Journal of Marine Science and Application

, Volume 12, Issue 2, pp 163–169 | Cite as

Two-dimensional numerical simulation of an elastic wedge water entry by a coupled FDM-FEM method

  • Kangping Liao
  • Changhong Hu
  • Wenyang Duan


Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method (FDM) and finite element method (FEM) was developed to analyze the fluid structure interaction (FSI) problem. The FDM, in which the Constraint Interpolation Profile (CIP) method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting (THINC/SW) scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary (IB) method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.


elastic wedge water entry coupled FDM-FEM method volume weighted method CIP method THINC/SW scheme hydroelastic behavior 


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  1. Arai M, Miyauchi T (1998). Numerical study of the impact of water on cylindrical shells, considering fluid-structure interactions. In Oosterveld M, Tan S (Eds.): Practical Design of Ships and Mobile Units, 59–68.CrossRefGoogle Scholar
  2. Faltinsen OM (1997). The effect of hydroelasticity on ship slamming. Philosophical Transactions of the Royal Society A, 355, 575–591.zbMATHCrossRefGoogle Scholar
  3. Faltinsen OM (2000). Hydroelastic slamming. Journal of Marine Science and Technology, 5, 49–65.CrossRefGoogle Scholar
  4. Hu CH, Kashiwagi M (2004). A CIP-based method for numerical simulation of violent free surface flows. Journal of Marine Science and Technology, 6, 143–157.CrossRefGoogle Scholar
  5. Hu CH, Kashiwagi M, Kishev Z, Sueyoshi M, Faltinsen O (2006). Application of CIP method for strongly nonlinear marine hydrodynamics. Ship Technology Research, 53(2), 74–87.Google Scholar
  6. Hu CH, Kashiwagi M (2009). Two-dimensional numerical simulation and experiment on strongly nonlinear wave-body interaction. Journal of Marine Science and Technology, 14, 200–213.CrossRefGoogle Scholar
  7. Kajishima T, Takiguchi S, Hamasaki H, Miyake Y (2001). Turbulence structure of particle-laden flow in a vertical plane channel due to vortex shedding. JSME International Journal Series B, 44(4), 526–535.CrossRefGoogle Scholar
  8. Kajishima T, Takiguchi S (2002). Interaction between particle clusters and particle-induced turbulence. International Journal of Heat and Fluid Flow, 23(5), 639–646.CrossRefGoogle Scholar
  9. Khabakhpasheve T, Korobkin A (2003). Approximate models of elastic wedge impact. 18th International Workshop on Water Waves and Floating Bodies, Le Croisic, France.Google Scholar
  10. Korobkin A (2000). Elastic wedge impact. Lecture note.Google Scholar
  11. Korobkin A, Gueret R, Malenica S (2006). Hydroelastic coupling of beam finite element model with Wagner theory of water impact. Journal of Fluid and Structures, 22, 493–504.CrossRefGoogle Scholar
  12. Liao KP, Hu CH (2013). A coupled FDM-FEM method for free surface flow interaction with thin elastic plate. Journal of Marine Science and Technology, 18(1), 1–11.CrossRefGoogle Scholar
  13. Lu CH, He YS, Wu GX (2000). Coupled analysis of nonlinear interaction between fluid and structure during impact. Journal of Fluid and Structures, 14, 127–146.CrossRefGoogle Scholar
  14. Luo HB, Hu JJ, Guedes Soares C (2010). Numerical simulation of hydroelastic response of flat stiffened panel under slamming loads. Proceedings of the 29th International Conference on Offshore Mechanics and Arctic Engineering (OAME), Shanghai, China (OMAE2010-20027).Google Scholar
  15. Luo HB, Wang H, Guedes Soares C (2012). Numerical and experimental study of hydrodynamic impact and elastic response of one free-drop wedge with stiffened panels. Ocean Engineering, 40, 1–14.CrossRefGoogle Scholar
  16. Maki KJ, Lee DH, Troesch AW, Vlahopoulos N (2011). Hydroelastic impact of a wedge-shaped body. Ocean Engineering, 38, 621–629.CrossRefGoogle Scholar
  17. Meyerhoff WK (1965). Die berechnung hydroelastischer stoβe. Schiffstechnik, 12, 18–30.Google Scholar
  18. Mittal R, Iaccarino G (2005). Immersed boundary methods. Annual Review of Fluid Mechanics, 37, 239–261.MathSciNetCrossRefGoogle Scholar
  19. Oberhagemann J, Hotmann M, El Moctar O, Schellin TE, Kim D (2009). Stern slamming of a LNG carrier. Journal of Offshore Mechanics and Arctic Engineering, 131(3), 1–10.CrossRefGoogle Scholar
  20. Panciroli R, Abrate S, Minak G (2013). Dynamic response of flexible wedge entering the water. Composite Structures, 99, 163–171.CrossRefGoogle Scholar
  21. Panciroli R, Abrate S, Minak G, Zucchelli A (2012). Hydroelasticity in water-entry problems: comparison between experimental and SPH results. Composite Structures, 94(2), 532–539.CrossRefGoogle Scholar
  22. Peskin CS (1972). Flow patterns around heart valves: a numerical method. Journal of Computational Physics, 10, 252–271.MathSciNetzbMATHCrossRefGoogle Scholar
  23. Peskin CS (2002). The immersed boundary method. Acta Numerica, 11, 479–517.MathSciNetzbMATHCrossRefGoogle Scholar
  24. Schellin TE, el Moctar O (2007). Numerical prediction of impact-related wave loads on ships. Journal of Offshore Mechanics and Arctic Engineering, 129, 39–47.CrossRefGoogle Scholar
  25. Takewaki A, Nishiguchi A, Yabe T (1985). Cubic interpolated Pseudo-particle method (CIP) for solving hyperbolic-type equations. Journal of Computational Physics, 61(2), 261–268.MathSciNetzbMATHCrossRefGoogle Scholar
  26. Wilkinson JPD, Cappelli AP, Salzman RN (1968). Hydroelastic interaction of shells of revolution during water impact. AIAA Journal, 6, 792–797.zbMATHCrossRefGoogle Scholar
  27. Xiao F, Satoshi I, Chen CG (2011). Revisit to the THINC scheme: A simple algebraic VOF algorithm. Journal of Computational Physics, 230, 7089–7092.CrossRefGoogle Scholar
  28. Yabe T, Ishikawa T, Wang PY, Aoki T, Kadota Y, Ikeda F (1991). A universal solver for hyperbolic equations by cubic-polynomial interpolation II. two- and three-dimensional solvers. Computer Physics Communications, 66, 233–242.MathSciNetzbMATHCrossRefGoogle Scholar
  29. Yabe T, Xiao F, Utsumi T (2001). The constraint interpolation profile method for multiphase analysis. Journal of Computational Physics, 169, 556–593.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Interdisciplinary Graduate School of Engineering ScienceKyushu UniversityKasuga, FukuokaJapan
  2. 2.Research Institute for Applied MechanicsKyushu UniversityKasuga, FukuokaJapan
  3. 3.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina

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