The phenomenon of violent sloshing appears widely in the field of Naval Architecture and Ocean Engineering, especially in liquid cargo carriers, such as the LNG (liquefied natural gas) carriers. During this process, the motion of liquid in partially filled tanks may cause large global and local loads on the tank walls when the frequency of sloshing is close to the natural frequency of the liquid tank. This consequence would be very serious in engineering practice, which may cause damage to the hull structure and even affect the stability of the carrier [

1]. Therefore, sloshing is an old topic, but it still needs to be studied in depth.

At present, lots of studies on the violent sloshing flows have been carried out by the linear and nonlinear potential flow theory and the scaled model experiment. Faltinsen [

2,

3,

4] used the incompressible potential flow theory to simulate liquid sloshing and obtained the formulas that have been widely used in the field of sloshing simulation. However, the method can be used to study sloshing tanks with relatively simple geometry and internal structure. In addition, Akyildiz et al. [

5] investigated the pressure distribution on a rectangular tank during the process of sloshing by an experimental method. Sames et al. [

6] studied sloshing in a rectangular tank with a baffle, and a cylindrical tank was also considered. Indeed, the experimental method can be applied to study the sloshing in the tank with more complex shapes, but it also requires high expenses for the site and facility. Hence, the numerical method has been getting more important in the simulation of liquid sloshing in recent years. The conventional numerical methods are carried out by using Euler grids. Wu et al. [

7] simulated the sloshing waves in a 3D tank based on the finite element method (FEM). In the conventional grid-based methods, in order to track the moving free surface, some additional techniques, such as the Volume-of-Fluids, are used in the methods. The VOF uses the volume fraction of fluid in gird to define the free surface. However, the problems of numerical diffusion become serious when the surface cell becomes extremely complicated, such as in a liquid sloshing, which can easily fail to simulate because of the large deformation of grids. Recently, a kind of mesh-less method named smoothed particle hydrodynamics (SPH) has attracted quite a few researchers’ attention [

8]. It does not depend on any grids, and the computation is purely based on a group of discrete points that can move freely. So, it can capture the free surface flow conveniently, which is more suitable for treating the problems of large deformation of free-surfaces. Delorme and Colagrossi et al. [

9] investigated impact pressure in the case of shallow water sloshing by the SPH method, compared the results with experimental ones, and then discussed the influence of viscosity and density re-initialization on the SPH results. Gotoh and Khayyer [

10] simulated the violent sloshing flows using the incompressible SPH (ISPH) method and presented two schemes to enhance the accuracy of the simulation of impact pressures. Zheng and You [

11] compared the effect of different baffle configurations on mitigating sloshing by the ISPH method. A great deal of research [

12,

13] shows that the ISPH method can improve the accuracy and stability of the calculation pressure, and the pressure field is smoother.

As a matter of fact, the marine environment is always very complex when sloshing happens. If an oil fire occurs, it would be a big disaster and hard to control, and the water jet flow outside would get into the tank to put out the oil tank fire, which would influence the impact effect of sloshing. Such a consequence may cause more serious damage to the hull structure, which would be very serious in engineering practice. With regard as the problem of jet flows, Hatton et al. [

14,

15] studied the trajectories of large water jets that are used in the design of fire-fighting systems, particularly those used in offshore situations, and evaluated the effects of flow-rate, pressure, and nozzle size during the process of the system design. Fischer et al. [

16] used three different CFD codes, namely, the CHYMES multiphase flow model, the FEAT finite element code, and the Harwell-FLOw3D finite volume code, to simulate the problem of a laminar jet of fluid injected into a tank of fluid at rest and make a detailed comparison. Aristodemo et al. [

17] studied the plane jets propagating into still fluid tanks and current flows by using the WCSPH method. Andreopoulos et al. [

18] carried out an experiment on the flow generated by a plane with a buoyant jet discharging vertically into shallow water.

In this paper, the liquid sloshing with a water jet flow from the top of the tank will be studied by using the incompressible SPH (ISPH) method. Through the comparison of different situations, the sloshing effects and characteristics of the impact pressure are studied. The aim of this study is to summarize the influence of the water jet flow on sloshing, so as to give a reference for practical engineering.