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.

迄今为止，基于连续伴随的最优流量控制已经非常成功。然而，该方法显示出高雷诺数下的不稳定流动情况以及应用非代表性尺度的模型时的缺陷。这些缺陷导致在确定成本函数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，这当然不是所有模型的情况。利用离散伴随函数可以根据计算出的原始流动状态以数字方式确定梯度，从而达到机器精度。对于高雷诺数下的不稳定湍流，这个问题尚未得到深入研究。尽管离散方法是基于数值（即离散原始）流解的精确方法，但与“精确”流解决方案相比，它仍然包含建模和离散化误差。本提案的目的是比较连续方法和离散方法，通过在几个定义的流动情况下在很长的时间范围内最大限度地减少向远场的声音发射。通过使用 DNS 和大涡模拟，使用不同的分辨率和雷诺数进行比较。离散伴随是使用应用于同一流求解器的自动微分工具（AD-Tools）开发的，它作为连续伴随控制的基础。该比较试图确定各种方法的优点和缺点，并旨在确定控制高雷诺数湍流的成功方法。