Undeterred by its inherent limitations, Reynolds-averaged Navier-Stokes (RANS) based modeling is still considered the most recognized approach for several computational fluid dynamics (CFD) applications. Recently, in the turbulence modeling community, quantification of model-form uncertainties in RANS has attracted significant interest. We present a stochastic RANS solver with an efficient implementation of the intrusive polynomial chaos (IPC) method in OpenFOAM. The stochastic solver quantifies and propagates the uncertainties associated with the output of the RANS model (eddy viscosity or Reynolds stress tensor). Two distinct high-dimensional variants of the uncertainties are considered, namely, the random eddy viscosity field (REVF) and the random Reynolds stress tensor field (RRSTF). The randomness is introduced in the approximated eddy viscosity field and the Reynolds stress tensor, while asserting the realizability. The stochastic RANS solver has been tested on various benchmark problems for RANS turbulence modeling. In this study, we discuss two important problems where the stochastic RANS solver shows significantly better performance than the traditional uncertainty quantification (UQ) methods. The first problem analyzed is the flow over periodic hills with a REVF, while the second stochastic problem considered is the flow in a square duct with a RRSTF. Along with the comparison for three different RANS turbulence models, a detailed analysis of the stochastic solver based on various influential model parameters is also presented. The IPC based stochastic solver demonstrated the potential to be used in the UQ analysis of further complex CFD applications, especially when a large number of deterministic simulations is not feasible, e.g., wind farm CFD simulations.

中文翻译：

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RANS湍流建模中模型形式不确定性的量化和传播通过侵入多项式混沌

不受其固有局限性的影响，基于雷诺平均纳维斯托克斯 (RANS) 的建模仍然被认为是几种计算流体动力学 (CFD) 应用中最受认可的方法。最近，在湍流建模界，RANS 中模型形式不确定性的量化引起了极大的兴趣。我们提出了一种随机 RANS 求解器，该求解器在 OpenFOAM 中有效地实现了侵入式多项式混沌 (IPC) 方法。随机求解器量化并传播与 RANS 模型（涡流粘度或雷诺应力张量）输出相关的不确定性。考虑了不确定性的两个不同的高维变体，即随机涡粘场（REVF）和随机雷诺应力张量场（RRSTF）。在近似涡粘性场和雷诺应力张量中引入了随机性，同时断言了可实现性。随机 RANS 求解器已针对 RANS 湍流建模的各种基准问题进行了测试。在这项研究中，我们讨论了两个重要问题，其中随机 RANS 求解器显示出比传统不确定性量化 (UQ) 方法更好的性能。分析的第一个问题是具有 REVF 的周期性山丘上的流动，而考虑的第二个随机问题是具有 RRSTF 的方形管道中的流动。除了对三种不同的 RANS 湍流模型进行比较外，还对基于各种影响模型参数的随机求解器进行了详细分析。