Numerical evaluation of urban-warming mitigation strategies in an urban-porous media. An application of stabilized finite elements methods

• Published in: Journal of mathematics in industry Vol. 14; no. 1; pp. 26 - 20
• Main Authors: García-Chan, Néstor, Licea-Salazar, Juan A., Gutierrez-Ibarra, Luis G.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2024; Springer Nature B.V; SpringerOpen
• Subjects: Air temperature; Applications of Mathematics; Brinkman model; Concrete pavements; Darcy-Brinkman-Forchheimer model; Energy consumption; Finite element method; Galerkin Least-Squares; Heat; Math. Appl. in Environmental Science; Mathematical analysis; Mathematical and Computational Biology; Mathematical and Computational Engineering; Mathematical Methods in Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Normal distribution; Porosity; Porous media; Pressure stabilization; Radiation; Roofing; Selected topics from 22nd ECMI Conference on Industrial and Applied Mathematics; Solid phases; Streets; Temperature; Thermal exchange model; Thermal stress; Urban areas; Urban warming modeling; Mexico; Finite element method; 65L06; 35K61; Pressure stabilization; Galerkin Least-Squares; 35Q35; Darcy-Brinkman-Forchheimer model; 35K05; Thermal exchange model; 65M60; Urban warming modeling
• ISSN: 2190-5983; 2190-5983
• DOI: 10.1186/s13362-024-00163-8

In this paper, we explore the effectiveness of strategies for mitigating urban warming from a numerical simulation standpoint. To achieve this, a reinterpretation of porosity on an urban context allows us to identify the urban surface covered by streets, and the urban surface covered by buildings as the fluid and solid phases of an urban-porous media, respectively. Using a Gaussian distribution we define the urban porosity at all points within an urban zone. Once the urban porosity is defined, a Darcy-Brinkman-Forchheimer type model is coupled with a thermal exchange model to obtain the wind field, and the air temperature. The convective nature of the model, and the porosity gradients lead us to use stabilized finite element methods in order to avoid the appearance of spurious oscillations in numerical solutions: we use a pressure stabilizer for the Darcy-Brinkman-Forchheimer model and a least-squares stabilizer for the thermal exchange model. Numerical experiments were conducted on a domain modeled after the Metropolitan Zone of Guadalajara City, Mexico, to evaluate strategies such as white roofs, concrete-paved streets instead of asphalt, and large urban parks. The results reveal significant differences in urban temperatures, which in turn helps to alleviate thermal stress for city inhabitants.