Numerical investigation of the fully nonlinear wave force on a vertical cylinder in shallow water using Green-Naghdi theory

A finite element model based on high-level Green-Naghdi (GN) theory is developed and used to investigate the nonlinear wave force on a vertical cylinder. In this model, auxiliary variables are introduced to remove the third spatial derivative terms in the governing equations of GN theory to employ the Galerkin finite element method with linear elements. The impermeability boundary condition is exactly satisfied on the curved cylinder surface by a direct numerical method. The stream-function theory is used to generate nonlinear incident waves, and a relaxation zone is placed near the outer boundary to absorb the reflected waves. Numerical results are compared with experimental data, demonstrating the accuracy of the present method. Numerical simulations were carried out to examine the influences of the ratio of wave height to water depth, the ratio of water depth to wavelength, and the ratio of cylinder radius to wavelength on the wave force on the vertical cylinder.