## 3 Results
### Flow around the DrivAer Model  
The turbulent flow around the DrivAer model is presented in this section for a Reynolds number \(Re_{L}=4.87\times 10^{6}\)[6; 11; 13; 41], based on the model length \(L=4.6\) m  
Figure 11: Simplified DrivAer model—Time-averaged pressure coefficient distribution on the symmetry plane for the body (**left**) and underbody (**right**) of the car, high-Reynolds number. Figure 12: Simplified DrivAer model—Time-averaged pressure coefficient distribution on the plane \(z=0.06\), high-Reynolds number  
and the freestream conditions. The rear mirrors are not considered and the underbody is smooth. The domain is a box of dimension \(10.87L\times 2.17L\times 2.43L\), where \(x\) is the streamwise direction, \(y\) the spanwise direction and \(z\) the direction normal to the ground. The inlet section is at \(2.67L\) from the car. A no-slip boundary condition is applied to the model, the wheels rotate with a prescribed angular velocity and the ground moves at the same velocity of the free stream. Computations with a symmetric half-body configuration are performed, and the symmetry condition is prescribed to the \(y=0\) plane. All the simulations are performed with a very coarse mesh, consisting of 406,304 cubic-edges hexahedral elements. Figures 4 and 5 show the computational domain and some details near the rear end and the front wheel. Notice the small amount of elements used to discretize the car, especially if compared to the references. In fact, [PERSON] et al. [13] carried out LES on the full and symmetric half-body geometry with meshes of 24, 80 and \(130\times 10^{6}\) elements for the full geometry and \(65\times 10^{6}\) elements for the symmetric half-body geometry. [PERSON] et al. [11] and [PERSON] et al. [41] carried out Reynolds-averaged Navier-Stokes (RANS) simulations, using \(k\)-\(\omega\) SST and \(k\)-\(\omega\) SAS SST models on a mesh made of \(19.4\times 10^{6}\) and \(110\times 10^{6}\) elements, respectively. [PERSON] et al. [12] carried out WMLES on the full geometry with meshes of 6.5, 53 and \(79\times 10^{6}\) elements. [PERSON] et al. [6] performed RANS simulations with meshes of 18, 37 and \(80\times 10^{6}\) elements, while meshes of 80 and \(100\times 10^{6}\) elements were used for DES-type simulations. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Method** & \(\mathbf{c_{D}}\) & \(\mathbf{c_{L}}\) \\ \hline \multirow{2}{*}{[PERSON] et al. [11]} & RANS \(k\)-\(\omega\) SST & \(0.124\) & - \\  & Experiment & \(0.125\) & - \\ \hline \(DG-\mathbb{P}^{n}\) (low Re) & ILES & \(0.1561\) & \(-0.1352\) \\ \hline \(DG-\mathbb{P}^{n}\) (high Re) & ILES & \(0.1605\) & \(-0.0753\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simplified DrivAer model—Predicted drag, \(c_{D}\), and downforce, \(c_{L}\), coefficients for low- and high-Reynolds number case. Results are compared with reference data. Figure 13: Simplified DrivAer model—Time-averaged pressure contours (**top-left**) and time-averaged pressure coefficient distribution on the windscreen (**top-right**), the front side window (**bottom-left**) and the back window (**bottom-right**), low-Reynolds number. Averaging time is \(\sim T_{C}\), where \(T_{C}\) is a convective time computed according to the freestream velocity and the length of the model. The time step has been set to \(\Delta t=fT_{C}\), where \(f=6\times 10^{-4}\). The maximum polynomial degree of the solution is \(\mathbb{P}^{2}\). Figure 14 shows the polynomial degree distribution \(\mathbb{P}^{n}\) of the solution on the surface of the car model. The front part of the model, the windshield, the A-pillar, the wheels and the rear part of the model require higher order elements. As expected, the comparison of the polynomial degree distribution between the present and the simplified (see Figure 8) DrivAer configuration shows that rotating wheels require high-order elements. The DoFs per equation are 2,112,776.