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Main Authors: Garcia-Chan, N., Alvarez-Vazquez, L. J., Martinez, A., Vazquez-Mendez, M. E.
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2411.19625
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author Garcia-Chan, N.
Alvarez-Vazquez, L. J.
Martinez, A.
Vazquez-Mendez, M. E.
author_facet Garcia-Chan, N.
Alvarez-Vazquez, L. J.
Martinez, A.
Vazquez-Mendez, M. E.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2411_19625
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city
Garcia-Chan, N.
Alvarez-Vazquez, L. J.
Martinez, A.
Vazquez-Mendez, M. E.
Numerical Analysis
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.
title A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city
topic Numerical Analysis
url https://arxiv.org/abs/2411.19625