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Optimal Control Strategies for Mitigating Urban Heat Island Intensity in Porous Urban Environments

Author

Listed:
  • Nacer Sellila

    (IFSTTAR Marne la Vallée, Université Gustave Eiffel, 5 Boulevard Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France)

  • Mohammed Louaked

    (Laboratoire de Mathématiques Nicolas Oresme, Université de Caen, Campus II, Bd. Maréchal Juin, B.P. 5186, 14032 Caen, France)

  • Waleed Mouhali

    (ECE-Paris Engineering School, LyRIDS, 37 Quai de Grenelle, CS-71520, 75015 Paris, France)

  • Houari Mechkour

    (ECE-Paris Engineering School, LyRIDS, 37 Quai de Grenelle, CS-71520, 75015 Paris, France)

Abstract

This work is intended as an attempt to explore the use of optimal control techniques for designing green spaces and for dealing with the environmental problems related to urban heat islands appearing in cities. A three-dimensional model is established for numerical studies of the effects of urban anthropogenic heat and wind velocity in urban and rural regions. The transport mechanism of fluid in the cities is governed by the Navier–Stokes–Forschheimer porous media system. We introduce the penalty approximation method to overcome the difficulty induced by the incompressibility constraint. The partial differential equation optimal control problem is solved by using a Spectral Projected Gradient algorithm. To validate the method, we implement a numerical scheme, based on a finite element method, employing the free software FreeFem++ 14.3. We show the results for the optimized and non-optimized situations to compare the two cases.

Suggested Citation

  • Nacer Sellila & Mohammed Louaked & Waleed Mouhali & Houari Mechkour, 2023. "Optimal Control Strategies for Mitigating Urban Heat Island Intensity in Porous Urban Environments," Mathematics, MDPI, vol. 11(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4737-:d:1285893
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    References listed on IDEAS

    as
    1. Néstor García-Chan & Juan A. Licea-Salazar & Luis G. Gutierrez-Ibarra, 2023. "Urban Heat Island Dynamics in an Urban–Rural Domain with Variable Porosity: Numerical Methodology and Simulation," Mathematics, MDPI, vol. 11(5), pages 1-18, February.
    2. Tingzhen Ming & Shengnan Lian & Yongjia Wu & Tianhao Shi & Chong Peng & Yueping Fang & Renaud de Richter & Nyuk Hien Wong, 2021. "Numerical Investigation on the Urban Heat Island Effect by Using a Porous Media Model," Energies, MDPI, vol. 14(15), pages 1-23, August.
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    1. Néstor García-Chan & Juan A. Licea-Salazar & Luis G. Gutierrez-Ibarra, 2023. "Urban Heat Island Dynamics in an Urban–Rural Domain with Variable Porosity: Numerical Methodology and Simulation," Mathematics, MDPI, vol. 11(5), pages 1-18, February.
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