Numerical simulations of optimal control problems for the Reynolds averaged Navier–Stokes system closed with a two-equation turbulence model
Numerical simulations of optimal control problems for the Reynolds averaged Navier–Stokes system closed with a two-equation turbulence model
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DOI：
10.1016/j.compfluid.2015.11.007
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发表时间：
2016-02
影响因子：
2.8
通讯作者：
S. Manservisi;F. Menghini
中科院分区：
文献类型：
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作者：
S. Manservisi;F. Menghini
最近几年，流体力学中的最优控制理论因其在新的工程设备的设计和现有设备的优化中的应用而变得流行起来。近年来，湍流的最优控制已引起人们的重视，但湍流建模及其控制仍是一个悬而未决的问题。在这项工作中，我们研究了流动的分布式最优控制问题，该流动由雷诺平均的N-S系统模拟，闭合在一个两方程k的−ω湍流模型中，该模型考虑了湍流粘性的限制。用拉格朗日乘子方法导出了完整的伴随系统，允许直接根据湍流动能写出代价泛函。我们评估由两项组成的代价泛函，第一项用于速度匹配剖面问题，第二项用于增强或减少湍流。通过与标准消息传递接口库并行的有限元代码，对优化系统进行了数值求解。给出了二维和三维空间的数值结果，验证了该数值方法的有效性。
Optimal control theory in fluid dynamics has become popular in the last several years because of its use in the design of new engineering devices and optimization of existing ones. In recent years the optimal control of turbulent flows has gained attention but turbulence modeling and its control is still an open problem. In this work we study a distributed optimal control problem for a flow modeled by the Reynolds averaged Navier–Stokes system closed by a two-equationk−ωturbulence model which takes into account the limits imposed on turbulent viscosity. The complete adjoint system is derived with a Lagrangian multiplier approach allowing to write a cost functional directly based on the turbulence kinetic energy. We assess a cost functional composed of two terms, the first for a velocity matching profile problem and the second for turbulence enhancement or reduction. The optimality system is solved numerically with a finite element code parallelized with standard message passing interface libraries. Numerical results in two and three-dimensional spaces are reported to show the validity of this numerical approach.