###### Abstract
[12] investigated the potential of the wall modelled large-eddy (WMLES) in simulating unsteady flow features over a realistic car model. WMLES proved to be able to predict unsteady flow features, but a detailed analyses on the vortical structures around the car is not provided. Recently, [PERSON] et al. [13] adopted a LES (Large Eddy Simulation) approach to predict the turbulent flow around the fastback geometry, providing a detailed and systematic analysis of the unsteady flow features. In the present study an efficient order-adaptive discontinuous Galerkin (DG) method [14] for incompressible flows is used to perform the implicit LES [15] around the DrivAer fastback model. High-order DG finite elements methods proved to be very well suited [16; 17; 18; 19; 20; 21; 22; 23; 24; 25] for ILES, where the unfiltered incompressible Navier-Stokes equations are solved, and the numerical dissipation introduced by the discretizaton itself, e.g., by numerical fluxes and the viscous stabilisation, plays the role of an explicit subgrid-scale (SGS) model that dissipates the smallest scale eddies. The DG solver is characterised by (_i_) the local adaptation of the polynomial degree of the solution over the mesh, (_ii_) a multi-constraint domain decomposition algorithm to ensure the computational balance over the processes, (_iii_) the adaptation of the degree of exactness for quadrature rules and (_iv_) a \(p\)-MG multilevel preconditioner for the linear solver on the implicit time integration. Moreover, the non-trivial task of the high-order mesh generation is strongly simplified with the \(p\)-adaptive algorithm, as the local mesh refinements related to a priori knowledge of the flow features are avoided. In particular, the aim of this work is to assess the feasibility of the ILES approach in the accurate simulation of the high-Reynolds turbulent flow around a simplified car model with a moderate number of degrees of freedom (DoFs). Two different models have been considered: (_i_) a simplified DrivAer fastback model, where the handles, the rear-view mirrors and the wheels have been removed, the underbody has been smoothed, and the front radiator grid has been closed; (_ii_) the DrivAer fastback model, where the handles and the rear-view mirrors were removed, and a smoothed underbody and a closed front radiator grids were considered to reduce the complexity of the \"original\" DrivAer model. The first model has been used to investigate the effect of the Reynolds number and of the absence of the wheels on the aerodynamic performance. Two different Reynolds number have been considered, \(Re_{L}=2.435\times 10^{6}\) and \(Re_{L}=4.87\times 10^{6}\), based on the model length \(L\) and the freestream conditions (\(u_{\infty}=8\) m/s and \(u_{\infty}=16\) m/s, respectively). The second model has been used to assess the predicting capability of the proposed ILES approach with a moderate number of DoFs, comparing the results with experimental data and numerical results available in literature. The paper is organised as follows. The present computational methodology is presented in Sections 2.1 and 2.2, while Section 2.3 gives some information about the mesh generation process. Sections 3.1 and 3.2 report the results for the two considered DrivAer geometries. Finally, the conclusions are given in Section 4.