Journal of Marine Science and Application

, Volume 11, Issue 2, pp 143–149

# Numerical simulation for water entry of a wedge at varying speed by a high order boundary element method

• Guoxiong Wu
Article

## Abstract

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dt α , where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.

## Keywords

high order boundary element method complex velocity potential fluid/structure impact water entry

## References

1. Batchelor GK (1967). An introduction to fluid dynamics, Cambridge University Press, Cambridge, UK.
2. Cumberbatch E (1960). The impact of a water wedge on a wall, Journal of Fluid Mechanics, 7, 353–374.
3. Dobrovol’skaya ZN (1969). On some problem of similarity flow of fluid with a free surface. Journal of Fluid Mechanics, 36, 805–829.
4. Duan WY, Xu GD, Wu GX (2009). Similarity solution of oblique impact of wedge-shaped water column on wedged coastal structures. Coastal Engineering, 56, 400–407.
5. Fantinsen OM (2002). Water entry of a wedge with finite deadrise angle. Journal of Ship Research, 46, 39–51.Google Scholar
6. Greenhow M, Vinje T, Brevig P, Taylor J (1982). A theoretical and experimental study of the capsize of Salter’s duck in extreme waves. Journal of Fluid Mechanics, 118, 221–239.
7. Hughes OF (1972). Solution of the wedge entry problem by a numerical conformal mapping. Journal of Fluid Mechanics, 56, 173–192.
8. Lu CH, He YS, Wu GX (2000). Coupled analysis of nonlinear interaction between fluid and structure during impact. Journal of Fluids and Structures, 14, 127–146.
9. Semenov, YA, Iafrati A (2006). On the nonlinear water entry problem of asymmetric wedges. Journal of Fluid Mechanics, 547, 231–256.
10. Wehausen JV, Laitone EV (1960). Surface waves. In Handbuch der Physik 9, Springer, 446–778.Google Scholar
11. Wu GX (1998). Hydrodynamic force on a rigid body during impact with liquid. Journal of Fluids and Structures, 12, 549–559
12. Wu GX (2006). Numerical simulation of water entry of twin wedges. Journal of Fluids and Structures, 22, 99–108.
13. Wu GX (2007a). Fluid impact on a solid boundary. Journal of Fluids and Structures, 23, 755–765.
14. Wu GX (2007b). Liquid column and liquid droplet impact, Quarterly Journal of Mechanics and Applied Mathematics, 60, 497–511.
15. Wu GX, Sun H, He YS (2004). Numerical simulation and experimental study of water entry of a wedge in free fall motion. Journal of Fluids and Structures, 19, 277–289.
16. Xu GD, Duan WY, Wu GX (2008). Numerical simulation of oblique water entry of asymmetrical wedge. Ocean Engineering, 35, 1597–1603.
17. Xu GD, Duan WY, Wu GX (2010). Simulation of water entry of a wedge through free fall in three degrees of freedom, Proceedings of the Royal Society of London A, 466, 2219–2239.
18. Zhao R, Faltinsen OM (1993). Water entry of two-dimensional bodies. Journal of Fluid Mechanics, 246, 593–612.