The numerical implementation approach (named NM_LSA) of the Neumann-Michell (NM) theory by using the Linear-semi-analytical method for panel integral is established to solve ship waves. The NM theory is a boundary-integral equation method, which is discretized by using 4-node isoparametric elements with linear flow potential distribution in this paper. To overcome the difficulty of panel integral of wave component in the Green function, the NM_LSA employs the analytical panel integral related to the elementary wave. The filter function based on parabolic extrapolation within a layer bordering the free surface is used to remove unwanted short waves. The analytical panel integral of elementary wave over a triangular panel is derived and applied to compute the spatial integral of wave potential.

In addition, another numerical implementation approach (named NM_LG) of the NM theory by using Linear-gauss method for panel integral is established. Two sets of filter parameters and five hulls are selected to validate the above mentioned numerical methods. The simulation results obtained by different numerical methods show good agreement with experimental measurements. Moreover, the time consumption of wave drag computation per Froude number via the NM_LSA is reduced by about 40 % compared to that via the NM_LG.

建立了Neumann-Michell(NM)理论的数值实现方法(NM_LSA)，采用面板积分的线性半解析方法求解船舶波浪。NM理论是一种边界积分方程方法，本文采用具有线性流势分布的4节点等参单元对其进行离散化。为了克服格林函数中波分量面板积分的困难，NM_LSA采用了与基波相关的解析面板积分。在与自由表面接壤的层内基于抛物线外推的滤波器函数用于去除不需要的短波。推导出基本波在三角形面板上的分析面板积分，并将其应用于计算波势的空间积分。

此外，还建立了NM理论的另一种数值实现方法（命名为NM_LG），该方法是利用Linear-gauss方法进行面板积分。选择两组滤波器参数和五个船体来验证上述数值方法。不同数值方法得到的模拟结果与实验测量结果吻合良好。此外，与通过 NM_LG 相比，通过 NM_LSA 计算每个弗劳德数的波浪阻力计算的时间消耗减少了约 40%。