Optimal Control of Unsteady Flows Using Discrete Adjoints
Optimal Control of Unsteady Flows Using Discrete Adjoints
复制标题
使用离散伴随的非定常流优化控制
DOI：
10.2514/6.2011-3720
复制
发表时间：
2011
期刊：
影响因子：
2.5
通讯作者：
F. Thiele
中科院分区：
文献类型：
--
作者：
Anil Nemili;N. Gauger;F. Thiele
我们提出了一种用于粘性流最优控制的离散伴随方法的开发，该方法由不稳定不可压缩雷诺平均纳维斯托克斯方程控制。伴随求解器是通过在逆向微分模式下应用自动微分（AD）技术而开发的。非定常伴随方程通常需要在原始方程的前向时间积分过程中存储完整的流动历史，然后在求解后向时间积分中的伴随方程时使用该历史记录。对于大规模应用程序，存储流解决方案的内存要求可能会变得非常昂贵。为了减少过多的内存需求，采用了二项式检查点策略。给出了围绕旋转圆柱体和 NACA4412 翼型的最佳主动流控制测试用例的数值结果，以验证自动微分生成的导数代码。将基于前向和伴随模式 AD 码的灵敏度与从有限差分中获得的值进行比较。
We present the development of a discrete adjoint approach for the optimal control of viscous ows, governed by unsteady incompressible Reynolds Averaged Navier Stokes equations. The adjoint solver is developed by applying the automatic di erentiation (AD) techniques in reverse mode of di erentiation. The unsteady adjoints usually require the storage of complete ow history during the forward-in-time integration of the primal equations, which is then used while solving the adjoint equations in backward-in-time integration. For large scale applications, the memory requirements for storing the ow solutions can become prohibitively expensive. To reduce the excessive memory demands, the binomial checkpointing strategy has been employed. Numerical results are presented for the test cases of optimal active ow control around a rotating cylinder and a NACA4412 airfoil to validate the automatic di erentiation generated derivative codes. The sensitivities based on forward and adjoint mode AD codes are compared with the values obtained from nite di erences.