The numerical solution of partial differential equations that govern fluid dynamics with turbulence and combustion is challenging due to the multiscale nature of the dynamical system and the need to resolve small-scale physical features. In addition, the uncertainties in the dynamical system, including those in the physical models and parameters, initial and boundary conditions and numerical methods, impact the computational fluid dynamics (CFD) prediction of turbulence and chemical reactions. To improve the CFD prediction, this study focuses on the development and application of a maximum likelihood ensemble filter (MLEF), an ensemble-based data assimilation (DA), for flows featuring combustion and/or turbulence. MLEF finds the optimal analysis and its uncertainty by maximizing the posterior probability density function. The novelty of the study lies in the combination of advanced DA and CFD methods for a new comprehensive application to predict engineering fluid dynamics. The study combines important aspects, including an ensemble-based DA with analysis and uncertainty estimation, an augmented control vector that simultaneously adjusts initial conditions and model empirical parameters and an application of DA to CFD modeling of combustion and flows with complex geometry. The DA performance is validated by a turbulent Couette flow. The new CFD–DA system is then applied to solve the time-evolving shear-layer mixing with methane-air combustion and the turbulent flow over a bluff-body geometry. Results demonstrate the improvement of estimates of model parameters and the uncertainty reduction in initial conditions (ICs) for CFD modeling of flames and flows by the MLEF method.

中文翻译：

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计算火焰和流体动力学的最大似然集成滤波器

由于动力学系统的多尺度性质和解决小尺度物理特征的需要，控制具有湍流和燃烧的流体动力学的偏微分方程的数值解具有挑战性。此外，动力系统中的不确定性，包括物理模型和参数、初始和边界条件以及数值方法中的不确定性，会影响湍流和化学反应的计算流体动力学 (CFD) 预测。为了改进 CFD 预测，本研究的重点是最大似然集合滤波器 (MLEF) 的开发和应用，这是一种基于集合的数据同化 (DA)，用于具有燃烧和/或湍流特征的流动。MLEF 通过最大化后验概率密度函数来找到最优分析及其不确定性。该研究的新颖之处在于将先进的 DA 和 CFD 方法相结合，用于预测工程流体动力学的新综合应用。该研究结合了重要方面，包括基于集合的 DA 与分析和不确定性估计、同时调整初始条件和模型经验参数的增强控制向量以及将 DA 应用于具有复杂几何形状的燃烧和流动的 CFD 建模。DA 性能通过湍流 Couette 流进行验证。然后应用新的 CFD-DA 系统来求解随时间变化的剪切层与甲烷-空气燃烧的混合以及钝体几何形状上的湍流。