## 2 Numerical Methods
### Aerodynamics
\begin{array}{c}0\ for\ x<x_{0}-\frac{ \Delta x_{slope}}{2}\\ \mathrm{w}_{\mathrm{cw,max}}\frac{1}{2}\left(1-cos\left[\frac{x-\left(x_{0}- \frac{\Delta x_{slope}}{2}\right)}{\Delta x_{slope}}\pi\right]\right)\ for\ x_{0}-\frac{ \Delta x_{slope}}{2}\leq x\leq x_{0}+\frac{\Delta x_{slope}}{2}\\ \mathrm{w}_{\mathrm{cw,max}}\ for\ x_{0}+\frac{\Delta x_{slope}}{2}<x<x_{0}+ \Delta x_{cw}-\frac{\Delta x_{slope}}{2}\\ \mathrm{w}_{\mathrm{cw,max}}\frac{1}{2}\left(1-cos\left[\frac{x-\left(x_{0}+ \Delta x_{cw}+\frac{\Delta x_{slope}}{2}\right)}{\Delta x_{slope}}\pi\right] \right)\ for\ x_{0}+\Delta x_{cw}-\frac{\Delta x_{slope}}{2}\leq x\leq x_{0}+ \Delta x_{cw}+\frac{\Delta x_{slope}}{2}\\ 0\ for\ x>x_{0}+\Delta x_{cw}+\frac{\Delta x_{slope}}{2}\end{array} \right. \tag{8}\]  
In this instance, the crosswind's maximum velocity magnitude is indicated by \(\mathrm{w}_{\mathrm{cw,max}}\), the length of the transient inlet and exit sections of the crosswind are denoted by \(\Delta x_{slope}\), equivalent to 1.5 times the GTS's length. The symbol, \(x_{0}\), signifies the distance between the crosswind's starting location and the origin of the coordinate system, while \(\Delta x_{cw}\) represents the crosswind's length, set at five times the GTS's length. As illustrated in Figure 4a, utilizing a velocity inlet boundary condition on the right-hand side of the flow domain brought the crosswind into computation. Figure 4 provides the geometric details of the flow domain, the corresponding computational boundary conditions, and the mesh used in the aerodynamics simulation. The pressure outlet boundary condition was applied to the inlet, outlet, and left lateral surfaces, assuming atmospheric pressure on these boundary surfaces. No-slip boundary conditions were applied to the GTS surfaces and the flow domain's ground. In addition, the symmetry boundary condition was applied to the top surface of the flow domain. The velocity of the  
GTS was \(v_{x}=91.6\) m/s. Overset mesh was utilized to let the motion of the GTS in the computational domain. The flow had the Reynolds number of \(Re_{w}=2\times 10^{6}\), calculated using GTS width. Prior to being used in the vehicle dynamics calculations, the force and moment data from the aerodynamics simulation were scaled back. StarCCM+ version 13.02 [32], the commercial computational fluid dynamics (CFD) software, was utilized for mesh generation and the solution of the governing equations. As shown in Figure 4, the mesh structures comprised two regions: an overlap region and a background region. The sizes of the overlap region were 5.3 \(\times\) 2.6 \(\times\) 1 vehicle lengths, while the background mesh was 22.6 \(\times\) 4.9 \(\times\) 1.4 vehicle lengths. The mesh comprised unstructured hexahedral cells totalling approximately 22 million, with approximately 40% (9 million) specifically utilized in the vicinity of the vehicle model, i.e., the overlap region. Twenty prism layers with a total thickness in the wall-normal direction of 0.0141 m, stretching of 1.25 m, and length of 0.0044 m were applied in order to resolve the boundary layer around the GTS. The dimensionless wall distance, \(y^{+}\), was maintained at a value less than 15. In the current investigation, the GTS's drag coefficient, \(C_{D}\), in the absence of a cross was 0.251. This number was reasonably close to the numerical and experimental values  
Figure 4: (**a**) The computational flow domain in three dimensions and (**b**,**c**) view of the mesh structure surrounding the GTS and the overset mesh, respectively. Colours on the right lateral surface of the flow domain represent the profile of the velocity inlet; such as blue indicates zero velocity and red indicates the maximum velocity of 9 m/s. Figure 3: Velocity profile of the crosswind. reported in the literature. For instance, at \(Re_{w}\) = 1.6 \(\times\) 10\({}^{6}\), the \(C_{D}\) values found in the experimental investigations by [PERSON] et al. [28] and [PERSON] et al. [29] were 0.247 and 0.249, respectively.