## 3 Results
### Flow around a Simplified DrivAer Model  
The simplified DrivAer model is considered to estimate the effect of the Reynolds number and of the absence of the wheels on the aerodynamics performance. Two different Reynolds number have been considered, \(Re_{L}=4.87\times 10^{6}\)[6; 11; 13; 41] (high-Reynolds number case) and \(Re_{L}=2.435\times 10^{6}\) (low-Reynolds number case), based on the model length \(L=4.6\) m and the freestream conditions (\(u_{\infty}=8\) m/s and \(u_{\infty}=16\) m/s for the lower and higher Reynolds number, respectively). The wheelhouses are closed to compare the predicted results with the complete model investigated in Section 3.2 and the data available in literature. Experimental data [11] are available only for \(Re_{L}=4.87\times 10^{6}\) with a freestream turbulence intensity \(Tu_{\infty}<0.005\). The simulations presented in the following have been performed considering a laminar inlet. 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 conditions is applied to the model, while the ground moves at the same velocity as the free stream. According to [13], a symmetric half-body configuration has been considered for the simulations, and the symmetry condition is prescribed on the \(y=0\) symmetry plane. All the simulations are performed with a very coarse mesh, consisting of 113,780 cubic-edges hexahedral elements. Figures 6 and 7 show the mesh with details near the side pillars and the rear end of the model. The averaging time is \(\sim T_{C}\) for the low-Reynolds number case and \(\sim 3.2T_{C}\) for the high-Reynolds number case, where \(T_{C}\) is a convective time computed according to the freestream velocity and the length of the model. The time step is set equal to \(\Delta t=fT_{C}\), where \(f=1\times 10^{-3}\). The maximum polynomial degree of the solution is \(\mathbb{P}^{2}\). Figure 8 shows the polynomial degree distribution \(\mathbb{P}^{n}\) of the solution, where the final number of DoFs per equation is 591,656 and 601,544 for the low- and high-Reynolds number case, respectively. The front part of the model, the cowl top, the windshield, the A-pillar and the rear part of the model are the regions with higher order elements. Figure 8 shows only the order distribution on the model surface, but high order elements are present also in the wake region. The polynomial degree distribution of the solution after the adaptation process is very similar between the low- and high-Reynolds number cases. Figure 9 shows the pressure coefficient, \(c_{P}\), distribution on the symmetry plane for the body (left) and underbody (right) of the car for the low Reynolds number case. The predicted results are in good agreement with the experimental results [11] and the LES results [13] (all references are for the \(Re_{L}=4.87\times 10^{6}\) and full model case). After the stagnation point on the front part of the model, flow accelerates and the pressure decreases. The minimum value is lower in the simulation. A first separation appears at the junction between the bomet and the windshield (\(x/L\sim 0.23\)), while a second one appears at the cowl of the windshield (\(x/L\sim 0.3\)). The pressure decreases as the flow accelerates over the windshield. The flow passes on the roof, and the pressure slightly increases, while in the experiment it is almost constant. The different behaviour of the \(c_{P}\) on the roof could be ascribed to the support that holds the model in the wind tunnel during the measurements. The pressure rises more steeply on the rear window. The rear part of the model, after the end of the rear window, shows widespread results. However, high-fidelity simulations, i.e., reference LES and the proposed ILES simulations, share a similar trend. On the underbody (see left side of Figure 9) the flow separates after the front grid of the radiator and reattaches near the front wheels.