Numerical Simulation Of Wave Action On Structures Using The Time-Domain Green Function

A three-dimensional time-domain approach is used to study the wave loads and motion of bodies. In this approach, the exact body boundary condition is satisfied on the wetted body surface while the free-surface boundary conditions are linearized. The problem is solved by using a transient free-surface Green function source distribution. The velocity potential is obtained numerically from a discretized boundary integral equation on the body surface, using a high-order boundary element method.The method is based on using the transient free-surface Green function. Accurate and fast computation of the Green function and its derivations is a hard job. This study is concerned with the Green function and its derivations. Asymptotic expansions and convergent ascending-series expansions for the Green function and its derivations are obtained to replace the numerical evaluation of the relevant integrals. Analysis is required to develop suitable forms for representing singular features when both the source and field points lie on the free surface. A computational approach based on the use of multidimensional Chebyshev polynomial approximations, which greatly decreases the computing cost in numerical evaluation of the Green function, is used. To accelerate the computation further, Chebyshev polynomials can be converted into simpler equivalent ordinary polynomials. In the whole domain the Green function is rapidly oscillatory and includes singularity. It is not very effective to approximate the Green function in the whole domain directly. The approach used in the paper is to divide the physical domain into several zones, and use different approximations in each zone. The flexibility in truncation can be exploited to preserve the form of the polynomial approximations in different sub domain. The polynomial approximation is compared with the directly computing approach. It is found that the algorithm of Chebyshev polynomial approximation with not too many terms can achieve a desired accuracy.Extensive results are presented which validate and demonstrate the efficacy of the method. These results include linear motion and forces without forward speed. Results of diffraction and radiation of a hemi-sphere, a sphere, a cylinder, a box and a taper are presented. The present computations agree with analysis solutions and frequency domain results very well.