## 2 Computational Setup  
### Computational Mesh  
The geometry and dimension of the square-back [PERSON] model are determined from the work of [PERSON] et al. [2], where L = 1044 mm, H = 288 mm and W = 389 mm are the length, height, and width of the model, respectively (Figure 1).  
The computational domain is a rectangular box with dimensions of the length, height, and width of 26H, 5H and 3H, respectively. The domain extends to seven body heights upstream of the front surface of the model and eighteen body heights behind the rear surface of the model as shown in Figure 2. Such domain size ensures that the outflow does not interact and affect the development of the near-wake region.  
The flow is displaced from right to left, and a uniform velocity inlet boundary condition U\({}_{0}\) = 30 m/s is applied at the right-hand surface of the computational domain, resulting in a Reynolds number Re of 2.1 \(\times\) 10\({}^{6}\) associated with the model length. At the left-hand surface of the computational domain, a pressure outlet boundary condition is used. The XZ plane (y = 0) is known as the ground of the computational domain, and a no-slip boundary condition is applied. A similar boundary condition is also specified for the square-back Ahmed model. The XY plane (z = 0) is used as a symmetry plane, and a symmetry condition is imposed on it. Finally, a slip boundary condition is applied to the side walls of the computational domain.  
Figure 1: The square-back Ahmed model and dimensions in mm.  
Figure 2: Computational domain and boundary conditions.  
In this study, the numerical simulation was performed using the ANSYS 2021 package [25]. A CAD model was designed with the Design Modeler module. A hexagonal mesh was then generated using ANSYS ICEM from imported CAD geometry. The multi-block technique manually divided the computational domain was into numerous block regions (Figure 3a). A mesh refinement was performed in the normal direction to the wall near the model and the near-wake region. In the actuated cases, more refinement was applied in the vicinity of the continuous slots at the rear surface of the body where the control devices are installed. These settings resulted in a hexa mesh with an O-grid structure around the model (Figure 3b). A first layer thickness of 0.03 mm was used on the model and obtained a y+ \(\leq\) 3 (Figure 4). A maximum size of 3 mm \(\times\) 3 mm is specified for surface mesh on the model. The mesh resolutions of \(\Delta\)x+ \(\leq\) 127 and \(\Delta\)z+ \(\leq\) 136 obtained. Such resolution is suitable to perform a Wall-Modeled LES.  
A mesh independence test with five mesh levels, i.e., 6.4, 12.6, 19.5, 25.3, and 28.6 million elements, was conducted to demonstrate numerical accuracy. Figure 5 shows that the drag coefficient in the unactuated case is irrelevant to the mesh size when the element number exceeds 19.5 million. In this case, the drag coefficient C\({}_{\text{DD}}\) = 0.249 is achieved with a deviation of 0.4% compared with the experimental result from the study of [PERSON] et al. [2] and the numerical result of Roum  
Figure 4: Y plus distribution on the square-back [PERSON] model.  
Figure 5: Mesh dependent test.  
Figure 3: Computational mesh. (**a**) Block structure; (**b**) mesh.