## 4 Partitioned Strong Coupling Formulation
(\(S_{n}=\frac{2d_{w}}{I_{w}}\), and \(d_{w}\) and \(I_{w}\) are the diameter and length of the mesh bar [44]). Figure 2: A physical model of the net panel and its geometrical description. ### Numerical Verification

To verify the present numerical method, the drag coefficients of the present numerical simulations are compared with analytical models that consider the solidity ratio \(S_{n}\), the attack angle \(\alpha\), and the Reynolds number \(Re\). Since this paper studies flexible net panels, the net panel's attack angle should be considered. Aside from the angle of attack, the effects of the solidity ratio and the Reynolds number are too profound to be negligible. Two analytical models used for estimating the drag coefficients of flexible net panels are illustrated in Table 2.

A seventh-order polynomial is employed to approximate the drag coefficient of a circular cylinder (i.e., single net twine) at \(10^{3/2}\leq Re\leq 10^{4}\), as can be seen in [PERSON] and Faltinsen [19]. This formula is valid for a knodless fabric net model with \(S_{n}\leq 0.5\) and an angle of attack in the range of \(\pi/4\leq\alpha\leq\pi/2\). The corrected towing velocity of the net twines, which considers relative motion, gives more accurate results. Figure 4 exhibits the dependence of the drag coefficients of the flexible net panels on the Reynolds number. The drag coefficients of the present numerical simulations and the analytical model predictions are illustrated in Table 3.

The overall trends of the drag coefficients in Figure 4 decrease as the Reynolds number increases. When \(Sn=0.16\), the present numerical simulations overestimate the drag coefficients comparing with those of [PERSON] et al. [47]. The present numerical simulations underestimate the drag coefficients compared to analytical predictions by [PERSON] and [PERSON] [19]. When \(Sn=0.33\) and the Reynolds number is less than 600, the present numerical simulations slightly overestimate the drag coefficient when compared with those of the analytical predictions. However, when the Reynolds number is over 600, the present numerical simulations underestimate the drag coefficients compared to the analytical predictions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Researchers** & **Empirical Formulae** \\ \hline [PERSON] et al. [47] & \(C_{D}=0.04+\left(-0.04+S_{n}-1.24S_{n}{}^{2}+13.7S_{n}{}^{3}\right)\sin\alpha\) \\ [PERSON] and [PERSON] [19] & \(C_{D}=C_{D}^{\omega\beta}\frac{S_{n}(2-S_{n})}{2(1-S_{n})^{2}}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Analytical models for estimating the drag coefficients. Figure 3: The schematics of the computational domain: (**a**) overall fluid domain and the solid subdomain, and (**b**) grids of the undeformed net panel in the solid subdomain. Table 3 shows that when \(Sn=0.16\), the present numerical simulations overestimate the drag coefficients by approximately 15.6% on average compared to those of [PERSON] et al. [47]. Compared to the analytical predictions from [PERSON] and [PERSON] [19], the present numerical simulations, on average, underestimate the drag coefficients by roughly 15.3%. [PERSON] and [PERSON] [1] reported that the analytical model in [PERSON] et al. [47] did not consider the effect of the Reynolds number; this may cause the discrepancy between the analytical prediction and numerical simulations/experimental tests. The analytical models in [PERSON] and [PERSON] [19] consider the effect of the Reynolds number and the relative motions between the fluid and the wetting, but it seems that the interference between net twines has been neglected. In particular, the net panel's flow field is so complicated that it should be considered to obtain more accurate results. When \(Sn=0.33\), the relative difference in the drag coefficients between the present numerical simulations and the analytical predictions from [PERSON] et al. [47] is below 10%, under the condition that the Reynolds number is from 300 to 1200. The Reynolds numbers used in [PERSON] et al.