In this paper, the Hermite-type radial point interpolation method (RPIM) is proposed to develop the meshless numerical wave tank (NWT) for simulating the propagation of fully nonlinear water waves. The Hermite-type interpolation scheme, the radial basis functions (RBFs), and the polynomial functions are used to construct shape functions. These shape functions have better stability and can use any distribution nodes in the computational domain. The strong form of governing equation is transformed to a linear system of algebraic equations by the collocation approach. The material node approach is used to describe the fully nonlinear free surface boundary conditions, and the fourth-order Runge-Kutta (RK4) scheme is applied to update the free surface particles and the velocity potential. The numerical results are compared with other available solutions to confirm the accuracy and efficiency of the proposed numerical procedure. In addition, the accuracy and stability of Hermite-type RPIM compared with RPIM in this study. The numerical results demonstrate that good improvement in the accuracy of the numerical results is obtained after using the Hermite interpolation scheme.

本文提出了一种Hermite型径向点插值方法（RPIM），以开发用于模拟完全非线性水波传播的无网格数值波箱（NWT）。Hermite型插值方案，径向基函数（RBF）和多项式函数用于构造形状函数。这些形状函数具有更好的稳定性，并且可以使用计算域中的任何分布节点。通过搭配方法将控制方程的强形式转换为代数方程的线性系统。材料节点方法用于描述完全非线性的自由表面边界条件，四阶Runge-Kutta（RK4）方案用于更新自由表面粒子和速度势。将数值结果与其他可用解决方案进行比较，以确认所提出数值程序的准确性和效率。此外，与本研究相比，Hermite型RPIM的准确性和稳定性。数值结果表明，使用Hermite插值方案后，数值结果的准确性得到了很好的提高。