Simulation of fully nonlinear water wave propagation over the flat bottom and uneven bottom by meshless numerical wave tank

A numerical wave tank (NWT) is developed by employing the local radial point interpolation collocation method, mixed Eulerian-Lagrangian approach, and the fourth-order Runge-Kutta method. The potential theory is used for a mathematical explanation of the wave-propagation problem. The Laplace equation in the Eulerian manner and the free surface conditions in the Lagrangian manner are used to simulate the fully nonlinear water waves. The incident waves are generated by imposing analytic forms of the potential on the upstream boundary. To avoid any reflection of the waves at the end of the tank, a damping zone is placed on the free surface before the downstream wall boundary. In order to demonstrate the efficiency and accuracy of the meshless NWT, the first-, second-, third-, and fifth-order Stokes waves are simulated and the numerical results are compared with the analytical solutions. In addition, the wave propagation of water waves in uneven bottom NWT is investigated. Fairly good agreements between the numerical results, the analytical solutions, and experimental data are observed.