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.

翻译：本文提出了一种基于将城市视为多孔介质的新型交通流模型，即将表征城市景观的街道与建筑街区分别视为多孔介质的流体相与固体相。此外，基于多孔介质模型中的质量交换原理，我们可以模拟车辆在街道与路外停车位之间的流转过程。因此，本模型并非标准守恒律，其数学形式表现为非稳态对流-扩散-反应偏微分方程与Darcy-Brinkman-Forchheimer偏微分方程组的耦合系统。为求解该模型，采用经典Galerkin P1有限元法结合强稳定保持型显式时间推进格式，足以保证数值解的稳定性。在受墨西哥瓜达拉哈拉市启发的城市多孔介质区域进行的数值实验，使我们能够模拟孔隙率项对交通速度的影响、高峰/低谷时段的交通流量，以及因停车位不足导致的街道拥堵现象。