## 2 Modeling and Numerical Methods
### Reference Model and Computational Method  
The 1:40 geometrical scale model of the flat-roof low-rise building [19] is employed as the reference model with height \(h\) of 200.0 mm, as shown in Figure 2a. The building model has a rectangular cross-section with a length \(l\) of 0.8875 \(h\) and a width \(w\) of 0.59 \(h\). Figure 2b shows the cross-sectional scheme of three actuator configurations at the roof centerline, which are named cases A, B, and C. The wall-jet direction for each case is also shown in this figure. Each copper electrode has a length of 0.85 \(h\), a width of 0.02 \(h\), and a thickness of 0.0005 \(h\). Since [PERSON] [21] pointed out that the effect of electrodes on the flow structure can be ignored, the present simulation does not consider this effect. The numerical simulations in absence and presence of the plasma actuation are conducted on a 3-dimensional computational grid, as shown in Figure 3a,b. The computational domain size is \(18\,h\times 8\,h\times 4\,h\) along the \(x\)-, \(y\)-, and \(z\)-axes, and the building model is mounted on the ground. The resulting blockage ratio is 2.77%, which does not exceed the 3% threshold value [22]. Since the size is very long in the \(x\)-axis direction, this domain is divided into 2 parts, named Zone-1 and Zone-2. In order to reduce the computation cost and capture the flow physics, the C-typed grid topology method is employed in Zone-1 to obtain hexagonal grids with a normalized minimal grid size of \(\Delta\beta\)/\(h\) = 0.0003 (\(\Delta z\) = 0.00006 m) on the roof surface, as shown in Figure 3c,d. This size is close to the suggested value of 0.00025 m from the large-eddy simulation (LES) of a cylinder with a plasma actuator [15]. The minimal grid size is raised by keeping a rate of 1.10 away from the building body surface. Zone-2 also adopts the structured grids, as shown in Figure 3b. The boundary conditions of the computational domain are shown in Figure 3a. The detailed definition method of the velocity inlet boundary can be found in [23]. The building and ground surfaces are also set as the no-slip stationary wall. When the wind speeds \(U_{\infty}\) are 4, 7, and 10 m/s (i.e., Reynolds numbers \(Re\) are \(5.3\times 10^{4}\), \(9.3\times 10^{4}\), and \(1.3\times 10^{5}\), respectively, based on the building height \(h\)), the dimensionless vertical profiles of the streamwise mean velocity and turbulence intensity at the inlet boundary from the present simulation are compared with the experimental data [19], as shown in Figure 4. In these figures, \(V_{z}\) and \(I_{z}\) are the mean velocity and turbulence intensity, respectively, at a specific height of \(z\), and \(I_{2h}\) means the turbulence intensity at the double building height. These figures show that numerical results are congruent with experimental data. Figure 2: The building model and actuator configurations [19]: (**a**) reference model; (**b**) cross-sectional scheme of three actuator configurations. Figure 3: Computational domain and grid arrangement: (**a**) side view and top view; (**b**) grids for each zone; (**c**) grids on the roof surface, where the normalized minimal grid size \(\Delta\)z/h is 0.0003; (**d**) grids on the windward wall, where the normalized minimal grid size \(\Delta\)z/h is 0.00037. The numerical simulations are performed using the software Fluent. For the steady simulations, [PERSON] et al. [24] studied the sensitivity of building wind pressures to different turbulence models and pointed out that the re-normalization group (RNG) k-epsilon model can obtain accurate results. This model with the non-equilibrium wall function is employed by the present study to obtain the initial flow field used for the transient simulation. For the unsteady simulations, the LES and detached eddy simulation (DES) turbulence models can provide more accurate predictions for the mean velocity fields around the building [23].