论文标题
对流冷却和数值实现的最佳控制
Optimal Control of Convection-Cooling and Numerical Implementation
论文作者
论文摘要
本文涉及通过对不可压缩速度场的主动控制来增强对流冷却的问题，该速度场（由固定扩散 - 转向模型描述）。这本质上导致双线性最佳控制问题。提出了对最佳控制的存在的严格证明，并得出了使用变异不平等解决控制的一阶最佳条件。此外，还建立了足够的条件以表征局部最小化器。最后，使用有限元方法与非线性迭代方案一起进行了数值实验，以证明和验证我们的控制设计的有效性。
This paper is concerned with the problem of enhancing convection-cooling via active control of the incompressible velocity field, described by a stationary diffusion-convection model. This essentially leads to a bilinear optimal control problem. A rigorous proof of the existence of an optimal control is presented and the first order optimality conditions are derived for solving the control using a variational inequality. Moreover, the second order sufficient conditions are established to characterize the local minimizer. Finally, numerical experiments are conducted utilizing finite elements methods together with nonlinear iterative schemes, to demonstrate and validate the effectiveness of our control design.
