Tham khảo tài liệu 'practical ship hydrodynamics episode 13', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Boundary element methods 231 usually the panel centre. The resistance predicted by these methods is for usual discretizations insufficient for practical requirements at least if conventional pressure integration on the hull is used. Soding 1993b proposed therefore a variation of the traditional approach which differs in some details from the conventional approach. Since his approach uses also flat segments on the hull but not as distributed singularities he called the approach patch method to distinguish it from the usual panel methods. For double-body flows the resistance in an ideal fluid should be zero. This allows the comparison of the accuracy of various methods and discretizations as the non-zero numerical resistance is then purely due to discretization errors. For double-body flows the patch method reduces the error in the resistance by one order of magnitude compared to ordinary first-order panel methods without increasing the computational time or the effort in grid generation. However higher derivatives of the potential or the pressure directly on the hull cannot be computed as easily as for a regular panel method. The patch method introduces basically three changes to ordinary panel methods patch condition Panel methods enforce the no-penetration condition on the hull exactly at one collocation point per panel. The patch condition states that the integral of this condition over one patch of the surface is zero. This averaging of the condition corresponds to the techniques used in finite element methods. pressure integration Potentials and velocities are calculated at the patch corners. Numerical differentiation of the potential yields an average velocity. A quadratic approximation for the velocity using the average velocity and the corner velocities is used in pressure integration. The unit normal is still considered constant. desingularization Single point sources are submerged to give a smoother distribution of the potential on the hull. As .
