Application of generalized finite difference method to propagation of nonlinear water waves in numerical wave flume

In this paper, a numerical wave flume is formed by combining the generalized finite difference method (GFDM), the Runge-Kutta method, the semi-Lagrangian technique, the ramping function and the sponge layer to efficiently and accurately analyze the propagation of nonlinear water waves. On the basis of potential flow, the mathematical description of wave propagation is a time-dependent boundary value problem, governed by a Laplace equation for velocity potential and two nonlinear free-surface boundary conditions. The incident waves are introduced by imposing horizontal velocity along upstream boundary, as a sponge layer is placed at the end of flume to absorb wave energy and avoid any reflection of waves. The GFDM, a newly-developed meshless numerical method, and the second-order Runge-Kutta method were, respectively, adopted for spatial and temporal discretizations of the moving-boundary problems. The GFDM, which is truly free from mesh generation and numerical quadrature, is easy-to-program, straightforward and efficient, especially for moving-boundary problems. Four numerical examples are adopted in this paper to validate the stability, the efficiency and the accuracy of the proposed meshless numerical wave flume. The GFDM results were compared with other numerical solutions and experimental data to verify the merits and robustness of the proposed meshless numerical model.