Fully nonlinear water entry of a cone into waves with gravity effect has been analyzed based on a three-dimensional(3D)higher-order boundary method(HOBEM).The total velocity potential at the initial time is divided into the incident and scattering components.In the subsequent time steps,the solution of the velocity potential is defined as a whole through instantaneous boundary conditions.Based on the image theory,a modified Green function is applied to establish the integral equations so that only half of the calculation domain is considered and the seabed can be excluded.The free surface elevation is tracked along a given azimuth plane in the polar coordinate system,while the horizontal motion of the water particle is updated by using a segment-spring analogy method,which redistributes nodes and maintains mesh connectivity according to linear stiffness.An auxiliary function is applied to solve the pressure distribution,instead of directly calculating time derivative of the velocity potential.The high accuracy of the present numerical method is achieved through a detailed convergence study and comparison with results in the literature.Simulations are emphatically performed to examine the effects of gravity,wave nonlinearity,entry location,and oblique entry.
展开▼
