The maximum likelihood ensemble filter for computational flame and fluid dynamics

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.