# Design of Road-Side Barriers to Mitigate Air Pollution near Roads
## 2 Methodology
### Simulation of the Dispersion Phenomena (the NR-CFD Model)
Specifically, the inlet boundary condition for speed and temperature profiles were established following up the Monin-Obukhov Similarity(MOS) theory. This theory states that any mean flow quantity in the atmospheric surface layer (e.g., momentum or energy), when normalized by an appropriate scaling parameter, is a unique function of \(\zeta\ =\ z/L\) where \(\zeta\) is known as the buoyancy parameter [30], and \(L\) is the Monin-Obukhov length, which describes the atmospheric stability condition. Based on the observation that (i) in the atmospheric surface layer (ASL) the wind speed (\(u\)) varies logarithmically with height 0, and that (ii) the surface roughness forces the mean wind speed to be zero at the ground surface, the MOS theory states that the vertical profiles of both wind speed and temperature in the ASL follow a logarithmic form that depends on \(L\)[32]. The resulting vertical profiles of wind speed and temperature for \(L\ =\ -10^{100}\) m were used as the inlet boundary conditions. It is important to note that for a neutral condition, the temperature profile is invariant with height. _Other boundary conditions:_ A wall boundary condition was used for both, the ground and barrier boundaries. Following the \(y+\) metric, the simulation of wind flow over a flat surface required finite volumes of \(\sim\)1 cm near the ground surface. As described before, the height of the computational domain was selected as the minimum where vertical interaction (other than turbulences) is negligible. Then, following best CFD practices, the symmetry condition (zero gradients) was selected as the upper boundary condition. A uniform velocity inlet at the road was specified to physically represent that the incoming wind flow faces a perpendicular wind flow with a high pollutant concentration (the source of pollutants). For the outlet condition, a pressure outlet condition of 1 atm was defined, which is valid considering the small height of the domain and the invariant temperature profile used. An adiabatic condition was used for the ground boundary. _Turbulence model:_ Turbulence models for the ASL should account for both shear and buoyancy produced turbulence [36]. Best results in the use of CFD have been obtained in capturing the turbulence phenomena by solving these equations with a high time and space resolution. This approach, known as direct numerical simulation (DNS), is computationally expensive and therefore has not been used to systematically study pollutant dispersion [37]. As an alternative, models that describe average-flow quantities, such as the Reynolds-Average Navier Stokes (RANS) approach, have been considered instead. In particular, the \(k\)-\(\varepsilon\) turbulence model has been widely used for modeling the ASL [38]. The \(k\)-\(\varepsilon\) model adds an equation for the turbulent kinetic energy (\(k\)) and an equation for the turbulent energy dissipation (\(\varepsilon\)). Both equations ensure the closure of the system of governing equations describing the atmospheric dynamics on the ASL. Most of the work dedicated to simulating microscale pollutant dispersion uses this model while also assuming isotropic turbulence, which are features of a neutral atmosphere [14; 22; 39]. [PERSON] and [PERSON] [36] measured \(k\) and \(\varepsilon\) at different heights for several atmospheric stability conditions on flat terrain without obstacles to the wind flow. They proceeded to simulate the wind flow via CFD, reproducing those experimental results by fixing average values for \(k\) and \(\varepsilon\) at the inlet boundary conditions (\(k\) = 1.2699 m\({}^{2}\)/s\({}^{2}\) and \(\varepsilon\) = 0.000544 m\({}^{2}\)/s\({}^{3}\) for the neutral stability) and specifying values for the coefficients found in the \(k\)-\(\varepsilon\) formulation that were dependent on both height \(z\) and Monin-Obukhov length \(L\)[38].