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

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.