考虑数值离散误差的湍流模型选择引入的不确定度量化

Quantification of turbulence model-selection uncertainties considering discretization errors

在流体力学数值模拟过程中存在着多种来源的不确定因素,科学、定量地描述这些因素对模拟结果的影响对模型确认、工业产品设计优化和性能评估等过程十分重要。数值离散、模型选择和模型预测偏差是模拟过程中3种重要的不确定性来源,为将这3种不确定性因素对模拟目标量的影响统一考虑,发展了考虑数值离散误差的贝叶斯模型平均方法。首先,通过对数值离散解和网格尺度进行拟合完成数值离散误差估计,得到每个备选模型真实解的置信区间。然后,通过嵌套方法和条件优化算法,结合贝叶斯模型平均方法构建目标量的概率盒,定义目标变量累积分布函数的上、下限,以此分析其置信区间。最后,针对NACA0012低速绕流和CHN-T1跨声速绕流问题,给出了同时考虑上述3种不确定性因素之后升、阻力系数的置信区间分析示例。

Various sources of uncertainty exist in numerical simulations of fluid mechanics.Characterization of the effects induced by uncertain factors on numerical results scientifically and quantitatively is extremely important for model validation,design,optimization and performance assessment processes of relevant products.Discretization errors,model selection and model prediction bias are three significant sources of uncertainties in numerical simulations.To take the three uncertain factors into account simultaneously,an improved Bayesian model averaging approach is proposed in this paper.The new approach begins with discretization error estimation,using curve fits between numerical predictions and grid scale to obtain the confidence interval of exact solutions to each model in possible model sets.The nested loop and conditional optimization algorithm combined with the traditional Bayesian model averaging approach are then used to construct the probability box for quantity-of-interest.Bounds of cumulative distribution function are then used for confidence interval estimation.The new approach is applied in the simulation of the low speed flow over NACA0012 airfoil and the transonic flow over CHN-T1,and the confidence intervals of the lift and drag coefficients are estimated.