Journal of Ocean Engineering and Technology (한국해양공학회지)

Korean Society of Ocean Engineers (한국해양공학회)
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Higher-order Spectral Method for Regular and Irregular Wave Simulations

  • Oh, Seunghoon (Korea Research Institute of Ships and Ocean Engineering) ;
  • Jung, Jae-Hwan (Korea Research Institute of Ships and Ocean Engineering) ;
  • Cho, Seok-Kyu (Korea Research Institute of Ships and Ocean Engineering)
  • Received : 2020.09.09
  • Accepted : 2020.10.14
  • Published : 2020.12.31
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Abstract

In this study, a nonlinear wave simulation code is developed using a higher-order spectral (HOS) method. The HOS method is very efficient because it can determine the solution of the boundary value problem using fast Fourier transform (FFT) without matrix operation. Based on the HOS order, the vertical velocity of the free surface boundary was estimated and applied to the nonlinear free surface boundary condition. Time integration was carried out using the fourth order Runge-Kutta method, which is known to be stable for nonlinear free-surface problems. Numerical stability against the aliasing effect was guaranteed by using the zero-padding method. In addition to simulating the initial wave field distribution, a nonlinear adjusted region for wave generation and a damping region for wave absorption were introduced for wave generation simulation. To validate the developed simulation code, the adjusted simulation was carried out and its results were compared to the eighth order Stokes theory. Long-time simulations were carried out on the irregular wave field distribution, and nonlinear wave propagation characteristics were observed from the results of the simulations. Nonlinear adjusted and damping regions were introduced to implement a numerical wave tank that successfully generated nonlinear regular waves. According to the variation in the mean wave steepness, irregular wave simulations were carried out in the numerical wave tank. The simulation results indicated an increase in the nonlinear interaction between the wave components, which was numerically verified as the mean wave steepness. The results of this study demonstrate that the HOS method is an accurate and efficient method for predicting the nonlinear interaction between waves, which increases with wave steepness.

Keywords

Acknowledgement

This study is the product of the "Development of core technology for computational fluid dynamics analysis of global performance of offshore structures (PES3500)" supported by the Korea Research Institute of Ships and Ocean Engineering.

References

  1. Bonnefoy, F., Le Touze, D., & Ferrant, P. (2006). A Fully-spectral Time-domain Model for Second-order Simulation of Wavetank Experiments. Part A: Formulation, Implementation and Numerical Properties. Applied Ocean Research, 28(1), 33-43. https://doi.org/10.1016/j.apor.2006.05.004
  2. Canuto, C., Hussaini, M., Quarteroni, A., & Zang, T. (1998). Spectral Methods in Fluid Dynamics. Springer Science & Business Media.
  3. Det Norske Veritas (DNV). (2010). Environmental Conditions and Environmental Loads (DNV-RP-C205). Det Norske Veritas.
  4. Dommermuth, D.G., & Yue, D.K.P. (1987). A High-order Spectral Method for the Study of Nonlinear Gravity Waves. Journal of Fluid Mechanics, 184, 267-288. https://doi.org/10.1017/S002211208700288X
  5. Dommermuth, D.G. (2000). The Initialization of Nonlinear Waves Using an Adjustment Scheme. Wave Motion, 32(4), 307-317. https://doi.org/10.1016/S0165-2125(00)00047-0
  6. Ducrozet, G., Bonnefoy, F., Le Touze, D., & Ferrant, P. (2016). HOS-ocean: Open-source Solver for Nonlinear Waves in Open Ocean Based on High-Order Spectral Method. Computer Physics Communications, 203, 245-254. https://doi.org/10.1016/j.cpc.2016.02.017
  7. Gatin, I., Vukcevic, V., & Jasak, H. (2017). A Framework for Efficient Irregular Wave Simulations Using Higher Order Spectral Method Coupled with Viscous Two Phase Model. Journal of Ocean Engineering and Science, 2(4), 253-267. https://doi.org/10.1016/j.joes.2017.09.003
  8. Fenton, J.D. (1985). A Fifth-order Stokes Theory for Steady Waves. Journal of Waterway Port Coastal and Ocean Engineering, 111, 216-234. https://doi.org/10.1061/(ASCE)0733-950X(1985)111:2(216)
  9. Kim, Y.J. (1993). Study of Nonlinear Wave Diffraction Using the 2-Dimensional Numerical Wave Tank. Journal of Ocean Engineering and Technology, 7(2), 187-196.
  10. Kim, D.Y. (2019). Statistical Analysis of Draupner Wave Data. Journal of Ocean Engineering and Technology, 33(3), 252-258. https://doi.org/10.26748/KSOE.2019.031
  11. Longuet-Higgins, M.S., & Cokelet, E.D. (1976). The Deformation of Steep Surface Waves on Water - I. A Numerical Method of Computation. Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 350(1660), 1-26. https://doi.org/10.1098/rspa.1976.0092
  12. Liam, L.S., Adytia, D., & van Groesen, E. (2014). Embedded Wave Generation for Dispersive Surface Wave Models. Ocean Engineering, 80, 73-83. https://doi.org/10.1016/j.oceaneng.2014.01.008
  13. Oh, S., Cho, S.K., Jung, D., & Sung, H.G. (2018). Development and Application of Two-dimensional Numerical Tank Using Desingularized Indirect Boundary Integral Equation Method. Journal of Ocean Engineering and Technology, 32(6), 447-457. https://doi.org/10.26748/KSOE.2018.32.6.447
  14. Shao Y.L., & Faltinsen O.M. (2014). A Harmonic Polynomial Cell (HPC) Method for 3D Laplace Equation with Application in Marine Hydrodynamics. Journal of Computational Physics, 274, 312-332. https://doi.org/10.1016/j.jcp.2014.06.021
  15. West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., & Milton, R.L. (1987). A New Numerical Method for Surface Hydrodynamics. Journal of Geophysical Research, 92(C11), 11803-11824. https://doi.org/10.1029/JC092iC11p11803
  16. Wu, G.X., Ma, Q.W., & Taylor, R.E. (1998). Numerical Simulation of Sloshing Waves in a 3D Tank Based on a Finite Element Method. Applied Ocean Resarch, 20(6), 337-355. https://doi.org/10.1016/S0141-1187(98)00030-3
  17. Zakharov, V.E. (1968). Stability of Periodic Waves of Finite Amplitude on the Surface of a Deep Fluid. Journal of Applied Mechanics and Technical Physics, 9, 190-194. https://doi.org/10.1007/BF00913182