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

Huang, Ji; Fan, Chia-Ming; Chen, Jiahn-Horng; Yan, Jin

doi:10.3390/math10061007

Open AccessArticle

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

¹

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

²

Doctoral Degree Program in Ocean Engineering Technology, National Taiwan Ocean University, Keelung 20224, Taiwan

³

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

⁴

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

^*

Author to whom correspondence should be addressed.

Mathematics 2022, 10(6), 1007; https://doi.org/10.3390/math10061007

Submission received: 13 February 2022 / Revised: 13 March 2022 / Accepted: 15 March 2022 / Published: 21 March 2022

(This article belongs to the Special Issue Numerical Methods for Computational Fluid Dynamics)

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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.

Keywords: meshless method; generalized finite difference method; nonlinear water waves; numerical wave flume; transient extreme waves; irregular waves; focused waves

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MDPI and ACS Style

Huang, J.; Fan, C.-M.; Chen, J.-H.; Yan, J. Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions. Mathematics 2022, 10, 1007. https://doi.org/10.3390/math10061007

AMA Style

Huang J, Fan C-M, Chen J-H, Yan J. Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions. Mathematics. 2022; 10(6):1007. https://doi.org/10.3390/math10061007

Chicago/Turabian Style

Huang, Ji, Chia-Ming Fan, Jiahn-Horng Chen, and Jin Yan. 2022. "Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions" Mathematics 10, no. 6: 1007. https://doi.org/10.3390/math10061007

APA Style

Huang, J., Fan, C.-M., Chen, J.-H., & Yan, J. (2022). Meshless Generalized Finite Difference Method for the Propagation of Nonlinear Water Waves under Complex Wave Conditions. Mathematics, 10(6), 1007. https://doi.org/10.3390/math10061007

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

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