Optimal Control of Convection-Cooling and Numerical Implementation

Cuiyu He; Weiwei Hu; Lin Mu

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arXiv · 2009.01936

Optimal Control of Convection-Cooling and Numerical Implementation

Cuiyu He·Weiwei Hu·Lin Mu

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Abstract

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.

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BibTeX RIS

Cuiyu He, Weiwei Hu, Lin Mu. 2021-03-23. Optimal Control of Convection-Cooling and Numerical Implementation. https://arxiv.org/abs/2009.01936

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