A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city

TL;DR

This paper introduces a novel macroscopic traffic flow model treating urban areas as porous media, coupling PDE systems to simulate car movement and parking interactions, validated through numerical experiments on a Guadalajara-inspired domain.

Contribution

It presents a new nonconservative traffic model based on porous media theory, coupling PDEs to account for parking and street interactions, with a stable numerical solution approach.

Findings

Porosity affects traffic speed and congestion.

Model captures rush-hour traffic dynamics.

Numerical simulations align with real urban traffic patterns.

Abstract

In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous media, respectively. Moreover, based in the interchange of mass in the porous media models, we can model the interchange of cars between streets and off-street parking-spaces. Therefore, our model is not a standard conservation law, being formulated as the coupling of a non-stationary convection-diffusion-reaction PDE with a Darcy-Brinkman-Forchheimer PDE system. To solve this model, the classical Galerkin P1 finite element method combined with an explicit time marching scheme of strong stability-preserving type was enough to stabilize our numerical solutions. Numerical experiences on an urban-porous domain inspired by the city of Guadalajara (Mexico) allow us to simulate the influence of the porosity terms on the traffic speed, the traffic flow at rush-valley hours, and the streets congestions due to the lack of parking spaces.