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Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions

Author

Listed:
  • Ji Huang

    (College of Ocean Engineering, Guangdong Ocean University, Zhanjiang 524088, China
    Doctoral Degree Program in Ocean Engineering Technology, National Taiwan Ocean University, Keelung 20224, Taiwan)

  • Chia-Ming Fan

    (Department of Harbor and River Engineering and Computation and Simulation Center, National Taiwan Ocean University, Keelung 20224, Taiwan)

  • Jiahn-Horng Chen

    (Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung 20224, Taiwan)

  • Jin Yan

    (College of Ocean Engineering, Guangdong Ocean University, Zhanjiang 524088, China)

Abstract

The propagation of nonlinear water waves under complex wave conditions is the key issue of hydrodynamics both in coastal and ocean engineering, which is significant in the prediction of strongly nonlinear phenomena regarding wave–structure interactions. In the present study, the meshless generalized finite difference method (GFDM) together with the second-order Runge–Kutta method (RKM2) is employed to construct a fully three-dimensional (3D) meshless numerical wave flume (NWF). Three numerical examples, i.e., the propagation of freak waves, irregular waves and focused waves, are implemented to verify the accuracy and stability of the developed 3D GFDM model. The results show that the present numerical model possesses good performance in the simulation of nonlinear water waves and suggest that the 3D “RKM2-GFDM” meshless scheme can be adopted to further simulate more complex nonlinear problems regarding wave–structure interactions in ocean engineering.

Suggested Citation

  • Ji Huang & Chia-Ming Fan & Jiahn-Horng Chen & Jin Yan, 2022. "Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions," Mathematics, MDPI, vol. 10(6), pages 1-22, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:1007-:d:775953
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    References listed on IDEAS

    as
    1. Ji Huang & Hongguan Lyu & Chia-Ming Fan & Jiahn-Hong Chen & Chi-Nan Chu & Jiayang Gu, 2020. "Wave-Structure Interaction for a Stationary Surface-Piercing Body Based on a Novel Meshless Scheme with the Generalized Finite Difference Method," Mathematics, MDPI, vol. 8(7), pages 1-22, July.
    2. Hong-Guan Lyu & Peng-Nan Sun & Xiao-Ting Huang & Shi-Yun Zhong & Yu-Xiang Peng & Tao Jiang & Chun-Ning Ji, 2022. "A Review of SPH Techniques for Hydrodynamic Simulations of Ocean Energy Devices," Energies, MDPI, vol. 15(2), pages 1-48, January.
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