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Numerical solutions of waves-current interactions by generalized finite difference method

机译：广义有限差分法求解波流相互作用的数值解

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摘要

In this paper, a meshless numerical wave flume, based on the generalized finite difference method (GFDM), is adopted to accurately and efficiently simulate the interactions of water waves and current. The GFDM, a newly-developed meshless method, is truly free from mesh generation and numerical quadrature. The proposed meshless numerical wave flume is the combination of the GFDM, the second-order Runge-Kutta method, the semi-Lagrangian approach, the sponge layer and the ramping function. The problems of wave-current interactions in flumes with horizontal and inclined bottoms are accurately and stably investigated by the proposed meshless scheme, respectively. The changes of waveform can be obviously found, while the cases of coplanar, opposing and no currents are stably simulated. Besides, the distribution of steady current in the flume with inclined bottom, which is governed by an inverse Cauchy problem, is acquired by the GFDM in a stable manner. Numerical results of wave-current interactions are compared with other solutions to verify the accuracy of the proposed meshless scheme. Additionally, different parameters of the proposed meshless numerical scheme are examined to validate the consistency and stability of the proposed numerical wave flume for solutions of wave-current interactions. (C) 2018 Elsevier Ltd. All rights reserved.
机译：本文采用基于广义有限差分法（GFDM）的无网格数值波槽，可以准确有效地模拟水波与水流的相互作用。 GFDM是一种新开发的无网格方法，真正摆脱了网格生成和数值正交的困扰。拟议的无网格数值波槽是GFDM，二阶Runge-Kutta方法，半拉格朗日方法，海绵层和斜坡函数的组合。通过提出的无网格方案，分别准确，稳定地研究了水平和倾斜底部水槽中的波流相互作用问题。可以清楚地发现波形的变化，同时可以稳定地模拟共面，反向和无电流的情况。此外，GFDM以稳定的方式获得了由反柯西问题控制的，底部倾斜的水槽中稳定电流的分布。将波流相互作用的数值结果与其他解决方案进行比较，以验证所提出的无网格方案的准确性。此外，检查了所提出的无网格数值方案的不同参数，以验证所提出的数值波浪槽的波动和相互作用的稳定性和稳定性。 （C）2018 Elsevier Ltd.保留所有权利。

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