## 1 Introduction
Recent relevant studies based on different mesh-based techniques, such as the finite volumes proposed in [13], or the particle finite element method (p-FEM) [14] are examples of the different strategies used to tackle different sloshing problems. However, in this work, the Lagrangian meshless method Smoothed Particle Hydrodynamics (SPH) has been used instead to discretize the liquid phase of the problem, assuming that the gas phase plays a negligible role. The SPH method has been widely extended to different applications in the past decades, such as free surface flows [15]. The SPH technique already has an important background solving complex computational engineering problems [16; 17], which includes fluid-structure interaction problems [18] and violent sloshing problems in the presence of complex geometries [19]. Recently, a thorough validation on sloshing flows occurring in tanks of different shapes has been carried out by [PERSON] [20]. A very focused application of a reformulated and adapted version of weakly compressible SPH to this violent problem was performed by [21; 22]. In this two-part paper, a tank-fluid system is first periodically excited with a prescribed law of motion, and the nonlinear features are observed. The force between the wall and the fluid and the global energy balance are both computed. Then, a validation against experimental results using a fluid-structure interaction formulation is carried out in the second part of the work. After this work, SPH can be considered an efficient and accurate methodology when compared to mesh-based methods to simulate free surface flows, and particularly violent sloshing flows. A very detailed study on the initial stages of this sloshing problem where the Rayleigh-Taylor instability alters the free surface is performed in [23]. Normally, the Rayleigh-Taylor instability (RTI) appears when the density gradient due to the presence of different fluids and gravity is opposed. This situation is present at the initial stages of our problem, when the two different fluids are confined and the tank is accelerated upwards. In our case, the light fluid overlies a heavier fluid by the action of gravity, but the RTI is developed when a larger acceleration than gravity is applied to both fluids in the direction opposite to the force of gravity. As explained before, the density gradient is opposed to the difference between the inertial force and gravity. In order to understand what is causing the initial free surface deformation, the Rayleigh-Taylor instability can be studied comparing the results from the SPH simulations and other results obtained when the Navier-Stokes equations are perturbed and linearized; see [23]. Very few SPH approaches [24; 25] contain a detailed quantitative comparison to other classical numerical formulations where well-established results such as the growth rate of the linear parts of the RTI are monitored. This paper shows a dual approach, experimental and numerical, to the study of the violent vertical sloshing flows described above in the context of aeronautics applications. This paper will be focused on the comparison of both methodologies in terms of the most primitive results obtained from both approaches. Consequently, the visualization and kinematics of the flow evolution will be compared, and the physical insights of the sloshing force will be deeply studied. The present article is organized as follows: in Section 2, the process followed to transform the aeronautical problem into a simpler problem is laid out, and is later studied deeply from both an experimental and numerical point of view. In Section 3, both the numerical and the experimental methodologies are explained. In Section 4, the obtained results are presented for both methodologies, applied and compared. Finally, the conclusions are summarized and discussed in Section 5.