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

Néstor García-Chan, Lino J. Alvarez-Vázquez, Aurea Martínez and Miguel E. Vázquez-Méndez

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 233, issue C, 60-74

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 traffic congestion due to the lack of parking spaces.

Keywords: Urban-porous media; Nonconservative macroscopic model; Darcy–Brinkman–Forchheimer equations; Traffic flow model; Off-street parking (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425000163
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:233:y:2025:i:c:p:60-74

DOI: 10.1016/j.matcom.2025.01.016

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().