一种稀疏网格方法用于贝叶斯不确定性量化及其在大涡模拟湍流模型中的应用
A sparse grid method for Bayesian uncertainty quantification with application to large eddy simulation turbulence models
AI总结：
本文提出一种自适应分层稀疏网格替代建模方法，用于大涡模拟模型的贝叶斯不确定性量化，通过减少计算成本提升参数估计精度。
摘要：
存在广泛共识，湍流模型的准确性受其对物理输入数据的敏感性、用户选定参数的不确定性以及模型不完善性的影响。然而，将贝叶斯推断应用于系统地量化参数不确定性，通过探索后验概率密度函数（PPDFs），受到大量模型执行带来的计算成本过高以及单次湍流模拟计算时间的阻碍。本文提出了一种自适应分层稀疏网格替代建模方法，用于大涡模拟（LES）的贝叶斯推断。首先，使用相对少量的模型执行构建输出的自适应分层稀疏网格替代模型。利用此类替代模型，可以在参数空间中的任意点快速评估似然函数，而无需模拟计算昂贵的LES模型。该方法本质上与[62]中为地物理和地下水模型开发的方法相似，但在此处进行了调整和应用，以解决更为具有挑战性的湍流模型不确定性量化问题。通过二维圆柱周围流动在亚临界雷诺数下的Smagorinsky模型的数值演示，证明了该方法在不显著损失后验概率估计精度的情况下，显著减少了昂贵的LES执行次数。在此，模型参数通过与不同位置流动尾涡中平均流速和雷诺应力相关的合成数据进行校准。将讨论用户选定的LES参数对输出数据质量的影响。
英文摘要：
There is wide agreement that the accuracy of turbulence models suffer from their sensitivity with respect to physical input data, the uncertainties of user-elected parameters, as well as the model inadequacy. However, the application of Bayesian inference to systematically quantify the uncertainties in parameters, by means of exploring posterior probability density functions (PPDFs), has been hindered by the prohibitively daunting computational cost associated with the large number of model executions, in addition to daunting computation time per one turbulence simulation. In this effort, we perform in this paper an adaptive hierarchical sparse grid surrogate modeling approach to Bayesian inference of large eddy simulation (LES). First, an adaptive hierarchical sparse grid surrogate for the output of forward models is constructed using a relatively small number of model executions. Using such surrogate, the likelihood function can be rapidly evaluated at any point in the parameter space without simulating the computationally expensive LES model. This method is essentially similar to those developed in [62] for geophysical and groundwater models, but is adjusted and applied here for a much more challenging problem of uncertainty quantification of turbulence models. Through a numerical demonstration of the Smagorinsky model of two-dimensional flow around a cylinder at sub-critical Reynolds number, our approach is proven to significantly reduce the number of costly LES executions without losing much accuracy in the posterior probability estimation. Here, the model parameters are calibrated against synthetic data related to the mean flow velocity and Reynolds stresses at different locations in the flow wake. The influence of the user-elected LES parameters on the quality of output data will be discussed.
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