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.

采用局部径向点插值搭配方法、混合欧拉-拉格朗日方法和四阶龙格-库塔方法开发了数值波浪水池（NWT）。势论用于波传播问题的数学解释。使用欧拉方式的拉普拉斯方程和拉格朗日方式的自由表面条件来模拟完全非线性的水波。入射波是通过在上游边界上施加势能的解析形式而产生的。为了避免水箱末端的波浪反射，在下游壁边界之前的自由表面上放置了一个阻尼区。为了证明无网格 NWT 的效率和准确性，第一个、第二个、第三个、并模拟了五阶斯托克斯波，并将数值结果与解析解进行了比较。此外，还研究了水波在不平坦底部 NWT 中的波传播。观察到数值结果、解析解和实验数据之间相当好的一致性。