A review of uncertainty quantification methods for Computational Fluid Dynamics
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摘要: 随着计算流体力学（CFD）算法和软件的不断发展和完善，CFD数值模拟已经在涉及流体力学的各个领域发挥着日益重要的作用。不确定性因素在CFD计算过程中普遍存在，并且会对数值模拟结果造成影响。发展CFD不确定度量化方法，既能满足工程实践中对CFD可信度评估的需求，同时也能够支撑飞行器的精细化设计。本文旨在总结不确定度量化方法及其在CFD领域中的发展与应用。首先介绍CFD计算中的不确定性来源，以及不确定性的表现形式—随机不确定性和认知不确定性。然后按照不确定性的表现形式介绍对应的不确定度量化方法。最后介绍不确定度量化方法在CFD计算中的发展与应用，并且给出进一步开展不确定度量化工作的建议。Abstract: With the rapid development of Computational Fluid Dynamics (CFD) algorithms and software, CFD has been playing an increasingly important role in various fields involving fluid mechanics. However, unavoidable uncertainties in CFD simulations have great influence on the numerical results. Therefore, developing CFD uncertainty quantification methods which characterizes all major uncertainty sources during the simulation and quantify their effects on the quantities of interest can not only satisfy the demands of CFD credibility evaluation in engineering practices, but also support the precise design of aircrafts. The development and application of uncertainty quantification methods in CFD are summarized in this paper. Firstly, the premise of CFD uncertainty quantification, i.e., uncertainty sources are introduced. Generally, uncertainties can be categorized into stochastic and epistemic ones. Their corresponding uncertainty quantification methods have been proposed. Then the development and application of uncertainty quantification methods are surveyed in typical CFD processes including the geometry generation, meshing, turbulence modeling, and inflow conditions. In the end, sensitivity analysis methods are introduced, which are used to make out the influence of different uncertainty factors on numerical results. Summarizing the previous work on uncertainty, suggestions for the future development of uncertainty quantification methods in CFD are given.
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图 7 MD30P30N多段翼型采用雷诺应力摄动法表面压力系数及摩擦力系数不确定带
Figure 7. The mean and root-mean-square of (a) pressure and (b) friction coefficients on MD30P30N with uncertainty bounds
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