Numerical simulation of air pollution due to traffic flow in urban networks

As it is well known, traffic flow is the main pollution source in many urban areas, where the number of vehicles ranges from many thousands to millions. Thus, estimating the pollution emission rate due to traffic flow in big cities is a very hard task. To approach this environmental issue, in this paper we propose a methodology that consists of combining the 1D Lighthill-Whitham-Richards traffic model for road networks with a classical 2D advection-diffusion-reaction pollution model for the atmosphere. Here, the pollution model uses a source term that takes into account the traffic flow contamination by means of a Radon measure supported on a road network within an urban domain. Furthermore, we establish the existence of solution of the coupled model, and detail a complete numerical algorithm to compute it (mainly, interfacing a finite volume scheme based on the supply-demand method for the traffic model, with a characteristics-Lagrange finite element method for the pollution model). Finally, several numerical experiences for a real urban domain (the Guadalajara Metropolitan Area in Mexico) are presented.