바닥의 움직임에 따른 비선형 파랑 생성의 모의를 위한 고차 스펙트럼법
A High-order Spectral Method for Simulation of Nonlinear Wave Generation due to Bottom Movement
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
연구에서는 바닥의 움직임에 따른 비선형 파랑 생성을 모의할 수 있는 고차 스펙트럼법을 제시하였다. 동역학적 및 운동학적 자유수면 경계조건을 지배방정식으로 하였으며, 각 경계조건의 비선형항은 유사 스펙트럼법을이용하여 실제 공간에서 연산한 후 Fourier 공간에서 다시 정의하였다. 지배방정식의 시간 적분은 4차 Runge-Kutta 법을 적용하여 해석하였다. 계산된 속도포텐셜은 Taylor 급수 전개를 통해 평균수면에서 다시 정의하였으며, 이는 연속방정식과 운동학적 바닥경계조건을 항상 만족한다. 실제 공간과 Fourier 공간에서의 연산을 위해 고속 Fourier 변환을 이용하였다. 모델의 정확도를 검증하기 위해 기존의 실험결과와 비교하였으며, 선형의 결과에 비해 실험결과와더욱 일치하였다. 최대 섭동차수(M)를 3차 이상 적용할 경우 결과는 거의 수렴하였다.
Abstract
In this study, we presented a high-order spectral method capable of simulating the generation of nonlinear waves due to bottom movement. The governing equations were based on dynamic and kinematic free surface boundary conditions, and the nonlinear terms of each boundary condition were calculated in physical space using a pseudo-spectral method, then redefined in Fourier space. The time integration of the governing equations was analyzed using the fourth-order Runge-Kutta method. The computed velocity potential was redefined at the mean water level through Taylor series expansion, which always satisfies the continuity equation and kinematic bottom boundary condition. Fast Fourier Transform was used for calculations in both physical and Fourier spaces. To verify the model's accuracy, we compared it with existing experimental results, which showed a closer match to experimental data than the linear results. When applying maximum perturbation order (M) of 3 or more, the results converged closely.
참고문헌 (25)
- Cooley, J. W., "The fast Fourier transform and it’s applications", IEEE Transactions on Education, 12(1), pp.27~34 (1969)
- Craig, W., "Numerical simulation of gravity waves", Journal of Computational Physics, 108, pp.73~83 (1993)
- Craig, W., "Hamiltonian long-wave expansions for water waves over a rough bottom", Proc. R. Soc. A, 461, pp.839~873 (2005)
- Dommermuth, D. G., "A high-order spectral method for the study of nonlinear gravity waves", Journal of Fluid Mechanics, 184, pp.267~288 (1987)
- Ducrozet, G., "A modified high-order spectral method for wavemaker modeling in a numerical wave tank", European Journal of Mechanics B, 2012, pp.34, 19~34
- Dutykh, D., "Linear theory of wave generation by a moving bottom", Comptes Rendus Mathematique, 343(7), pp.499~504 (2006)
- Fuhrman, D. R., "Tsunami generation, propagation, and run-up with a high-order Boussinesq model", Coastal Engineering, 56(7), pp.747~758 (2009)
- Gouin, M., "Development and validation of a non-linear spectral model for water waves over variable depth", European Journal of Mechanics B, 2016, pp.57, 115~128
- Guyenne, P., "A high-order spectral method for nonlinear water waves over moving bottom topography", SIAM Journal of Scientific Computation, 30(1), pp.81~101 (2007)
- Hammack, J. L., "A note on tsunamis : their generation and propagation in an ocean of uniform depth", Journal of Fluid Mechanics, 60(4), pp.769~799 (1973)
- Jung, J. -S., "A simplified numerical method for simulating the generation of linear waves by a moving bottom", Journal of Korean Society of Coastal and Ocean Engineers, 35(2), pp.41~48 (2023)
- Jung, J. -S., "Linear spectral method for simulating the generation of regular waves by a moving bottom in a 3-dimensional space", Journal of Korean Society of Coastal and Ocean Engineers, 36(2), pp.70~79 (2024)
- Jung, J. -S., "Generation of linear waves with bottom wave makers using analytical solution and extended mild-slope equations", Journal of Waterway Port Coastal and Ocean Engineering, 149(5), pp.04023013~ (2023)
- Klahn, M., "On the accuracy and applicability of a new implicit Taylor method and the high-order spectral method on steady nonlinear waves", Proc. R. Soc. A., 476, pp.20200436~ (2020)
- Lee, S.-J., "Generation of long water waves by moving disturbances", Ph.D., pp.1985
- Liu, Y., "On generalized Bragg scattering of surface waves by bottom ripples", Journal of Fluid Mechanics, 356, pp.297~326 (1998)
- Lu, H., "Modelling of long waves generated by bottom-tilting wave maker", Coastal Engineering, 122, pp.1~9 (2017)
- Oh, S., "Higher-order spectral method for regular and irregular wave simulations", Journal of Ocean Engineering and Technology, 34(6), pp.406~418 (2020)
- Pham, V. K., "Numerical simulation of submarine landslide-induced tsunami using two-layer extended Boussinesq equations", Proc. 4th Int. Conf. on Sustainability in Civil Engng., ICSCE 2022, 344, pp.235~241 (2022)
- Reeve, D. E., "Experimental study of wave trains generated by vertical bed movements", Applied Ocean Research, 147, pp.103971~ (2024)
- Saad, Y., "GMERS : A generalized minimal residual algorithm for solving nonsymmetric linear systems", SIAM Journal of Scientific Computation, 7(3), pp.856~869 (1986)
- Seiffert, B. R., "Simulation of breaking waves using the high-order spectral method with laboratory experiments : wave-breaking energy dissipation", Ocean Dynamics, 68(1), pp.65~89 (2018)
- West, B. J., "A new numerical method for surface hydrodynamics", Journal of Geophysical Research: Oceans, 92(C11), pp.11803~11824 (1987)
- Wu, T. Y. T., "Generation of upstream advancing solitons by moving disturbances", Journal of Fluid Mechanics, 184, pp.75~99 (1987)
- Zakharov, V. E., "Stability of periodic waves on finite amplitude on the surface of a deep fluid", Zhurnal Prikladnoi Mekhaniki I Technicheskoi Fiziki, 9(2), pp.86~94 (1968)