## 2 Materials and Methods
### Grid Verification  
To assess the impact of grid density on simulation results, this study employed four grids of varying densities. The corresponding numbers of grid cells are 32,244, 37,220, 46,447, and 53,132. Among the three grids, the rates of BOG production and temperature distribution differences were compared. Considering factors such as simulation accuracy and computational time, it is appropriate to select the grid with 37,220 cells for numerical computation.  
To evaluate the impact of mesh resolution on the simulation accuracy, four different structured meshes were generated using ANSYS ICEM 2024 R2, with total cell countsof 32,244, 37,220, 46,447, and 53,132, respectively. Special attention was given to mesh refinement near the vapor-liquid interface and wall boundaries to better resolve thermal gradients and interface dynamics. The mesh quality was ensured by maintaining an orthogonal quality above 0.99.  
A mesh independence study was performed by monitoring the boil-off gas (BOG) mass generated under identical boundary conditions. The results, presented in Table 2, indicate that the BOG mass converges when the number of cells exceeds approximately 37,000. The difference in predicted BOG mass between the finest grid and the 37,220-cell grid is less than 1.5%, indicating sufficient numerical accuracy. Hence, the mesh with 37,220 cells was adopted for subsequent simulations to balance computational cost and accuracy.  
These results demonstrate that the simulated BOG mass is insensitive to further mesh refinement beyond 37,220 cells, confirming mesh convergence.  
Model validation was performed by replicating the experimental setup of [PERSON] and [PERSON] [23], who investigated water sloshing in a cylindrical tank of 0.89 m length and 0.35 m diameter. Two validation cases were considered: Case #1 with f = 0.40 Hz (T = 2.5 s) and Case #2 with f = 0.59 Hz (T = 1.7 s), both using an angular amplitude of 3\({}^{\circ}\). Simulation results showed excellent agreement with experimental interface shapes.  
A detailed comparison of the phase distribution between simulations and experiments is shown in Figure 2. The numerical results exhibit excellent agreement with experimental snapshots, particularly in capturing the interface shape evolution under sloshing conditions. For all tested cases, the simulated interface morphology aligns closely with the experimental observations, demonstrating the model's capability to resolve complex free-surface dynamics.  
Further validation is performed by comparing the predicted pressure and temperature variations against experimental data, as illustrated in Figure 3. The numerical results accurately reproduce the temporal trends of both parameters, with deviations remaining below 5.0%. The consistent overlap confirms the model's robustness in predicting thermodynamic and hydrodynamic coupling effects.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Grid Size (Cells)** & **BOG Mass (kg)** \\ \hline
32,244 & 1.943 \\
37,220 & 2.008 \\
46,447 & 2.023 \\
53,132 & 2.028 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Grid independence study results.  
Figure 2: Comparison of interface shape between experimental results [20] and simulation results.