# Numerical Assessment of Side-Wind Effects on a Bus in Urban Conditions
## 2 Materials and Methods
### Numerical Setup  
The wall-adapting local eddy-viscosity-large-eddy simulation (WALE-LES) [21] method was chosen for the aerodynamic analysis. As to the low-velocity flow regime periodic alterations were expected, and an unsteady model was chosen. A further convergence analysis showed that the 0.05 s time step was enough to depict the unsteady deviations and converged results, yet coarse enough to considerably decrease the computational demand. The modelled duration was 80 s, during which at least 20 s was needed to initialise the flow, and 1 min of flow was examined; thus, the total number of time steps was 1600. The model was isothermal, and for velocity and pressure-based solver, the semi-implicit method for pressure-linked equations-consistent pressure-velocity coupling scheme was used. Furthermore, for pressure discretisation, PRESTOI was used, and for momentum and transient formulations, bounded central differencing was applied.  
In Figure 2, two flows are indicated with blue arrows. The main flow represents the flow around the body of the bus; thus, it is assumed that the velocity is the cruising speed (\(v_{c}\)) of the vehicle. If the wind comes in front of the bus, the velocity of the wind (\(v_{w}\)) should be added to \(v_{c}\) and subtracted, when it comes from behind the vehicle. The baseline cruising speed was attained from the bus driving cycle for Debrecen [17; 18]. In the simulation, this value was rounded up to 20 km/h. While the mentioned value describes the nominal operation scenario, 10 km/h and 15 km/h cruising speeds were also assessed in the drag loss evaluation. Perpendicular to the main flow, side wind was also added to the model. This represents the most extreme condition, i.e., when the load on the vehicle is the most asymmetrical. Based on meteorological datasets [20], in the Debrecen city region, the most  
Figure 4: Results of mesh sensitivity analysis.  
Figure 3: Vertical cross-section view of mesh2.  
common wind speed (\(v_{w}\)) is 2 m/s; to investigate the side-wind effects, 0 m/s, 1.5 m/s, and 1 m/s scenarios were also modelled. Furthermore, in Figure 2, the blue areas represent the velocity inlet boundaries, while the yellow ones the pressure outlet boundaries.  
The ground and bus surfaces were no-slip walls, and to obtain a more realistic result, the ground and wheels were moving. The ground and shroud of the tyre had a wall velocity of the cruising speed. For the rim rotation, angular velocity was added, which was calculated from the cruising speed and the radius from the centre of the wheel. Since the surface velocities were corresponding to the cruising speed, it limited the research by assuming that the wind was always perpendicular to the bus.  
In this study, two types of simulations were used; a symmetric one which is a classical wind tunnel simulation, where the main flow exerted force on the body, and an asymmetric one in which side wind was also added to the model. Symmetric scenarios were created to examine the differences between the 0 m/s inlet velocity and the symmetric boundary conditions. Thus, in the symmetric scenarios, the sides were set to symmetric (zero pressure inlet) conditions. In total, three symmetric and ten asymmetric simulations were carried out. The boundary condition settings are listed in Table 2.