Abstract
The convergent efficiency and numerical stability of temporal discretization schemes for Navier-Stokes (N-S) equations are significant for engineering turbulent flow simulations. Through analysis of the original scalar and matrix versions of the symmetric successive over relaxation (SSOR) implicit temporal schemes, a novel scalar-matrix hybrid-SSOR scheme based on the local Mach number, which combines the advantages of both the scalar and matrix SSOR, is proposed and implemented in several flow simulations from low to hypersonic speeds. According to the results, the new hybrid-SSOR presents a few advantages and shows the best convergent performance for turbulent flows across a wide range of Mach numbers, mainly because of its high efficiency and excellent numerical stability. The hybrid-SSOR is expected to be widely implemented in engineering flow simulations.
摘要
N-S方程的时间离散格式的收敛效率和数值稳定性对工程湍流计算的意义十分重要. 通过对原始标量型和矩阵型对称超松弛隐式时间格式的分析, 提出了一种基于当地马赫数的混合型对称超松弛隐式时间格式. 该格式兼顾了标量型和矩阵型对称超松弛格式的优点, 被应用于从低速到高超声速的多个湍流流动的计算. 通过计算结果的对比表明, 新的混合型对称超松弛格式在较宽速域的湍流流动模拟中, 由于其高的计算效率和优异的数值稳定性, 表现出了最好的收敛特性. 该新型混合对称超松弛格式将有望广泛应用于工程湍流流动的计算.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (Grant Nos. 11902334, 91952302, and 91852113) and the National Numerical Wind Tunnel Project. The authors would also like to thank the National Key Research and Development Program of China (Grant No. 2019YFA0405300) and the National Key Project (Grant No. GJXM92579).
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Jian Liu proposed the Hybrid-SSOR scheme and wrote the most content of the article. Jianqiang Chen analyzed the computational results and provided several useful advices for the improvements of the Hybrid-SSOR scheme. Yufeng Yang implemented the temporal schemes, such as matrix-SSOR and Hybrid-SSOR, into the computational code. Zipei Zhang generated the computational grids and computed all the cases. Zhixiang Xiao organized the manuscript and revised the revisions.
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Liu, J., Chen, J., Zhang, Z. et al. Assessment of a new hybrid-SSOR implicit temporal scheme for turbulent flows across a wide range of Mach numbers. Acta Mech. Sin. 39, 322398 (2023). https://doi.org/10.1007/s10409-022-22398-x
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DOI: https://doi.org/10.1007/s10409-022-22398-x