Time domain Rankine-Green panel method for offshore structures

To solve the numerical divergence problem of the direct time domain Green function method for the motion simulation of floating bodies with large flare, a time domain hybrid Rankine-Green boundary element method is proposed. In this numerical method, the fluid domain is decomposed by an imaginary control surface, at which the continuous condition should be satisfied. Then the Rankine Green function is adopted in the inner domain. The transient free surface Green function is applied in the outer domain, which is used to find the relationship between the velocity potential and its normal derivative for the inner domain. Besides, the velocity potential at the mean free surface between body surface and control surface is directly solved by the integration scheme. The wave exciting force is computed through the convolution integration with wave elevation, by introducing the impulse response function. Additionally, the nonlinear Froude-Krylov force and hydrostatic force, which is computed under the instantaneous incident wave free surface, are taken into account by the direct pressure integration scheme. The corresponding numerical computer code is developed and first used to compute the hydrodynamic coefficients of the hemisphere, as well as the time history of a ship with large flare; good agreement is obtained with the analytical solutions as well as the available numerical results. Then the hydrodynamic properties of a FPSO are studied. The hydrodynamic coefficients agree well with the results computed by the frequency method; the influence of the time interval and the truncated time is investigated in detail.