# Modelling Pollutant Dispersion in Urban Canyons to Enhance Air Quality and Urban Planning
## 2 Materials and Methods
### CFD Model
\[\overline{u}_{j}\frac{\partial C}{\partial x_{i}}-\frac{\partial}{\partial x _{i}}\left[\left(D_{a}+\frac{\
u_{t}}{Sc_{t}}\right)\frac{\partial c}{ \partial x_{i}}\right]=S_{p} \tag{7}\]  
where \(c\) is the time-averaged concentration of the species (pollutant in this application), \(D_{a}\) is the molecular diffusion coefficient, and \(S_{ct}\) is the turbulent Schmidt number with a value of 0.7 as recommended by previous studies [13]. \(S_{p}\) is the source of pollutant in units of kg/s\(\cdot\)m\({}^{3}\). Its value depends on different factors related to traffic conditions in the street, which affect the amount of pollutant that is released. In this study, its value is fixed at \(10^{-5}\) kg/s\(\cdot\)m\({}^{3}\). It is also important to mention that the species considered in this study is CO as a tracer for evaluating the air quality inside anyons, as is usually conducted when studying outdoor pollutant ventilation [39; 40; 41]. The main reason for considering this pollutant is that it is one of the primary pollutants derived from traffic. In addition, the concentration of CO must be measured to ensure that its levels in the streets remain below a certain threshold [42], as this pollutant is linked with several respiratory and cardiovascular diseases. To effectively solve these equations, it is imperative to define additional parameters within the Fluent environment. \(\{C_{\varepsilon 1},C_{\varepsilon 2},C_{\
u},\eta_{0},\beta\}=\{1.42;1.68,0. 0845;4.38;0.012\}\)[43]. Regarding the rest of the configuration of the Fluent environment, the SIMPLE scheme has been chosen to solve the coupled equations of pressure and velocity, using the least squares cell-based discretisation scheme for the gradient. Furthermore, a second-order discretisation is used for the rest of the magnitudes to achieve better accuracy, using the hybrid initialisation to start the simulation. Finally, when all the residuals are below the value of \(10^{-5}\), convergence is considered to be achieved, and the simulation is stopped. On the other hand, a set of alternative methods for street canyon modelling is available. The main decision to develop the model is the geometrical characteristics. [PERSON] et al. [44]developed a 3D model of an urban canyon and assessed the ventilation effectiveness along the length of the street, obtaining that this parameter increases the street ventilation when the street is short. Along with that study, [PERSON] et al. [2] compared the ventilation results for two specific AR values using a 3D and 2D model, determining that the results were similar when the street was long. This is very interesting as it allows us to use a bidimensional model for obtaining representative results for a specific part of a long street. Consequently, other authors have adopted the simplification of an infinitely long street to recreate the urban canyon with a two-dimensional approach [45; 46]. This approach allows for relatively fast simulations using a model with low computational cost and simple geometry (Figure 2). However, it demands a good configuration set for Fluent, a good-quality mesh, and appropriate boundary conditions for it to provide good results. The numerical model is split into two zones, the \"outer zone\" where the fluid develops and the \"inner zone\" which is the surroundings of the street and the canyon itself. The grid merges different features to reduce the number of cells to maintain a low computational cost while providing fine meshing to ensure the simulation is conducted correctly (Figure 3). After testing different options (as suggested in a previous study [47]), the final mesh has a size of \(H/20\) in the outer zone and \(H/(100\cdot\text{AR})\) in the inner zone, because more precision is needed here. The dependence of the cell size on both the height reference and the aspect ratio prevents excessive growth of the number of cells, thus decreasing the computational cost. The modelling of the UBL is realised by choosing appropriate boundary conditions.