## 4 Results and Discussion
### Pressure Measurements  
In this subsection, the possibility of reconstructing the pressure contribution of the sloshing force \(F_{slosh}^{p}\) as a sum of a discrete number of pressure sensors multiplied by their corresponding areas is explored. This computation is important to test the accuracy of the pressure fields computed by the SPH formulation, which will be compared in future work with the measurements given by the experimental pressure sensors; see [55] as an example of these sensors used in sloshing experiments. This fact reveals that the sloshing force is in first approximation caused by a succession of impact pressures. In Figure 18, a scheme is shown where 34 pressure sensors are used--17 on the top wall \(p_{i}^{u}\) and 17 on the bottom wall \(p_{i}^{b}\). The pressure signal is computed by a smoothed interpolation using the particles which are within a smoothing length distance \(h\) from the sensor position. In Figure 19, the top and bottom pressure signals obtained from the middle sensor 9 are plotted as a function of time for both the water and glycerine. The pressure signals presented in this section have been filtered around the natural frequency of the experiment using a fourth-order Butterworth filter. The pressure values have been normalized with the hydrostatic pressure value at the tank bottom \(\rho gh_{l}\) where \(h_{l}\) represents the liquid height. In both glycerine and water cases, the bottom pressures are larger than the upper values largely due to the weight contribution. It was also observed that at the end of the simulation, the sensor value tends toward zero in the upper case and toward the final hydrostatic value for the bottom case. Focusing on the glycerine, it was observed that the upper signal starts  
Figure 17: Normalized dissipated energy by the pressure and viscous components of the sloshing force and the structural damping force coming from the linear guide. close to the first impact \(t_{fi}\sim 0.41\) s and finishes quickly, approximately 2 s later. This is because the glycerine impacts with the upper wall finishing at \(t_{li}\sim 2.46\) s. The rest of the upper signal is nearly zero as the glycerine behaves similarly to a standing wave confined at the bottom of the tank, something clearly shown by the bottom signal. Additionally, Figure 20 displays the map of the nondimensional pressure maxima extracted from the 34 pressure signals over time and the normalized \(x/L\) coordinate. In this figure, it can be observed that the impacts against the upper wall are mostly localized to the middle region of the tank \(x/L\in(0.4,0.6)\) presenting maximum nondimensional pressures of 8.66 and 6.84 for water and glycerine, respectively. The pressure impacts against the upper wall for the glycerine are less intense and frequent when compared to the water, which could be related to the fact that the glycerine test case presents less liquid-induced dissipation as indicated in Table 2. When looking at the pressure maps for the bottom wall presented in Figure 20, higher pressure maxima than the ones registered for the upper wall with a maximum pressure of 10.63 and 9.9 for water and glycerine, respectively, are observed. The pressure impacts against the bottom wall are larger than the ones registered for the upper wall due to the influence of the liquid's weight. The decay rate of the pressure maxima appears to be higher for the glycerine case, indicating that the pressure impacts and the violent regime of the flow last for shorter times. This observation is backed up by Figure 7.  
Figure 19: Normalized pressure signals at the top and bottom middle sensors (sensors \(p_{9}^{b}\) and \(p_{9}^{u}\)) for the water and glycerine cases. Figure 18: Outline of the pressure sensor distribution when 34 sensors are used.