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An accurate and robust AUSM-family scheme on two-dimensional triangular grids

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Abstract

Most numerical schemes for solving high-speed compressible flow problems exhibit an instability that usually occurs inside the numerical shock structure in low-dissipative shock-capturing finite volume methods. In examining several test cases, the flux-difference splitting and the AUSM family of schemes cannot satisfy the robustness requirement, which manifests as the carbuncle phenomenon on two-dimensional triangular grids. This paper presents an accurate and robust AUSM-family scheme (\(\hbox {AUSMDV}^+\) scheme) that is verified against shock-induced anomalies on two-dimensional triangular grids. The linearized discrete analysis of an odd–even decoupling problem is applied to investigate the perturbation damping mechanism of these schemes. The corresponding recursive equations show that the \(\hbox {AUSMDV}^+\) scheme is less sensitive to these anomalies than are other schemes in the AUSM family. Finally, the presented scheme is extended to achieve second-order solution accuracy. Its robustness and efficiency are then evaluated on both structured and unstructured triangular grids. The \(\hbox {AUSMDV}^+\) scheme yields a physically meaningful solution for all test cases without introducing an additional shock fix technique.

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Acknowledgements

The author is pleased to acknowledge the College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand, for funding this research work (Grant No. Res-CIT0225/2018).

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  1. Department of Mechanical Engineering Technology, College of Industrial Technology, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    S. Phongthanapanich

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Correspondence to S. Phongthanapanich.

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Communicated by C.-H. Chang.

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Phongthanapanich, S. An accurate and robust AUSM-family scheme on two-dimensional triangular grids. Shock Waves 29, 755–768 (2019). https://doi.org/10.1007/s00193-019-00892-5

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