Numerical calculations of hydrodynamic forces on large offshore structures are often based on the method of integral equations and require a discretization of the submerged surface of the structure into a large number of facets. The accuracy of numerical results is influenced significantly by the precision of this discretization, and the accuracy using moderate levels of discretization may be improved by using suitable extrapolation schemes. In the present paper, two such schemes, the Shanks transformation and the Richardson extrapolation, are summarized, and the improvements obtained by applying them are compared for a number of fundamental cases. The Richardson extrapolation scheme is found to provide a notable increase in the accuracy of hydrodynamic coefficient estimates using more moderate levels of discretization.
Wave loads on large fixed offshore structures are usually calculated by solving a linear wave diffraction problem based on the assumptions of an inviscid fluid and an irrotational flow. Likewise, the estimation of the response of a large floating offshore structure to external excitation, such as from waves, earthquakes or impact, requires a knowledge of added masses and damping coefficients, which are in turn obtained by solving the corresponding linear wave radiation problem. For structures of arbitrary shape, the diffraction and radiation problems are usually solved numerically by the method of integral equations, in which the submerged surface of the structure is represented by a finite number of facets and the distribution of flow variables over this surface is approximated by point values at the facet centroids. Thus the precision of the discretization may have a significant effect on the accuracy of the numerical results. Sarpkaya and Isaacson (1981) have summarized guidelines on the size and distribution of facets. In brief, a larger number of facets yields more accurate results, but at the expense of increased computer time and storage requirements.
