# A Comparative Study on Violent Sloshing with Complex Baffles Using the ISPH Method
## 3 Model Validation and Convergence Analysis
### Model Validations through Experiment  
In this section, a sloshing tank without any baffle is simulated by the ISPH method and the results are compared with the experimental data of [PERSON] and [PERSON] [27] as well as numerical computations from STAR-CCM+. A schematic view of the numerical tank is shown in Figure 1, where the geometry of the sloshing tank and the location of the pressure sensors are provided. In the experiment, the tank experienced a forced harmonic rolling motion with an amplitude \(10^{\circ}\) and an excitation period 1.85 s. The initial water depth is 0.12 m and the tank is rotated at the geometric center. Although the study of [PERSON] and [PERSON] [27] focused on violent flow dampening through an elastic plate, their fluid model was first validated without the existence of the plate. Generally speaking, a large deformation of the free surface and dynamic impact pressure inside the tank are the two main factors for the evaluation of sloshing hazards and these were recorded in the experiment. In the ISPH computation, a particle size \(dx=0.002\) m is used, corresponding to the same basic cell size in STAR-CCM+. Both models used a time step of \(dt=0.0003\) s for consistency. The numerical data is extracted for 8 s after the initial transient period or initial cycle, which lasts for around 1-2 times the sloshing period \(T\), so as to include sufficient data series to illustrate the repeatability of the flow histories. There is no information available on the experimental transient phase. Figure 2 provides the comparisons of the free surface profiles between the experimental photos and the numerical results for half of the sloshing period \(T\). Both of the ISPH and STAR-CCM+ computations are shown for a comparison with their internal pressure contours. Overall features of the violent sloshing process have been captured by the two numerical models in a very satisfactory manner. These include the turbulent bore propagation at the time origin, running against the tank wall, plunging down and collapsing, and then propagating in the opposite direction. Generally speaking, it seems that the ISPH captured the sloshing free surface much better than STAR-CCM+ and produced closer surface profiles with the experimental recordings. Even if the flow situation is rather complex,  
For quantification of the model accuracy and the pressure time histories at two sensor points (P1 and P2) are compared between the ISPH/STAR-CCM+ computations and the experimental data of Liao and Hu in Figure 3a,b, respectively. Although both models seem to over-predict the measured peak values at P1 and under-predict them at P2, the arrival time of peak pressure, its amplitude and evolution, especially the two-peak pressure patterns, have all been captured with good accuracy. It should be noted that the impact pressure in violent flows is always a difficult parameter to forecast, but the present ISPH method provides a promising reproduction due to its mesh-free nature. Furthermore, it should also be noted that the pressure history patterns of Figure 3a,b look quite different. This is due to the fact that P1 is located on the tank bottom, which is always submerged under the liquid, while P2 is near the alternation region between the water and air; thus it experiences more pressure fluctuations and the relevant pressure peaks become much narrower. Although both of the ISPH and STAR-CCM+ computations provided a reasonable match with the experimental pressures, the former looks better in the general agreement with an averaged error of 0.4% at both pressure gauging points. On the other hand, STAR-CCM+ reached an averaged error of 0.8% at P1 and 1.5% at P2. Further comparisons of the spatial variation of the water surface profiles are shown in Figure 4a-d, for half of the sloshing period \(T\). Again, a generally better agreement with the experimental surface data by the ISPH computations is clearly demonstrated.