Numerical simulation of viscous liquid sloshing by moving-particle semi-implicit method

Abstract

A meshless numerical simulation method, the moving-particle semi-implicit method (MPS) is presented in this paper to study the sloshing phenomenon in ocean and naval engineering. As a meshless method, MPS uses particles to replace the mesh in traditional methods, the governing equations are discretized by virtue of the relationship of particles, and the Poisson equation of pressure is solved by incomplete Cholesky conjugate gradient method (ICCG), the free surface is tracked by the change of numerical density. A numerical experiment of viscous liquid sloshing tank was presented and compared with the result got by the difference method with the VOF, and an additional modification step was added to make the simulation more stable. The results show that the MPS method is suitable for the simulation of viscous liquid sloshing, with the advantage in arranging the particles easily, especially on some complex curved surface.

Keywords

sloshing / liquid tank / viscous fluid / incompressible fluid / free surface / meshless / moving-particle semi-implicit method (MPS)

References

[1] Valentine D. T., Frandsen J. B. Numerical investigation of two-dimensional sloshing: Nonlinear internal waves[J]. Journal of Offshore Mechanics and Arctic Engineering, 2005, 127(4): 300-305

[2] Lee S. J., Kim M. H., Lee D. H., Kim J. W., Kim Y. H. The effects of LNG-tank sloshing on the global motions of LNG carriers[J]. Ocean Engineering, 2007, 34(1): 10-20

[3] Koshizuka S., Oka Y. Moving-particle semi-implicit method for fragmentation of incompressible fluid[J]. Nuclear Science and Engineering, 1996, 123(3): 421-434

[4] Sueyoshi M., Naito S. A study of nonlinear fluid phenomena with particle method (Part1)[J]. Journal of Kansai Society Naval Architects, 2001, 236: 191-198

[5] Sueyoshi M., Naito S. A study of nonlinear fluid phenomena with particle method (Part2)[J]. Journal of Kansai Society Naval Architects, 2002, 237: 181-186

[6] Sueyoshi M., Naito S. A study of nonlinear fluid phenomena with particle method (Part3)[J]. Journal of Kansai Society Naval Architects, 2003, 239: 81-86

[7] Ataie-Ashtiani B., Farhadi L. A stable moving-particle semi-implicit method for free surface flows[J]. Fluid Dynamics, 2006, 38(4): 241-256

[8] Zhu R. Q. Time domain simulation of liquid sloshing and its interaction with flexible structure[D]. 2002, Wuxi: China Ship Scientific Research Center