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从准度、精度和效率3方面回顾了近几十年来高超声速流动数值模拟研究的进展。在物理模型方面,介绍了高超声速数值模拟中高温气体效应、稀薄气体效应以及湍流效应的建模与模拟,基于雷诺平均Navier-Stokes(RANS)方程重点对现阶段较为关注的高超声速边界层转捩的模式理论研究进行了介绍。在空间离散算法方面,主要介绍了高超声速数值模拟中常用的二阶精度迎风格式以及高阶精度格式的发展及其应用。在时间推进方面,主要回顾了隐式时间推进方法的发展及其应用。在误差和不确定度估计方面,主要介绍了其概念、来源以及常用的分析方法,同时给出了迭代误差估计、Richardson外插法以及敏感性导数方法等初步研究结果。最后,讨论了高超声速流动数值模拟中下一步需关注的问题。
This paper reviews the progress of numerical simulation of hypersonic flow in recent three decades from the aspects of accuracy, precision and efficiency. In the physical model, the modeling and simulation of high temperature gas effect, lean gas effect and turbulence effect in hypersonic numerical simulation are introduced. Based on the Reynolds-average Navier-Stokes (RANS) equation, the focus on the hypersonic boundary layer turn模 mode theory is introduced. In spatial discrete algorithm, the second-order precision upwind format and high-order precision format commonly used in hypersonic numerical simulation are mainly introduced. In terms of time advancement, we mainly review the development of implicit time promotion methods and their applications. In terms of error and uncertainty estimation, the concepts, sources and commonly used analysis methods are introduced. The preliminary results of iterative error estimation, Richardson extrapolation and sensitivity derivation are given. Finally, the next step in the numerical simulation of hypersonic flow is discussed.