用贝叶斯方法从流 MRI 数据中同时重建平均流场并学习湍流模型参数。
Bayesian inference of mean velocity fields and turbulence models from flow MRI
- 基于贝叶斯反问题，联合估计平均流场与湍流模型参数
- 在 FDA 喷嘴湍流实验中成功重建流场且无过拟合
- 适用于任意可微湍流模型，可扩展至非定常流动
我们求解一个贝叶斯逆雷诺平均纳维-斯托克斯（RANS）问题，通过融合平均流数据，联合重建平均流场并学习未知的 RANS 模型参数。设计了一种算法，从湍流平均流数据中学习代数有效粘性模型的最可能参数，并估计其不确定性。通过流动磁共振成像（flow MRI）实验，获取了理想化医疗设备——FDA 喷嘴中受限湍流射流的平均流数据。该算法成功重建了平均流场，并学习到最可能的湍流模型参数，未出现过拟合现象。该方法可适用于任意可微的湍流模型，无论是代数（显式）还是多方程（隐式）模型，并可自然推广至非定常湍流流动。
原文摘要 · Abstract (English)
We solve a Bayesian inverse Reynolds-averaged Navier-Stokes (RANS) problem that assimilates mean flow data by jointly reconstructing the mean flow field and learning its unknown RANS parameters. We devise an algorithm that learns the most likely parameters of an algebraic effective viscosity model, and estimates their uncertainties, from mean flow data of a turbulent flow. We conduct a flow MRI experiment to obtain mean flow data of a confined turbulent jet in an idealized medical device known as the FDA (Food and Drug Administration) nozzle. The algorithm successfully reconstructs the mean flow field and learns the most likely turbulence model parameters without overfitting. The methodology accepts any turbulence model, be it algebraic (explicit) or multi-equation (implicit), as long as the model is differentiable, and naturally extends to unsteady turbulent flows.
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