Title: Determining a priori a RANS model's applicable range via global epistemic uncertainty quantification Show Chinese title

Title: 通过全局认识论不确定性量化确定RANS模型的适用范围

Abstract: Calibrating a Reynolds-averaged Navier-Stokes (RANS) model against data leads to an improvement. Determining {\it a priori} if such an improvement generalizes to flows outside the calibration data is an outstanding challenge. This work attempts to address this challenge via global epistemic Uncertainty Quantification (UQ). Unlike the available epistemic UQ methods that are local and tell us a model's uncertainty at one specific flow condition, the global epistemic UQ method presented in this work tells us also whether a perturbation of the original model would generalize. Specifically, the global epistemic UQ method evaluates a potential improvement in terms of its "effectiveness" and "inconsistency". Any improvement can be put in one of the following four quadrants: first, high effectiveness, low inconsistency; second, high effectiveness, high inconsistency; third, low effectiveness, low inconsistency; and fourth, low effectiveness, high inconsistency. An improvement would generalize if and only if it is in the high effectiveness and low inconsistency quadrant. To demonstrate the concept, we apply the global epistemic UQ to full Reynolds stress modeling of a stratified shear layer. The global epistemic UQ results point to a model coefficient in the pressure-strain correlation closure (among others) as effective and consistent for predicting the quantity of interest of shear layer's growth. We calibrate the model coefficient such that our RANS matches direct numerical simulation data at one flow condition. We show that the calibrated model generalizes to several other test flow conditions. On the other hand, when calibrating a high inconsistency term, we get a model that works at only the calibrated condition. Show Chinese abstract

Abstract: 将雷诺平均纳维-斯托克斯（RANS）模型与数据进行校准可以带来改进。 确定{\it 先验}这种改进是否能推广到校准数据以外的流动是一个悬而未决的挑战。 本研究尝试通过全局认知不确定性量化（UQ）来解决这一挑战。 与现有的局部认知UQ方法不同，这些方法仅告诉我们模型在特定流动条件下的不确定性，本文提出的全局认知UQ方法还告诉我们对原始模型的扰动是否具有泛化能力。 具体而言，全局认知UQ方法根据其“有效性”和“不一致度”来评估潜在的改进。 任何改进都可以归入以下四个象限之一：第一，高有效性，低不一致度；第二，高有效性，高不一致度；第三，低有效性，低不一致度；第四，低有效性，高不一致度。 只有当改进处于高有效性和低不一致度的象限时，它才能推广。 为了演示这一概念，我们将全局认知UQ应用于分层剪切层的完整雷诺应力建模。 全局认知UQ结果表明，在压力应变相关闭合（以及其他一些项）中有一个模型系数对于预测剪切层增长的相关量是有效且一致的。 我们校准该模型系数，使得我们的RANS在一种流动条件下与直接数值模拟数据相匹配。 我们证明了校准后的模型可以推广到其他几种测试流动条件。 另一方面，当校准一个高不一致性的项时，我们得到的模型只在校准条件下有效。