# A Comparative Study on Violent Sloshing with Complex Baffles Using the ISPH Method
## 1 Introduction  
The phenomenon of liquid sloshing is frequently observed in marine and offshore engineering. It occurs in a partially filled container due to external excitation on the inside liquid. If the excitation frequency is close to the natural frequency of the tank, the liquid container is subject to tremendous impact load, which may cause serious damage to the hull structure. Such a consequence would be very serious in engineering practice [1]. Therefore, it is necessary to study the sloshing characteristics and analyze the influence of excitation frequency, aiming to find the solutions on damping the liquid sloshing and reducing the impact loads. Now, the common techniques for analyzing the sloshing problem include theoretical, experimental, and numerical methods. Theoretical approaches, such as the analytical solution [2; 3; 4] or the potential flow theory based method [5; 6], can be used to study sloshing tanks of relatively simple geometry and internal structure. Experimental works, on the other hand, have been carried out to study the sloshing behavior in tanks with more complex shapes under different external excitations [7], in spite of the high expenses of site and facility. In recent years, numerical simulations have been playingan increasingly greater role in the study of liquid sloshing, and most are carried out by using grid-based methods, such as the finite element [8] and finite difference [9] methods. However, these conventional methods cannot easily track the movement of the free-surface automatically, which undergoes large deformations in the violent sloshing. To track the moving free surface in a conventional Eulerian grid approach, additional surface tracking techniques such as the Marker-in-Cell and Volume-of-Fluids must be used. The former uses the marker particles to define the free surface while the latter solves a transport equation for the volume fraction of fluid. However, in both cases the Navier-Stokes (N-S) equations are solved on a fixed Eulerian grid and potential problems of numerical diffusion can arise due to advection terms in the N-S equations. This problem becomes serious when the deformation of the free surface is large, such as in a liquid sloshing when the treatment of the surface cells becomes extremely complicated. As one potential substitute, the mesh-free numerical modeling method has attracted a lot of attention in the last decade [10]. The Smoothed Particle Hydrodynamics (SPH) method, which originates in astrophysics, provides a promising tool to model a wide range of free surface flow problems. One of the great advantages of the SPH modeling technique is that particles move in Lagrangian coordinates and the advection term in the N-S equation is directly calculated by the particle motion through particle interaction models. Thus, free surfaces can be conveniently and accurately tracked by the particles without numerical diffusion or extra surface tracking algorithms, which is always required in the traditional Eulerian approaches. For both the grid and particle modeling techniques, the discretization scheme heavily depends on the density of points and therefore on their total numbers; i.e., spatial resolution. However, each point in the SPH can move freely, which is more suitable to treat the large deformation and discontinuous free-surfaces. The mesh-less methods have become one of the most promising approaches for simulating the violent liquid sloshing and also include the Moving Particle Semi-implicit (MPS) method [11] and Mesh-less Local Petrov-Galerkin method based on the Rankine source solution (MLPG_R) [12]. In coastal and offshore applications, the SPH method is one of the most popular particle modeling tools and has shown to provide a promising solution platform on liquid sloshing and its interaction with various complex internal baffles [13; 14; 15; 16; 17]. Currently, changing the geometric shape of the sloshing tank and installing the baffles are the two major practices to dampen the liquid sloshing.