*3.4. Validation of Numerical Model*

To ensure reliability, and that the model used numerical simulation and obtained a convergent and accurate solution within a reasonable calculation time, this paper considers different grid densities and time steps. Tables 2 and 3 list the results of different grid parameters and time steps, in which *CD* denotes the mean drag coefficient over the time domain, *CL* stands for the root mean square (RMS) of the lift coefficient, and *St* represents the Strouhal number.


**Table 2.** Verification of grid density independence (Re = 2.2 <sup>×</sup> 104).

**Table 3.** Validation of time-step independence (Re = 2.2 <sup>×</sup> <sup>10</sup>4).


As shown in Table 2, the results under the three different grid densities were similar. The scheme with medium grid resolution was adopted in this study so that a balance between computational efficiency and cost could be achieved.

Meanwhile, the transient numerical method was adopted and time-step independent verification was carried out to evaluate the uncertainty of the value. The independence of the time steps was verified by using different time step sizes of 0.0006 s~0.001 s/step for numerical simulation. According to the calculation results for different time steps, a small time step cannot improve the simulation accuracy but takes a long time. Therefore, the time step of 0.0008 s per step was selected. The calculated results of the square at Re = 2.2 × 104 were similar to the results presented by Cao [34] and Trias [35], indicating that the turbulence model adopted can obtain more reliable results.
