A. Chierici, L. Chirco, V. Giovacchini, S. Manservisi
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引用次数: 0
Abstract
. In recent years, the optimal control in fluid dynamics has gained attention for the design and the optimization of engineering devices. One of the main challenges concerns the application of the optimal control theory to turbulent flows modeled by the Reynolds averaging Navier-Stokes equations. In this work we propose the implementation of an optimal boundary control problem for the Reynolds-Averaged Navier-Stokes system closed with a two-equations turbulence model. The optimal boundary velocity is sought in order to achieve several objectives such as the enhancement of turbulence or the matching of the velocity field over a well defined domain region. The boundary where the control acts can be the main inlet section or additional injection holes placed along the domain. By minimizing the augmented Lagrangian functional we obtain the optimality system comprising the state, the adjoint, and the control equations. Furthermore, we propose numerical strategies that allow to solve the optimality system in a robust way for such a large number of unknowns.
. 近年来,流体动力学中的最优控制在工程装置的设计和优化中得到了广泛的关注。其中一个主要的挑战是如何将最优控制理论应用于由Reynolds平均Navier-Stokes方程模拟的湍流。在这项工作中,我们提出了用两方程湍流模型封闭的reynolds - average Navier-Stokes系统的最优边界控制问题的实现。寻找最优边界速度是为了实现几个目标,如增强湍流或匹配速度场在一个明确的区域。控制作用的边界可以是主入口部分或沿区域放置的附加注射孔。通过最小化增广拉格朗日泛函,得到由状态方程、伴随方程和控制方程组成的最优系统。此外,我们提出了数值策略,允许以鲁棒的方式解决如此大量的未知数的最优性系统。