Journal of Marine Science and Application

, Volume 16, Issue 4, pp 395–404

# Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method

• Chengping Rao
• Youlin Zhang
• Decheng Wan
Article

## Abstract

Fluid-Structure Interaction (FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method (MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit (MPS) method is used to calculate the fluid domain, while the Finite Element Method (FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

## Keywords

mesh-free method moving particle semi-implicit finite element method fluid-structure interaction solitary wave MLParticle-SJTU solver

## References

1. Aliabadi SK, Tezduyar TE, 1993. Space-time finite element computation of compressible flows involving moving boundaries and interfaces. Computer Methods in Applied Mechanics and Engineering, 107(1–2), 209–223.
2. Altomare C, Crespo AJ, Domínguez JM, Gómez-Gesteira M, Suzuki T, Verwaest T, 2015. Applicability of smoothed particle hydrodynamics for estimation of sea wave impact on coastal structures. Coastal Engineering, 96, 1–12. DOI:
3. Antoci C, Gallati M, Sibilla S, 2007. Numerical simulation of fluid-structure interaction by SPH. Computers & Structures, 85(11–14), 879–890. DOI:
4. Betsy S, 2014. Experiments and computations of solitary-wave forces on a coastal-bridge deck. Part I: Flat Plate. Coastal Engineering, 88,194–209. DOI:
5. Boussinesq J, 1872. Théorie des ondes et des remous qui se propagent le long d’un canal rectangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond. Journal de Mathématiques Pures et Appliquées, 17, 55–108. (in French)
6. Chen JKL, Noguchi H, Koshizuka S, 2007. Fluid-shell structure interaction analysis by coupled particle and finite element method. Computers & Structures, 85(11–14), 688–697. DOI: Google Scholar
7. el Moctar O, Ley J, Oberhagemann J, Schellin T, 2017. Nonlinear computational methods for hydroelastic effects of ships in extreme seas. Ocean Engineering, 130, 659–673. DOI:
8. Goring DG, 1978. Tsunamis-the propagation of long waves onto a shelf. PhD thesis, California Institute of Technology, Pasadena.Google Scholar
9. Hirt CW, Nichols BD, 1981. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225.
10. Hou G, 2012. Numerical methods for fluid-structure interaction -a review. Communications in Computational Physics, 12(2), 337–377. DOI:
11. Hsiao KM, Lin JY, Lin WY, 1999. A consistent co-rotational finite element formulation for geometrically nonlinear dynamic analysis of 3-D beams. Comput. Methods Appl. Mech. Engrg, 169, 1–18. DOI:
12. Idelsohn SR, 2008. Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the PFEM. Comput. Methods Appl. Mech. Eng., 197, 1762–1776. DOI:
13. Iura M, Atluri SN, 1995. Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames. Computers and Structures, 55(3), 453–462. DOI:
14. Khayyer A, Gotoh H, 2013. Enhancement of performance and stability of MPS mesh-free particle method for multiphase flows characterized by high density ratios. Journal of Computational Physics, 242, 211–233. DOI:
15. Khayyer A, Gotoh H, 2015. A multi-phase compressible-incompressible particle method for water slamming. Proceedings of the Twenty-fifth International Ocean and Polar Engineering Conference, Kona, Hawaii, USA, 1235–1240. DOI: Google Scholar
16. Khayyer A, Gotoh H, Shao SD, 2008. Corrected incompressible SPH method for accurate water-surface tracking in breaking waves. Coastal Engineering, 55(3), 236–250. DOI:
17. Kondo M, Koshizuka S, 2011. Improvement of stability in moving particle semi-implicit method. International Journal for Numerical Methods in Fluids, 65(6), 638–654. DOI:
18. Korteweg DJ, De Vries G, 1895. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 39, 422–443. DOI:
19. Koshizuka S, 1996. Moving-particle semi-implicit method for fragmentation of incompressible fluid. Nuclear Science & Engineering the Journal of the American Nuclear Society, 123(3), 421–434.
20. Lee BH, Park JC, Kim MH, Hwang SC, 2011. Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads. Computer Methods in Applied Mechanics & Engineering, 50(24), 5921–5933. DOI:
21. Liang DF, Jian W, Shao S, Chen R, Yang K, 2017. Incompressible SPH simulation of solitary wave interaction with movable seawalls. Journal of Fluids and Structures, 69, 72–88. DOI:
22. Longatte E, Verremana V, Souli M, 2009. Time marching for simulation of fluid-structure interaction problems. Journal of Fluids and Structures, 25, 95–111. DOI:
23. Lucy LB, 1977. A numerical approach to the testing of the fission hypothesis. The Astronomical Journal, 82, 1013–1024.
24. Newmark NM, 1959. A method of computation for structural dynamics. Journal of the Engineering Mechanics Division, 85(3), 67–94.Google Scholar
25. Sriram V, Ma QW, 2012. Improved MLPG_R method for simulating 2D interaction between violent waves and elastic structures. Journal of Computational Physics, 231(22), 7650–7670. DOI:
26. Stanley O, Fedkiw R, 2003. Level set methods and dynamic implicit surfaces. Springer, New York, 17–21. DOI:
27. Tanaka M, Masunaga T, 2010. Stabilization and smoothing of pressure in mps method by quasi-compressibility. Journal of Computational Physics, 229(11), 4279–4290. DOI:
28. Tang ZY, Wan DC, 2015. Numerical simulation of impinging jet flows by modified MPS method. Engineering Computations, 32(4), 1153–1171. DOI:
29. Tang ZY, Zhang YL, Wan DC, 2016a. Multi-resolution MPS method for free surface flows. International Journal of Computational Methods, 13(4), 1641018-1–1641018-17. DOI:
30. Tang ZY, Zhang YL, Wan DC, 2016b. Numerical simulation of 3-D free surface flows by overlapping MPS. Journal of Hydrodynamics, 28(2), 306–312. DOI:
31. Walhorn E, Kölke A, Hübner B, Dinkler D, 2005. Fluid-structure coupling within a monolithic model involving free surface flows. Computers & Structures, 83(25–26), 2100–2111. DOI:
32. Zhang YL, Tang ZY, Wan DC, 2016. Numerical investigations of waves interacting with free rolling body by modified MPS method. International Journal of Computational Methods, 13(4), 1641013-1–1641013-14. DOI:
33. Zhang YL, Wan DC, 2017. Numerical study of interactions between waves and free rolling body by IMPS method. Computers & Fluids, 155, 124–133. DOI:
34. Zhang YX, Wan DC, 2011. Application of MPS in 3D dam breaking flows. Sci. Sin. Phys. Mech. Astron., 41, 140–154. DOI:
35. Zhang YX, Wan DC, 2012. Numerical simulation of liquid sloshing in low-filling tank by MPS. Chinese Journal of Hydrodynamics, 27(1), 100–107. (in Chinese) DOI: Google Scholar
36. Zhang YX, Wan DC, Hino T, 2014. Comparative study of MPS method and level-set method for sloshing flows. Journal of hydrodynamics, 26(4), 577–585. DOI: