###### Abstract  
The turbulent flow over the DrivAer fastback model is here investigated with an order-adaptive discontinuous Galerkin (DG) method. The growing need of high-fidelity flow simulations for the accurate determination of problems, e.g., vehicle aerodynamics, promoted research on models and methods to improve the computational efficiency and to bring the practice of Scale Resolving Simulations (SRS), like the large-eddy simulation (LES), to an industrial level. An appealing choice for SRS is the Implicit LES (ILES) via a high-order DG method, where the favourable numerical dissipation of the space discretization scheme plays directly the role of a subgrid-scale model. Implicit time integration and the \(p\)-adaptive algorithm reduce the computational cost allowing a high-fidelity description of the physical phenomenon with very coarse mesh and moderate number of degrees of freedom. Two different models have been considered: (i) a simplified DrivAer fastback model, without the rear-view mirrors and the wheels, and a smooth underbody; (ii) the DrivAer fastback model, without rear-view mirrors and a smooth underbody. The predicted results have been compared with experimental data and CFD reference results, showing a good agreement. car aerodynamics; DrivAer model; discontinuous Galerkin; Implicit LES; order-adaptive method +
Footnote †: journal: Applied Sciences  
**Acticle**  
**11 October 2021 28 October 2 these limitations, more accurate and costly turbulence approaches can be used, such as hybrid RANS-LES [6] or LES [7] methods, whose widespread diffusion in industry has been fostered by the ever increasing computational resources. Realistic car models were not available for CFD simulations before 2012, and only simplified geometries such as the Ahmed [8] or the SAE [9] bodies could be used for validation and sensitivity studies. However, these models were often characterised by few aerodynamic features representative of a car. To fill the gap between a very simple bluff body and a fully detailed production car, TU Munich in collaboration with the Audi AG and the BMW Group designed and made public the so-called DrivAer car model [10]. The model is available with three different rear end configurations: fastback, estate back, and notchback. Each model is available with a smoothed and a detailed underbody, with/without the side mirrors and wheels. [PERSON] et al. [11] carried out for the first time simulations with \(k\)-\(\omega\) SST and \(k\)-\(\omega\) SAS SST turbulence models on the fastback geometry. These results predicted reasonably well the averaged flow field around the vehicle, while some limitations appear for the detached regions. These results strengthen the belief that Scale-Resolving Simulations (SRS) are needed to correctly describe unsteady flow phenomena around vehicles. [PERSON] et al. [4] in 2014 carried out RANS simulations with an anisotropic two-equation explicit algebraic Reynolds stress and DES models on the fastback geometry. DES guaranteed a higher accuracy than RANS simulations in the prediction of drag and lift coefficients and reproduced correctly the instantaneous vortical structures. [PERSON] et al. [6] compared different turbulence models for RANS simulation, e.g., \(k\)-\(\epsilon\), \(k\)-\(\omega\) SST, Spalart-Allmaras, B-EVM and EB-RSM, and DES-type models, on the fastback and estate geometry. RANS simulations were not able to correctly predict force coefficients and pressure distribution around the cars. In particular, DDES (delayed detached-eddy) and IDDES (improved delayed detached-eddy) were also considered to investigate in depth the prediction capability of the most representative hybrid methods. They showed clear advantages over RANS in the prediction of the force coefficients and unsteady flow features. However, some limitations are still evident to correctly capture the pressure distribution and vortical structures in the rear end of the car. In 2018 [PERSON] et al.