This paper focuses on the numerical simulations of flow around a realistic generic car model called the DrivAer body. This new open-source model is based on the geometries of two medium sized cars, the Audi A4 and the BMW 3 series, and possesses more representative car features as the well-known generic Ahmed body. In this paper, only the fastback geometry is investigated. The flow solver used is ISIS-CFD developed by CNRS and Ecole Centrale de Nantes. This solver is based on a finite-volume method, and two turbulence modelizations are used: the Explicit Algebraic Reynolds Stress Model (EARSM) and a Detached Eddy Simulation (DES). Two meshes are used. For one, the walls are described with a wall function and the mesh contains 19 million cells. This mesh is called “Mesh 1”. For the second mesh, a low-Reynolds number turbulence model for the walls is used. In this case, the mesh contains 39 million cells, and is called “Mesh 2”. For the simulation with the EARSM model, the drag coefficient is well predicted while the lift coefficient is over-predicted with however a value lower with the “Mesh 2”. With both meshes, an automatic grid refinement has been used. In this case, from the “Mesh 1”, the new mesh contains 25 million cells while from the the “Mesh 2”, the new mesh contains 45 million cells. With these new meshes, the drag coefficient is similar and the lift coefficient est lower than the values obtained with the initial meshes but the predicted values over-predict the experimental value. DES simulations have been performed with all meshes. The aerodynamic coefficients are similar and in good agreement with the experimental values, even for the lift coefficient.