Tham khảo tài liệu 'practical ship hydrodynamics episode 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Numerical example for BEM 251 Figure Coordinate system used sources i are located inside contour 2. There is atmospheric pressure everywhere on the free surface z dynamic condition . Then Bernoulli s equation yields ột C 2 V 2 - gK 0 3. There is no flow through the free surface kinematic condition . the local vertical velocity of a particle coincides with the rate of change of the surface elevation in time ộz Kt 4. Differentiation of the dynamic condition with respect to time and combination with the kinematic condition yields ộtt C ộyộyt C ộz zt - gộz. 0 This expression can be developed in a Taylor expansion around z 0. Omitting all non-linear terms yields then ộtt - gộz 0 5. There is no flow through the body contour . the normal velocity of the water on the body contour coincides with the normal velocity of the hull or respectively the relative normal velocity between body and water is zero n - VỘ n v Here v is the velocity of the body n is the outward unit normal vector. 6. Waves created by the body must radiate away from the body lim ộ Re O e kze - klyD y i p is here a yet undetermined but constant amplitude. Using the harmonic time dependency of the potential we can reformulate the Laplace equation and all relevant boundary conditions such that only the time-independent complex amplitude of the potential Ộ appears 252 Practical Ship Hydrodynamics Laplace equation 0 yy C zz 0 for z 0 Decay condition lim ro 0 z 1 Combined free surface condition 0 C j z 0 at z 0 g The body boundary condition is here explicitly given for the radiation problem of the body in heave motion. This will serve as an example. The other motions sway roll and the diffraction problem are treated in a very similar fashion. The body boundary condition for heave is then nr irnen2 n2 is the z component of the two-dimensional normal vector n. The radiation condition for ộ is derived by differentiation of the initial radiation condition for Ộ with respect to y and z respectively. The .
