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摘要: 计算流体力学 (CFD) 在重大工程领域发挥了日益重要的作用, 可信度是制约其进一步大规模工程应用的关键因素. 国内外普遍认同验证与确认是CFD可信度评价和保证的必经途径. 通过系统的验证与确认, 可以有效识别代码中潜在的编程错误, 保证数值求解的可靠性, 客观评价模型在预期用途内的适用性, 在必要时提高模型的预测能力. 本文围绕着什么是验证与确认, 怎么做验证与确认这两个核心问题, 从基本概念、实施流程、主要方法、标模试验和平台工具等角度介绍了国内外在CFD验证与确认领域的研究进展, 重点对误差估计和不确定度量化方法展开介绍. 文章最后对现阶段验证与确认研究解决实际工程问题的不足进行了评述和总结, 对未来重点研究方向进行了展望.Abstract: Computational fluid dynamics (CFD) has played an increasingly important role in major engineering fields, and its credibility is the key constraint to its further extensive engineering application. It is widely accepted home and abroad that verification and validation is the only way to evaluate and guarantee the credibility of CFD. Through systematic verification and validation, the potential programming errors can be effectively identified, the reliability of numerical solving process can be guaranteed, the adequacy and prediction capability of mathematical models in the intended use can be objectively evaluated and improved when necessary. In this paper, with regard to two key issues, ‘‘what is verification and validation’’ and ‘‘how to perform verification and validation’’, the research progress of verification and validation in CFD is introduced from the aspects including basic concept, implementation processes, main methods, calibration model experiments and platform tools, with focusing on numerical error estimation and uncertainty quantification. At the end, the shortcomings of current research are reviewed and the key research directions are prospected.
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图 1 第三届AIAA高升力预测会议计算结果汇总(Rumsey et al. 2019)
图 5 高超声速巡航导弹确认层级示例 (Oberkampf & Trucano 2000)
图 6 不确定度量化的关键活动 (NASA 2016b)
图 8 验证与确认感兴趣的物理问题(Hallissy et al. 2014)
表 1 使用GCI估计数值离散误差时p和Fs的取值 (Roache 1998)
$ \left| {\dfrac{{\hat p - {p_{\rm{f}}}}}{{{p_{\rm{f}}}}}} \right| $ Fs p $ \leqslant 0.1 $ 1.25 $ {p_{\rm{f}}} $ $ \gt 0.1 $ 3.0 min(max(0.5, $ \hat p $),$ {p_{\rm{f}}} $) 
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