arrow
Volume 19, Issue 2-3
Analysis and Numerical Results for Boundary Optimal Control Problems Applied to Turbulent Buoyant Flows

Andrea Chierici, Valentina Giovacchini & Sandro Manservisi

Int. J. Numer. Anal. Mod., 19 (2022), pp. 347-368.

Published online: 2022-04

Export citation
  • Abstract

In this work, we introduce the mathematical analysis of the optimal control for the Navier-Stokes system coupled with the energy equation and a $\kappa$-$\omega$ turbulence model. While the optimal control of the Navier-Stokes system has been widely studied in past works, only a few works are based on the analysis of the turbulent flows. Moreover, the optimal control of turbulent buoyant flows are usually not taken into account due to the difficulties arising from the analysis and the numerical implementation of the optimality system. We first prove the existence of the solution of the boundary value problem associated with the studied system. Then we use an optimization method that relies on the Lagrange multiplier formalism to obtain the first-order necessary condition for optimality. We derive the optimality system and we solve it using a gradient descent algorithm that allows uncoupling state, adjoint, and optimality conditions. Some numerical results are then reported to validate the presented theoretical analysis.

  • AMS Subject Headings

76F70, 76D55, 49J20

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{IJNAM-19-347, author = {Chierici , AndreaGiovacchini , Valentina and Manservisi , Sandro}, title = {Analysis and Numerical Results for Boundary Optimal Control Problems Applied to Turbulent Buoyant Flows }, journal = {International Journal of Numerical Analysis and Modeling}, year = {2022}, volume = {19}, number = {2-3}, pages = {347--368}, abstract = {

In this work, we introduce the mathematical analysis of the optimal control for the Navier-Stokes system coupled with the energy equation and a $\kappa$-$\omega$ turbulence model. While the optimal control of the Navier-Stokes system has been widely studied in past works, only a few works are based on the analysis of the turbulent flows. Moreover, the optimal control of turbulent buoyant flows are usually not taken into account due to the difficulties arising from the analysis and the numerical implementation of the optimality system. We first prove the existence of the solution of the boundary value problem associated with the studied system. Then we use an optimization method that relies on the Lagrange multiplier formalism to obtain the first-order necessary condition for optimality. We derive the optimality system and we solve it using a gradient descent algorithm that allows uncoupling state, adjoint, and optimality conditions. Some numerical results are then reported to validate the presented theoretical analysis.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/20485.html} }
TY - JOUR T1 - Analysis and Numerical Results for Boundary Optimal Control Problems Applied to Turbulent Buoyant Flows AU - Chierici , Andrea AU - Giovacchini , Valentina AU - Manservisi , Sandro JO - International Journal of Numerical Analysis and Modeling VL - 2-3 SP - 347 EP - 368 PY - 2022 DA - 2022/04 SN - 19 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/20485.html KW - Optimal control, buoyancy, turbulence modeling, $\kappa$-$\omega$ model. AB -

In this work, we introduce the mathematical analysis of the optimal control for the Navier-Stokes system coupled with the energy equation and a $\kappa$-$\omega$ turbulence model. While the optimal control of the Navier-Stokes system has been widely studied in past works, only a few works are based on the analysis of the turbulent flows. Moreover, the optimal control of turbulent buoyant flows are usually not taken into account due to the difficulties arising from the analysis and the numerical implementation of the optimality system. We first prove the existence of the solution of the boundary value problem associated with the studied system. Then we use an optimization method that relies on the Lagrange multiplier formalism to obtain the first-order necessary condition for optimality. We derive the optimality system and we solve it using a gradient descent algorithm that allows uncoupling state, adjoint, and optimality conditions. Some numerical results are then reported to validate the presented theoretical analysis.

Andrea Chierici, Valentina Giovacchini & Sandro Manservisi. (2022). Analysis and Numerical Results for Boundary Optimal Control Problems Applied to Turbulent Buoyant Flows . International Journal of Numerical Analysis and Modeling. 19 (2-3). 347-368. doi:
Copy to clipboard
The citation has been copied to your clipboard