The Ahmed model is a standard bluff body used to study the flow behavior around an automobile. An important issue when investigating turbulent flow fields is the large computational load driven by accurate prediction approaches, such as the large eddy simulation model. In this paper, we present a powerful domain decomposition method-based parallel solver to efficiently utilize existing supercomputer resources. The 3D unsteady incompressible Navier–Stokes equations with a subgrid-scale (SGS) fluid model are discretized on a pure unstructured tetrahedral grid by a stable $P_1−P_1$ finite element method in space, while an implicit second-order backward differentiation formula is employed for the time discretization. We then solve the nonlinear algebraic system by means of the Newton–Krylov–Schwarz method by imposing a restricted additive Schwarz (RAS) right preconditioner for the parallel setting. We validate the proposed method toward the comparison of the flow field, including the velocity profiles and flow structures, with experimental investigations, and we show the parallel efficiency and scalability of the solver with up to 8192 processors.