## 7 Discussion  
This study investigated the impact of vertical baffles on the natural sloshing frequencies of a rectangular tank using the CEL method in combination with the IET. The results  
Figure 12: Time-domain responses for validation cases. Figure 13: Comparison with two closed-form equations. (**a**) Comparison with [PERSON] et al. (2006) [16]. (**b**) Comparison with [PERSON] et al. (2018) [17]. demonstrated that both the number and height of baffles significantly influence the dynamic behavior of the fluid. In tanks without baffles, the computed natural frequencies closely matched theoretical predictions, validating the applicability of traditional analytical models under simplified conditions. As the number or height of baffles increased, the natural frequencies decreased. This shift is attributed to the reduction in effective free surface area and the disruption of coherent sloshing paths caused by internal barriers. When the baffle height exceeded approximately 75% of the water depth, the fluid domain became segmented, resulting in localized vortex formation and entrapped fluid zones. These effects introduced nonlinearities in the fluid motion, leading to deviations from linear theoretical predictions. A key contribution of this study is the comparison of numerically obtained natural frequencies with closed-form solutions proposed by [PERSON] et al. (2006) [PERSON] et al. (2006) and [PERSON] et al. (2018) [PERSON] et al. (2018). Although good agreement was observed for the fundamental mode, the comparison was limited to this lowest frequency. Closed-form models, based on linear assumptions and two-dimensional simplifications, are insufficient to capture the three-dimensional flow structures and nonlinear phenomena introduced by tall or multiple baffles. In contrast, the CEL-based approach effectively accounts for such complexities, demonstrating its value in sloshing analysis for baffled tanks. The CEL method also offers the advantage of directly simulating fluid-structure interaction without simplifying the governing equations. This enables accurate modeling of key flow phenomena such as large free surface deformation, vortex shedding, and flow separation, features essential for understanding sloshing behavior in the presence of internal structures. In this study, the tank walls and baffles were assumed to be rigid, neglecting structural deformation under fluid-induced loads. While this assumption is valid for stiff-walled tanks, it may not apply to flexible or lightweight structures, where structural compliance can alter the fluid response. Future studies should address this limitation by implementing fully coupled fluid-structure interaction (FSI) models. The analysis focused primarily on the fundamental sloshing mode. Higher-order modes, which may respond differently depending on baffle configuration and potentially interact with structural modes, were not examined in detail. Such interactions could lead to complex dynamic behaviors including mode coupling and resonance. Comprehensive modal analysis, including frequency shifts and damping characteristics, will be essential to fully characterize the dynamic response of baffled fluid systems. In this context, distinguishing true physical behavior from numerical artifacts is critical for ensuring the reliability of simulation results. In addition, the present study was limited to rectangular tanks with vertical baffles. In practice, sloshing behavior can vary significantly with tank geometry, such as cylindrical, spherical, or irregular shapes, and the spatial arrangement of internal components. Future work should extend the proposed framework to a broader range of tank configurations to evaluate its robustness and general applicability. Lastly, as this study was based solely on numerical simulations, experimental validation is essential to confirm the accuracy and practical relevance of the findings.