Analysis and Computations of Optimal Control Problems for Boussinesq Equations
The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed co...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-06-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/7/6/203 |
| _version_ | 1797487567126396928 |
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| author | Andrea Chierici Valentina Giovacchini Sandro Manservisi |
| author_facet | Andrea Chierici Valentina Giovacchini Sandro Manservisi |
| author_sort | Andrea Chierici |
| collection | DOAJ |
| description | The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed convection flows. We consider different control mechanisms such as distributed, Dirichlet, and Neumann boundary controls. We introduce mathematical tools such as functional spaces and their norms together with bilinear and trilinear forms that are used to express the weak formulation of the partial differential equations. For each of the three different control mechanisms, we aim to study the optimal control problem from a mathematical and numerical point of view. To do so, we present the weak form of the boundary value problem in order to assure the existence of solutions. We state the optimization problem using the method of Lagrange multipliers. In this paper, we show and compare the numerical results obtained by considering these different control mechanisms with different objectives. |
| first_indexed | 2024-03-09T23:49:32Z |
| format | Article |
| id | doaj.art-398ef1c49e1a4e698089315fecf38939 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-09T23:49:32Z |
| publishDate | 2022-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-398ef1c49e1a4e698089315fecf389392023-11-23T16:37:02ZengMDPI AGFluids2311-55212022-06-017620310.3390/fluids7060203Analysis and Computations of Optimal Control Problems for Boussinesq EquationsAndrea Chierici0Valentina Giovacchini1Sandro Manservisi2Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409, USALaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyLaboratory of Montecuccolino, Department of Industrial Engineering, University of Bologna, Via dei Colli 16, 40136 Bologna, ItalyThe main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed convection flows. We consider different control mechanisms such as distributed, Dirichlet, and Neumann boundary controls. We introduce mathematical tools such as functional spaces and their norms together with bilinear and trilinear forms that are used to express the weak formulation of the partial differential equations. For each of the three different control mechanisms, we aim to study the optimal control problem from a mathematical and numerical point of view. To do so, we present the weak form of the boundary value problem in order to assure the existence of solutions. We state the optimization problem using the method of Lagrange multipliers. In this paper, we show and compare the numerical results obtained by considering these different control mechanisms with different objectives.https://www.mdpi.com/2311-5521/7/6/203optimal controlnatural convectionmixed convectionLagrange multipliers methodBoussinesq equations |
| spellingShingle | Andrea Chierici Valentina Giovacchini Sandro Manservisi Analysis and Computations of Optimal Control Problems for Boussinesq Equations Fluids optimal control natural convection mixed convection Lagrange multipliers method Boussinesq equations |
| title | Analysis and Computations of Optimal Control Problems for Boussinesq Equations |
| title_full | Analysis and Computations of Optimal Control Problems for Boussinesq Equations |
| title_fullStr | Analysis and Computations of Optimal Control Problems for Boussinesq Equations |
| title_full_unstemmed | Analysis and Computations of Optimal Control Problems for Boussinesq Equations |
| title_short | Analysis and Computations of Optimal Control Problems for Boussinesq Equations |
| title_sort | analysis and computations of optimal control problems for boussinesq equations |
| topic | optimal control natural convection mixed convection Lagrange multipliers method Boussinesq equations |
| url | https://www.mdpi.com/2311-5521/7/6/203 |
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