# Design of Road-Side Barriers to Mitigate Air Pollution near Roads
## 2 Methodology
### Simulation of the Dispersion Phenomena (the NR-CFD Model)
The convergence criteria for all the equation were set to 1 \(\times\) 10\({}^{-6}\) and a maximum of 5000 iterations were run for the finest mesh. A hybrid initialization scheme was used for all the cases that were run; this type of initialization is prefer since it allows a faster convergence of the numerical results. _Convergence and grid independence analysis:_ For the case of no-barrier presence, quad-type elements were used to discretize the general domain. Grid refinement was performed near the domain walls. The height of the first cell was 0.01 m, which is equivalent to a \(y+\) value of 150. This value satisfies the log-law of modeling that recommends \(30<y+<1000\)[42]. The overset meshing method was used aiming to mesh the different barrier geometries considered. This technique consists of partitioning and meshing certain regions of a given domain separately and then overlapping them so that their solution data can be interpolated [43]. This technique reduces the computational costs of meshing a domain each time a specific zone or a geometrical detail of said domain is changed. Thus, the general domain shown in Figure 1 was divided, partitioning the area near to the barrier and establishing its limits as an overset boundary condition while leaving the rest of the region as the \"background mesh\" with the previously described parameters. This allowed to individually mesh only the near-barrier region of the domain, which was considered of size 6 \(h\)\(\times\) 7 \(h\)[26], where mesh cells that could change as an effect of changing the geometry of the barrier and or moving it across the domain are affected (Figure 2). The boundary conditions of the overset partition were established as Overset in the CFD solver, ensuringthe interpolation of information from the cells in the overlapping areas. The height of the first cell was 0.001 m for the overset barriers, which is equivalent to a \(y+\) value of 30 [42]. Figure 2a shows the complete mesh in which the size of the elements cannot be seen due to the size of the scale. The background mesh is in green while the near-barrier mesh is in blue and the overset boundary is the black solid line. Figure 2b shows a view close to the barrier in which the size of the elements is now observable, especially of the background mesh. The overlap of the two meshes is also shown. Finally, Figure 2c shows a close up view of the mesh at the tip of the barrier in which is clear the refinement close to the barrier in order to correctly resolve the turbulent boundary layer. It can be also observed that the cells mainly grow in the direction normal to the wall. A mesh of 0.421 million of elements was used for the simulations, including the overset and the refinements. The background mesh has 0.343 million of elements while the near-barrier mesh has approximately 0.078 million of elements. This mesh was selected after a grid independence analysis from using five different meshes with total number of elements ranging from 0.02 to 1.0 million elements, using as criteria pollutant downwind concentration and vertical wind speed profile. On a server with 16 parallel processors, solution times ranged from 30 min to 4 h for the finest mesh.