_Applied sciences_  
_Article_  
**Numerical Computation of Sloshing-Induced Force in Complex Ship Tanks under the Excitation of Ship Rolling Motion Based on the MPS Method**  
[PERSON] \({}^{1}\)\({}^{1}\), [PERSON] \({}^{1}\), [PERSON] \({}^{2}\), [PERSON] \({}^{3,*}\) and [PERSON] \({}^{1}\)  
\({}^{1}\) Navigation College, Dalian Maritime University, No. 1 Linghai Road, Dalian 116026, China;  
xfsun,dlmu0163.com (X.S. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (Y.L.) \({}^{2}\) Department of Railway Transportation, Liaoning Railway Vocational and Technical College, No. 129 Songpoli, Jizhzhou 121000, China; [EMAIL_ADDRESS]  
\({}^{3}\) Marine Engineering College, Dalian Maritime University, No. 1 Linghai Road, Dalian 116026, China  
\({}^{*}\) Correspondence: [EMAIL_ADDRESS]  
**Abstract: Liquid sloshing in ship tanks would have a direct effect on ship dynamic stability, and thus is of great importance for navigation safety. To calculate the sloshing-induced force on real ship tanks, this paper presents an approach to numerically simulate the liquid-sloshing in complex tanks using the moving particle semi-implicit (MPS) method. The sloshing-induced force is numerically calculated and used to investigate the effect of different excitation conditions in which the realistic ship motions under different loading conditions have been taken into account. Simulation results show that the maximum sloshing-induced force is much bigger than the corresponding static one. Meanwhile, both the rolling angle and period have significant effects on liquid sloshing. **  
**Keywords: liquid sloshing; sloshing-induced force; MPS method; free surface effect; ship stability**  
**Citation: [PERSON]; [PERSON]; [PERSON]; [PERSON]; [PERSON] Numerical Computation of Sloshing-Induced Force in Complex Ship Tanks under the Excitation of Ship Rolling Motion Based on the MPS Method. _Appl. Sci._**2022, 12, 5130. [[https://doi.org/10.3309/app12105130](https://doi.org/10.3309/app12105130)]([https://doi.org/10.3309/app12105130](https://doi.org/10.3309/app12105130))  
Academic Editor: [PERSON]  
Received: 19 April 2022  
Accepted: 18 May 2022  
Published: 19 May 2022  
**Publisher: Note** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. **Cognition:** 2022 by the authors. to address the free surface flow problem in 1994 [23]. After that, SPH methods including weakly-compressible SPH (WCSPH) and incompressible SPH (ISPH) were used to simulate the phenomena of liquid sloshing in partially filled tanks [24; 25; 26; 27; 28; 29; 30; 31; 32; 33; 34]. However, the kernel in the SPH method is considered as a mass distribution of each particle. The superposition of the kernels represents the physical superposition of mass. Thus, the particle is like a spherical cloud [35]. This concept may be more fitted to compressible fluids. Another popular meshfree method is the moving particle semi-implicit (MPS) method. The original MPS method was proposed by [PERSON] and [PERSON] [36] to simulate the incompressible flow. In the original MPS method, there were several defects including non-optimal source term, gradient and collision models, and search of free-surface particles, which led to less accurate fluid motions and non-physical pressure fluctuations [37]. To overcome these defects, many researchers have put forward a series of improvements on the MPS method, including the improvement of the kernel function [38; 39], the Laplacian model [40], the collision model [41], the pressure Poisson equation (PPE) [42; 43; 44; 45], the pressure gradient model [46; 47], and the boundary condition [48; 49]. The MPS method has also been widely used to solve the problem of liquid sloshing [50; 51; 52; 53; 54; 55]. Liquid sloshing in ship tanks has a significant effect on ship dynamic stability.