A multi-model study of the air pollution related to traffic flow in a two-dimensional porous metropolitan area
Abstract
In this paper, a useful reinterpretation of the city as a porous medium justifies the application of well-known models on fluid dynamics to develop a multi-model study of urban air pollution due to traffic flow in a large city. Thus, to simulate the traffic flow through the city we use a nonconservative macroscopic traffic model combining the continuity equation with the Darcy-Brinkman-Forchheimer equations. For the air flow, regarding the emission rate of CO2 and its dispersion in the atmosphere, we combine a microscopic model -- based on regression techniques but depending on vehicles' velocity and acceleration -- with a classical convection-diffusion-reaction transport model. To solve numerically above PDEs models, the finite element method of Lagrange P1 type along with suitable time marching schemes (like the strong stability preserving scheme) were sufficient to obtain stable numerical solutions. Several computational tests were run on a realistic scenario inspired by the Metropolitan Area of Guadalajara (Mexico), showing not only the influence of the urban landscape (that is, the porosity) on traffic flow, air flow, and pollution transport, but also other interesting phenomena such as rarefaction traffic waves.
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