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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.19625 |
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| _version_ | 1866909408652427264 |
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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 |