The application of finite element analysis to the solution of Stokes wave diffraction problems

Abstract

Newcastle upon Tyne NEI 7RU, U.K. SUMMARYA new finite-element based method of calculating non-linear wave loads on offshore structures in extreme seas is presented in this paper. The diffraction wave field is modelled using Stokes wave theory developed to second order. Wave loads and free surface elevations are obtained for fixed surface-piercing structures by solving a boundary value problem for the second-order velocity potential. Special attention has been given to the radiation condition for the second-order diffraction field. Results are presented for three test examples, the vertical cylinders of Kim and Yue and of Chakrabarti, and an elliptic cylinder. These results demonstrate that early problems with the application of second-order theory arising from inadequate radiation conditions have been overcome.

Absorbing boundary condition on elliptic boundary for finite element analysis of water wave diffraction by large elongated bodies

“…For q= 0°, F x and M y were reported in Clark et al [11] and therefore, these values are included in this table. For q =45°and 90°, only force values are presented.…”

“…The diffraction problem of prismatic vertical cylinders with elliptic cross section (see Figure 5) which extend from the sea bed to above the still water surface is employed in the numerical study because the diffracted waves in such a case consist only of propagating modes, which are implied in the radiation boundary condition and hence the boundary damper approximation. Since, in the literature an elliptic cylinder with aspect ratio 2 (a B /b B = 2) has been considered [4,11], this case is studied here for the purpose of validation using the dimensions given by Clark et al [11]. However, an aspect ratio of 2 is too small for an elongated body and therefore an elliptic cylinder with aspect ratio 8 (a B /b B = 8) has been considered for detailed numerical study.…”

“…Bando et al [4] and Clark et al [11] have presented finite element analysis of wave diffraction by cylinders using the damper equation (13a). Krishnankutty and Vendhan [5] employed the version in Equation (13b) in terms of the three-dimensional potential and validated the numerical performance of such damper equations employed on S R in the form of a circular cylindrical surface ( Figure 1).…”