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Urban Heat Island Dynamics in an Urban–Rural Domain with Variable Porosity: Numerical Methodology and Simulation

Author

Listed:
  • Néstor García-Chan

    (Department of Physics, CUCEI, University of Guadalajara, Guadalajara 44430, Mexico
    These authors contributed equally to this work.)

  • Juan A. Licea-Salazar

    (Department of Mathematics, CUCEI, University of Guadalajara, Guadalajara 44430, Mexico
    These authors contributed equally to this work.)

  • Luis G. Gutierrez-Ibarra

    (Division of Basic Science, CUCEI, University of Guadalajara, Guadalajara 44430, Mexico
    These authors contributed equally to this work.)

Abstract

Heat transfer and fluid dynamics modeling in porous media is a widely explored topic in physics and applied mathematics, and it involves advanced numerical methods to address its non-linear nature. One interesting application has been the urban-heat-island (UHI) numerical simulation. The UHI is a negative consequence of the increasing urbanization in cities, which is defined as the presence of warm temperatures inside the urban canopy in contrast to the colder surroundings. Furthermore, an interesting phenomena occurs within a UHI context when the city transitions from a heat island to a cold island, matching the increases and decreases of solar radiation over the span of a day, as well as the decrease in the UHI intensity as a result of wind action. The numerical study in this paper had, as its main goal, to reproduce this phenomenon. Therefore, the key elements proposed in this work were the following: A 2D horizontal urban–rural domain that had a variable porosity with a Gaussian distribution centered in the city center. A non-stationary Darcy–Forchheimer–Brinkman model to simulate the flow in porous media, combined with an air–soil heat transport model linked by a balancing equation for the surface energy that includes the evapotranspiration of plants. In regards to the numerical resolution of the model, a classical numerical methodology based on the finite elements of Lagrange P 1 type combined with explicit and implicit time-marching schemes have been effective for high-quality numerical simulations. Several numerical tests were performed on a domain inspired by the metropolitan region of Guadalajara (Mexico), in which not only the temperature inversion was reproduced but also the simulation of the UHI transition by strong wind gusts.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:5:p:1140-:d:1079800
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    References listed on IDEAS

    as
    1. Carlos E. Villarreal-Olavarrieta & Néstor García-Chan & Miguel E. Vázquez-Méndez, 2021. "Simulation of Heat and Water Transport on Different Tree Canopies: A Finite Element Approach," Mathematics, MDPI, vol. 9(19), pages 1-20, September.
    2. Yang Liu & Hong Li & Yanwei Du & Jinfeng Wang, 2013. "Explicit Multistep Mixed Finite Element Method for RLW Equation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    3. Li, Xiaoma & Zhou, Yuyu & Yu, Sha & Jia, Gensuo & Li, Huidong & Li, Wenliang, 2019. "Urban heat island impacts on building energy consumption: A review of approaches and findings," Energy, Elsevier, vol. 174(C), pages 407-419.
    4. Liu Tian & Yongcai Li & Jun Lu & Jue Wang, 2021. "Review on Urban Heat Island in China: Methods, Its Impact on Buildings Energy Demand and Mitigation Strategies," Sustainability, MDPI, vol. 13(2), pages 1-31, January.
    5. 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.
    6. Qing-li Zhao & Zong-cheng Li & You-zheng Ding, 2013. "Expanded Mixed Finite Element Method for the Two-Dimensional Sobolev Equation," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, June.
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    1. 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.

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