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Unsteady optimal control of shear flows based on the discrete and continuous adjoint Navier-Stokes equations.

基于离散和连续伴随纳维-斯托克斯方程的剪切流非定常最优控制。

基本信息

批准号：
235772517
负责人：
Professor Dr.-Ing. Holger Foysi
金额：
--
依托单位：
Lehrstuhl für Strömungsmechanik
依托单位国家：
德国
项目类别：
Research Grants
财政年份：
2013
资助国家：
德国
起止时间：
2012-12-31 至 2016-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/235772517?language=en
关键词：
Unsteady optimal control shear flows

项目摘要

Optimal flow control based on the continuous adjoint has been very successful so far. Nevertheless, this method shows deficiencies for unsteady flow cases at high Reynolds numbers and when models for the non-represented scales are applied. These deficiencies lead to wrong gradient directions during the determination of the minimum of a cost functional and are caused by inconsistencies of the continuous adjoint of the numerically approximated (primal) flow state. As a consequence, only limited control horizons are possible, additionally, all terms in the flow equations of the primal simulation need to be differentiable, which is certainly not the case for all models. Making use of the discrete adjoint offers the possibility to reach machine precision in determining the gradient numerically, based on the calculated primal flow state. For unsteady turbulent flows at high Reynolds numbers this issue has not been investigated in depth. Although the discrete approach is exact based on the numerical (i.e. discrete primal) flow solution, it still contains the modelling and discretization errors when compared to the `exact` flow solution.The aim of this proposal is to compare the continuous and discrete approach, by minimizing the sound emission to the far-field over very long time horizons for several defined flow cases. The comparison is performed using different resolutions and Reynolds numbers, by making use of DNS and Large Eddy Simulation. The discrete adjoint is developed using automatic differentiation tools (AD-Tools) applied on the same flow solver, which serves as a basis for the continuous adjoint control. The comparison tries to identify strengths and weaknesses of the respective approaches and intends to determine successfull approaches to control turbulent flows at high Reynolds numbers.

到目前为止，基于连续伴随的最优流量控制取得了很大的成功。然而，这种方法在高雷诺数的非定常流动情况下以及在应用非表示尺度的模型时显示出不足。这些缺陷导致在确定成本泛函的最小值期间出现错误的梯度方向，并且是由数值近似(原始)流动状态的连续伴随的不一致引起的。因此，只有有限的控制范围是可能的，此外，原始模拟的流动方程中的所有项都需要是可微的，这肯定不是所有模型的情况。基于计算的原始流动状态，利用离散伴随提供了在数值确定梯度时达到机器精度的可能性。对于高雷诺数的非定常湍流，这一问题还没有得到深入的研究。虽然离散方法是基于数值(即离散原始)流动解的精确方法，但与精确流动解相比，它仍然存在建模和离散化误差。本建议的目的是比较连续和离散方法，在几种定义的流动情况下，通过最小化在很长时间范围内的声音发射到远场。在不同分辨率和雷诺数的情况下，利用数值模拟和大涡模拟的方法进行了比较。离散伴随是应用于同一流动求解器上的自动微分工具(AD-TOOLS)开发的，它是连续伴随控制的基础。这种比较试图找出各自方法的优点和缺点，并打算确定成功的控制高雷诺数湍流流动的方法。