Abstract Uncertainty quantification (UQ) has recently become an important part of the design process of countless engineering applications. However, up to now in computational fluid dynamics (CFD) the errors introduced by the turbulent viscosity models in Reynolds-Averaged Navier Stokes (RANS) models have often been neglected in UQ studies. Although Direct Numerical Simulations (DNS) are physically correct, obtaining a large enough set of DNS data for UQ studies is currently computationally intractable. UQ based only on RANS simulations or on DNS thus leads to physical and statistical inaccuracies in the output probability distribution functions (PDF). Therefore, three hybrid methods combining both RANS simulations and DNS to perform non-intrusive UQ are suggested in this work. Low-fidelity RANS simulations and high-fidelity DNS are combined to give an approximation of an output PDF using the advantages of both data sets: the physical accuracy via the DNS and the statistical accuracy via the RANS simulations. The hybrid methods are applied to the flow over 2D periodically arranged hills. It is shown that the Gaussian CoKriging (GCK) method is the best hybrid method and that a non-intrusive hybrid UQ approach combining both DNS and RANS simulations is possible, with both physically more accurate and statistically better PDF.

中文翻译：

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一种结合 DNS 和 RANS 模拟的混合方法来量化湍流建模中的不确定性

摘要 不确定性量化 (UQ) 最近已成为无数工程应用设计过程的重要组成部分。然而，到目前为止，在计算流体动力学 (CFD) 中，由雷诺平均纳维斯托克斯 (RANS) 模型中的湍流粘度模型引入的误差在 UQ 研究中经常被忽略。尽管直接数值模拟 (DNS) 在物理上是正确的，但为 UQ 研究获取足够大的 DNS 数据集目前在计算上是难以处理的。仅基于 RANS 模拟或 DNS 的 UQ 因此导致输出概率分布函数 (PDF) 的物理和统计不准确。因此，在这项工作中建议了三种结合 RANS 模拟和 DNS 来执行非侵入式 UQ 的混合方法。低保真 RANS 模拟和高保真 DNS 结合使用两个数据集的优点给出输出 PDF 的近似值：通过 DNS 的物理精度和通过 RANS 模拟的统计精度。混合方法应用于二维周期性排列的山丘上的流动。结果表明，高斯 CoKriging (GCK) 方法是最好的混合方法，并且结合 DNS 和 RANS 模拟的非侵入式混合 UQ 方法是可能的，具有物理上更准确和统计上更好的 PDF。