipation and improve numerical robustness. Unlike WENO-CU6 scheme, the present paper introduces a switch formula based on our new shock sensor to adaptively diminish numerical dissipation in a rational manner when departing from discontinuities. Based on the above improvements, the performances of several schemes are characterized in scalar equations, which indicate new scheme’s high order of accuracy, robustness with a reasonable computational efficiency in wavenumber space. A variety of benchmark cases of Euler equations are tested to further verify the new scheme’s performance. From multi-dimensional tests, EWENO-CU6 scheme shows a greater resolving power in practical flow cases involving both shocks and complex features. We emphasize that this method can be applied more broadly for any algorithm which contains the similar reference smoothness indicator in WENO-CU class schemes.

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Acknowledgements

This work is supported by National Natural Science Foundation of China Grant Nos. 11522222 and 11472305. Innovative Sustentation Fund for Excellent Ph.D. Students in Hunan province (No. CX2016B003). We would also like to thanks Prof. S. Pirozzoli for offering indispensable scalar equation code. Special thanks are due to Prof. N. D. Sandham and Z. W. Hu of University of Southampton for precious help and discussion on the numerical scheme.

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Authors and Affiliations

  1. Science and Technology on Scramjet Lab, National University of Defense Technology, Changsha, 410073, Hunan, China

    Guo-Yan Zhao, Ming-Bo Sun, Liang Li, Hong-Bo Wang, Guang-Xin Li, Yuan Liu, Yong-Chao Sun & Chang-Hai Liang

  2. State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing, 100081, China

    Yong Mei

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  1. Guo-Yan Zhao
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Zhao, GY., Sun, MB., Mei, Y. et al. An Efficient Adaptive Central-Upwind WENO-CU6 Numerical Scheme with a New Sensor. J Sci Comput 81, 649–670 (2019). https://doi.org/10.1007/s10915-019-01035-9

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  • DOI: https://doi.org/10.1007/s10915-019-01035-9

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