## 2 Research Method
### Numerical Analysis Techniques and Conditions  
#### 2.2.1 Numerical Analysis  
A powerful analysis program \"SolidWorks\" was used to calculate air resistance by employing computerized fluid dynamics (CFD) simulations. The software was used to present the local characteristics. Moreover, as an analysis based on several variables is required, a simplified SolidWorks Flow Simulation model was used to reduce the computation time. The numerical model considered is based on the resolution of the Navier-Stokes equations in conjunction with the standard k-\(\epsilon\) turbulence model [11]. To determine the convergence of the flow analysis, calculations were repeated until the residual fraction of each variable was less than \(10^{-4}\%\). For higher-fidelity results, more advanced modeling techniques and turbulence models need to be used. These equations were solved via a finite volume discretization method. A constant speed distribution corresponding to the vehicle speed for each model was established under the entrance conditions, and different types of vehicle models with lower speeds were considered for driving in platooning. The exit condition was set the atmospheric pressure. To consider the effectiveness of the moving ground, a parallel velocity component was applied to the ground, and sufficient computational area was provided to the rear of the vehicle model to ensure adequate flow-field development within the test domain. Symmetric conditions were applied to the other walls. In addition, to simplify the analytical boundary conditions, the direction of initial wind remained unchanged; the flow fields of air were defined as follows:  
- Turbulent flow;  
- Incompressible flow;  
- 3-D Steady flow;  
- Isothermal flow.  
The driving speed of the vehicle model was set to 110 km/h or less, and the 3D Navier-Stokes control equation was solved for the analyzing the incompressible turbulent flow field within the control volume, assuming an incompressible flow. The standard k-\(\epsilon\) model was used for the turbulence analysis.  
\(<\)Governing Equations\(>\)  
Continuity equation  
\[\frac{\partial U_{i}}{\partial x_{i}}+\frac{\partial U_{j}}{\partial y_{j}}+ \frac{\partial U_{k}}{\partial z_{k}}=0 \tag{1}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Small SUV** & **Medium SUV [10]** & **PBV** & **Truck [10]** \\ \hline \hline \multicolumn{4}{c}{**Side-sectional view**} \\ \hline \hline \multicolumn{4}{c}{(a\({}^{\prime}\))} & \multicolumn{1}{c}{(b\({}^{\prime}\))} & \multicolumn{1}{c}{(c\({}^{\prime}\))} & \multicolumn{1}{c}{(d\({}^{\prime}\))} \\ \hline \hline
**Full Length: 3900 mm** & Full Length: 4557 mm & Full Length: 4683 mm & Full Length: 8830 mm \\ \hline
**Full Width: 1600 mm** & Full Width: 1900 mm & Full Width: 2300 mm & Full Width: 2490 mm \\ \hline
**Full Height: 1200 mm** & Full Height: 1700 mm & Full Height: 2320 mm & Full Height: 3370 mm \\ \hline
**Projected area: 1,901,000 mm\({}^{2}\)** & Projected area: 3,211,000 mm\({}^{2}\) & Projected area: 4,845,000 mm\({}^{2}\) & Projected area: 8,383,000 mm\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Specifications of the vehicle models used in this study.  
Momentum equation  
\[\frac{\partial U_{i}}{\partial t}+\frac{\partial}{\partial x_{j}}(U_{i}U_{j})=- \frac{1}{\rho}\frac{\partial P}{\partial x_{i}}+\frac{\partial}{\partial x_{j}} \Bigg{[}v\left(\frac{\partial U_{i}}{\partial x_{j}}+\frac{\partial U_{j}}{ \partial x_{i}}\right)-\overline{u_{i}u_{j}}\Bigg{]}-g_{i} \tag{2}\]  
Turbulent kinetic energy  
\[\frac{\partial}{\partial x_{i}}(U_{j}k)=\frac{\partial}{x_{i}}\bigg{[}\left(v +\frac{v_{t}}{\sigma_{k}}\right)\frac{\partial k}{\partial x_{i}}\bigg{]}+G-\epsilon \tag{3}\]