# Design of Road-Side Barriers to Mitigate Air Pollution near Roads
## 2 Methodology
### Simulation of the Dispersion Phenomena (the NR-CFD Model)  
The physics of the dispersion phenomena occurring in the near-ground atmosphere are described by the mass, momentum, and energy conservation equations [30]. Nevertheless, the task of solving these equations is challenging because they are nonlinear partial differential equations. For the purposes outlined above, the challenge is to reproduce the dispersion phenomena at the microscale level (<250 m high and <1 km long). This challenge has been tackled by solving these governing equations using the CFD technique. In CFD, the space domain (Figure 1) is divided into small volumes, and the governing equations are solved over each volume using a numerical technique called finite volume method (FVM). The simulation of the dispersion phenomena occurring in the atmosphere also requires the specification of the conditions under which the governing equations need to be solved. _The pseudo-steady-state assumption:_ In the study of pollutant dispersion, researchers are interested in short (~1 h) and long-term (~1 year) average results. As an approximation, the pseudo-steady-state approximation can be used. That is, the evolution of the atmosphere is considered as a succession of states where at each time interval, the atmosphere is assumed to be under steady-state conditions [23]. The previous assumption is valid if the time step of the simulation is smaller than the response time of the atmosphere to changes in radiative forcing, which is about 1 h, and it corresponds to the rate at which meteorological data is usually reported [31; 32; 33]. Following up the above argument, a steady-state condition was used. This pseudo steady-state assumption has the following implications for the modeling of the baseline case, i.e., pollutant dispersion over a flat surface without any perturbation to the wind free flow:  
* The condition of horizontal homogeneity. The value of any property remains the same at any position with the same height. * The inlet boundary condition should be known. At every vertical position at the inlet, the value of each variable should be a known input data. * Agreement between the inlet and the ground boundary conditions. The condition of horizontal homogeneity requires that the ground boundary conditions for momentum and heat transfer agree with the inlet boundary conditions. Next, the boundary conditions considered for the present NR-CFD model will be detailed. A particular emphasis will be given to the physics behind the used boundary conditions. _Inlet boundary conditions:_ The inlet boundary conditions for temperature, velocity, and turbulence are determined by the atmospheric stability condition. It describes the degree of thermal turbulence in the atmosphere, and therefore its capacity for transporting and dispersing pollutants [30]. Across the years, several scales and parameters have been defined and used by different field researchers to quantify and classify different stability conditions, with the Monin-Obukhov Length (\(L\)) [34] being one of the most popular. [PERSON] et al. [23] developed a pollutant dispersion study in which several \(L\) values were modeled using a similar computation domain as in this work. They found that, when using dimensionless numbers, ground pollutant concentration downwind an emission source under any atmospheric stability condition is highly correlated to the concentration observed under neutral conditions in a way that each stability case concentration can be computed from the neutral case by simply multiplying it by a corresponding stability factor _fs_, also reported in said work [23]. Therefore, for the present work, a neutral atmospheric stability condition was considered, corresponding to \(L~{}=~{}-10^{100}\) m, which according to the 2-year observation by [PERSON] et al. [35] and the two-month period of experimentation from [PERSON] et al. [5] is the most repeated condition. In this work, the gained knowledge in the simulation of the atmospheric dynamics in a small computational domain was used.