Numerical implementation of the Neumann-Michell theory incorporating with the analytical panel integral for ship waves

Abstract 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.