## 3 Verification and Validation  
The drag and lift coefficients, \(C_{d}\) and \(C_{l}\), are respectively defined as:  
\[C_{d}=F_{d}/0.5\rho V_{h}^{2}\mathit{lw} \tag{5}\]  
\[C_{l}=F_{l}/0.5\rho V_{h}^{2}\mathit{lw} \tag{6}\]  
where \(F_{d}\) and \(F_{l}\) are wind loads acting on the whole building model along \(x\)- and \(z\)-directions, respectively (the directions are presented in Figure 2; \(V_{h}\) means the free stream velocity at the building height \(h\)). The time history of a physical quantity can be expressed as a non-dimensional coefficient \(C_{XXX}(t_{i})\), where \(t_{i}\) is the time instance and \(i\) indicates the sample sequence number (\(i\) = 1, 2,..., \(N\)). The mean and root-mean-square (RMS) values of this coefficient, \(C_{XXX,mean}\) and \(C_{XXX,rms}\), are respectively calculated as follows:  
\[C_{XXX,mean}=\sum\
olimits_{i=1}^{N}C_{XXX}(t_{i})/N \tag{7}\]  
\[C_{XXX,rms}=\sqrt{\sum\
olimits_{i=1}^{N}\left(C_{XXX}(t_{i})-C_{XXX,mean} \right)^{2}/\left(N-1\right)} \tag{8}\]  
where \(C_{XXX}\) can be \(C_{d}\) or \(C_{l}\). The mean and RMS pressure coefficients, \(C_{p,mean}\) and \(C_{p,rms}\), can also be calculated by the normalized pressure coefficient \(C_{p}\) (= (\(p(t)-p_{0}\))/0.5\(\rho V_{h}\)2) on the building surface, where \(p(t)\) is the pressure of the given location at time \(t\) and \(p_{0}\) is the reference static pressure of the free stream. The RMS pressure coefficient is also called the fluctuating pressure coefficient. To quantitatively describe the influence of plasma actuators on wind loads, the change rates of mean and fluctuating pressure coefficients, \(\eta_{p,mean}\) and \(\eta_{p,rms}\), are considered as the following equations:  
\[\eta_{p,mean}=\left\langle\left|C_{p,mean}^{*}\right|-\left|C_{p,mean}^{*} \right|\right\rangle/\left|C_{p,mean}^{*}\right| \tag{9}\]  
\[\eta_{p,rms}=\left(C_{p,rms}^{*}-C_{p,rms}^{*}\right)/C_{p,rms}^{*} \tag{10}\]  
where \(C_{p,mean}^{{}^{\prime}}\) and \(C_{p,mean}^{*}\) are the mean pressure coefficients without and with the plasma actuation, respectively; \(C_{p,rms}^{{}^{\prime}}\) and \(C_{p,rms}^{*}\) are the fluctuating pressure coefficient without and with the plasma actuation, respectively. If \(\eta_{p,mean}<0\), it means that the absolute value of the mean pressure coefficient decreases after the actuators are ignited; otherwise, the absolute value of the mean pressure coefficient increases after the actuators are ignited. If \(\eta_{p,rms}<0\), it means that the fluctuating pressure coefficient decreases with the plasma actuation; otherwise, the fluctuating pressure coefficient increases with the plasma actuation. The Strouhal number \(S_{t}\) is defined as:  
\[S_{t}=f_{s}h/V_{h} \tag{11}\]  
where \(f_{s}\) means the vortex shedding frequency obtained from the spectral analysis for the time signal of the drag coefficient, and \(V_{h}\) represents the free stream velocity at the building height \(h\). To check the mesh sensitivity, a comparative study is conducted by varying the grid numbers without the plasma actuation, and the detail information is shown in Table 1. In this table, \(\Delta z\)/\(h\) is the dimensionless first mesh size adjacent to the roof surface, \(\Delta y\)/\(h\) is the dimensionless mesh size close to the building surface in the \(y\)-axis direction. It can be seen from the table that the deviations are very small among the results of these grids. Moreover, the mesh number of Grid-2 is close to the recommended value of 4.8 million from the flow simulation around a rectangular building [23]. Therefore, Grid-2 is adopted by the later study. Concerning Grid-2, the normalized wall distance \(y\)+ of the first near-wall meshes has a maximum of about 4 at the corners of the windward wall and is less than 1 (generally around 0.4) for the remaining building surfaces. The comparative studies are performed based on case A without the plasma actuation to investigate the sensitivity of the roof pressure to subgrid-scale models and discretization schemes.