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Article

A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves

1
Department of Marine Environmental Informatics, National Taiwan Ocean University, Keelung 20224, Taiwan
2
Department of Hydraulics and Ocean Engineering, National Cheng Kung University, Tainan 701, Taiwan
3
Tainan Hydraulics Laboratory, National Cheng Kung University, Tainan 709, Taiwan
4
Center of Excellence for Ocean Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
5
Department of Harbor & River Engineering, National Taiwan Ocean University, Keelung 20224, Taiwan
*
Authors to whom correspondence should be addressed.
Academic Editor: Anargiros I. Delis
Water 2021, 13(22), 3195; https://doi.org/10.3390/w13223195
Received: 26 October 2021 / Revised: 8 November 2021 / Accepted: 8 November 2021 / Published: 11 November 2021
(This article belongs to the Special Issue Hydrodynamics in Ocean Environment: Experiment and Simulation)
In this paper, an explicit time marching procedure for solving the non-hydrostatic shallow water equation (SWE) problems is developed. The procedure includes a process of prediction and several iterations of correction. In these processes, it is essential to accurately calculate the spatial derives of the physical quantities such as the temporal water depth, the average velocities in the horizontal and vertical directions, and the dynamic pressure at the bottom. The weighted-least-squares (WLS) meshless method is employed to calculate these spatial derivatives. Though the non-hydrostatic shallow water equations are two dimensional, on the focus of presenting this new time marching approach, we just use one dimensional benchmark problems to validate and demonstrate the stability and accuracy of the present model. Good agreements are found in the comparing the present numerical results with analytic solutions, experiment data, or other numerical results. View Full-Text
Keywords: non-hydrostatic; shallow water equations; meshless method; weighted-least-squares non-hydrostatic; shallow water equations; meshless method; weighted-least-squares
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MDPI and ACS Style

Wu, N.-J.; Su, Y.-M.; Hsiao, S.-C.; Liang, S.-J.; Hsu, T.-W. A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves. Water 2021, 13, 3195. https://doi.org/10.3390/w13223195

AMA Style

Wu N-J, Su Y-M, Hsiao S-C, Liang S-J, Hsu T-W. A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves. Water. 2021; 13(22):3195. https://doi.org/10.3390/w13223195

Chicago/Turabian Style

Wu, Nan-Jing, Yin-Ming Su, Shih-Chun Hsiao, Shin-Jye Liang, and Tai-Wen Hsu. 2021. "A Weighted-Least-Squares Meshless Model for Non-Hydrostatic Shallow Water Waves" Water 13, no. 22: 3195. https://doi.org/10.3390/w13223195

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