Output-Based Error Estimation and Model Reduction for Chaotic Flows

Computational Fluid Dynamics;Chaos;Aerospace Engineering;Engineering;Aerospace Engineering

Shimizu, YukikoWang, Qiqi ;

University of Michigan

关键词: Computational Fluid Dynamics;    Chaos;    Aerospace Engineering;    Engineering;    Aerospace Engineering;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/149954/ykmizu_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

Turbulent flows are characterized by chaotic variations in state variables and are commonly found in many applications such as jet engine mixing and flow over bluff bodies. Large Eddy Simulations (LES) of these chaotic flows have already proven to be useful to the design process. However, LES is resource and time-intensive.Application of output-based methods for error estimation and mesh adaptation would decrease the cost of these chaotic simulations while still retaining their overall accuracy. However, a direct application of unsteady adjoint-based methods is not possible due to the flows’ inherent sensitivity to the initial conditions and the exponential growth of the corresponding adjoint solutions. This dissertation proposes the Hyper-Reduced Order Modeling-Least Squares Shadowing (HROM-LSS) method, which combines model reduction principles with adjoint sensitivity techniques for chaotic flows to calculate accurate adjoints that are cheaper to solve for than the Least Squares Shadowing (LSS) method on its own.All primal solutions are solved using the discontinuous Galerkin finite element method. Results of the HROM-LSS method for the Kuramoto-Sivashinsky equation and the NACA 0012 airfoil at high Reynolds numbers show promise for this combined method and have been shown to outperform the LSS method when calculating the effect of the discretization errors on the output. In particular, the average CPU times for the HROM-LSS method are reduced by as much as 97.44% for short time simulations and as much as 64% for longer simulations, making the HROM-LSS method a more practical option to calculate adjoint for chaotic flows in order to perform output-based error estimation for turbulent flows.