## 2 Numerical Setup  
The simulations performed in this study were carried out using a commercial finite volume solver computational fluid dynamics (CFD) package, STAR-CCM+ version 20.2.,where a full-scale square-back [PERSON] body model was placed in a computational domain with dimensions of 30 \(L\times\) 30 \(W\times\) 30 \(H\), where \(L\), \(W\), and \(H\) denote the length, width, and height of the [PERSON] body, respectively. The dimensions of the virtual wind tunnel resulted in a blockage ratio of 0.1% with respect to the frontal area of the geometry. The body was positioned 10\(L\) downstream of the inlet plane. The freestream velocity at the inlet was 40 m/s, corresponding to a Reynolds number based on the [PERSON] body height, \(Re_{H}\) of \(7.7\times 10^{5}\). A velocity of 40 m/s was chosen as the free-stream velocity because the flow becomes Reynold-independent at this speed [35]. The turbulence intensity and length scale at inlet boundary conditions were 0.25% and 10 mm, respectively. The pressure outlet condition was imposed as the boundary condition at the outlet. The top and side planes were set to zero-gradient (symmetry) conditions. A no-slip moving ground plane is defined, with the tangential velocity at the ground surface corresponding to the freestream velocity. The computational domain was discretized using an unstructured hexahedral cell mesh created by the \"trimmed cell\" mesher option of STAR-CCM+. The \"trimmed cell\" algorithm generates cells that are multiples of 2\(n\), either greater or smaller than the selected base size; hence, it enables us to refine the wake region and to better capture the unsteadiness and turbulent characteristics of flow caused by boundary layer separation. A base size of 4 mm was used for both the geometry surface and volume mesh around the vehicle body and underbody; however, a wake region with a size of 2 mm was generated in order to resolve the flow field in the wake region. The 28-prism layer cells with an overall thickness of 10 mm and a first layer height of 0.005 mm were used along the vehicle surface to properly compute the high gradient boundary layer and achieve a wall-\(y^{+}\) of less than 99% for most of the cells. Note that \(y^{+}\equiv yu_{\tau}/v\), where \(v\) denotes the fluid kinematic viscosity; \(\tau_{w}\) and \(\rho\) represent the wall shear stress and fluid density, respectively, and the friction velocity is denoted by \(u_{\tau}\equiv\sqrt{\tau_{w}/\rho}\). This setting resulted in a total cell count of 27 million cells for the volume mesh. [PERSON] et al. [17] recommended using data from particle image velocimetry (PIV) and direct numerical simulation (DNS) as inputs for DMD analyses, due to the capabilities of these approaches in capturing the dynamics of fluid flow fields. However, in most real-world automotive flow problems, these methods are impractical. Specifically, in computational fluid dynamics (CFD), coarse-grained simulations that rely on turbulence modeling approaches are often the only viable options. [PERSON] et al. [36] investigated the potential of DES methods to capture the flow field properly for POD and DMD analyses and concluded that DES data can be used as input for both POD and DMD algorithms. Therefore, in this paper, we used the improved delayed detached eddy simulation (IDDES) [37] methodology. It takes advantage of the less expensive shear stress transport (SST) \(k-\omega\)[38] unsteady Reynolds-averaged Navier-Stokes (RANS) turbulence model in the boundary layers and uses LES in the wake region. In their study on ground vehicle platooning involving two Ahmed bodies, [PERSON] et al. [39] demonstrated that IDDES is an effective methodology for investigating fluid flow problems characterized by complex aerodynamic interactions, including flow over an isolated Ahmed body. For a more in-depth discussion on the suitability of IDDES for CFD simulations of the Ahmed body, readers are directed to the works of [PERSON] et al. [40], [PERSON] et al. [41]. Furthermore, see [PERSON] et al. [42] and [PERSON] et al.