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，基于连续伴随的最佳流量控制已经非常成功。然而，此方法显示出高雷诺数在高雷诺数下以及应用非代表性尺度的模型时显示出不稳定流动案例的缺陷。在确定成本功能的最小值期间，这些缺陷导致错误的梯度方向，并由数值近似（原始）流量状态的连续伴随不一致引起。结果，只有有限的控制视野才有可能，此外，原始模拟的流程方程中的所有术语都需要可区分，这对于所有模型肯定不是这样。利用离散的伴随为基于计算的原始流状态确定梯度时达到机器精度的可能性。对于高雷诺数的不稳定动荡流，此问题尚未深入研究。尽管离散方法是基于数值（即离散原始）流解决方案精确的，但与“精确流动解决方案”相比，它仍然包含建模和离散错误。该提案的目的是比较连续和离散的方法，通过将几个定义的流动率的远距离的声音最小化，以最大程度地减少远端的声音。通过使用DNS和大型涡模拟，使用不同的分辨率和雷诺数进行比较。使用在同一流求解器上应用的自动分化工具（AD-Tool）开发离散的伴随，该工具是连续伴随控制的基础。比较试图确定各个方法的优势和劣势，并打算确定在高雷诺数下控制湍流的成功方法。