PTEBEM And Its Application In Ocean Engineering Analysis

With the rapid development of floating structures in Ship and Ocean Engineering,the demand for hydrodynamic analysis is continuously increasing,and the importance of second order wave loads have become increasingly prominent.Researchers have also encountered two problems.The first one is the accuracy of induced velocity at the non-smooth boundary.The error would be extremely large for source method(SM),which leads to divergence in the numerical simulation.The proposal and development of the first order Taylor expansion boundary element method(TEBEM)has solved this problem.The innovation of this method is to introduce the first order Taylor expansion term of the distributed dipole and close the equations by supplementing the partial derivative of the boundary integral equation with respect to the field point.Compared with the traditional constant panel method,the numerical accuracy of the tangential induced velocity is greatly improved by TEBEM,especially at the non-smooth boundary such as sharp corners.However,too many unknowns are introduced in TEBEM,which requires a lot of computational resources with low computational efficiency.It is particularly important to seek a method with higher efficiency and similar precision.The second one is to meet increasingly complex requirements,floating structures in finite water depth have gradually entered view of researchers and have been receiving more and more attention.Since the second order directives of Green's function are needed in TEBEM,which is significantly difficult to calculate.Therefore,how to accurately calculate the finite water depth Green's function and its derivatives is very important.The numerical method of the finite water depth Green's function is also the key research content.Based on the traditional first order TEBEM,the partial Taylor expansion boundary element method(PTEBEM)is proposed in this paper to improve computational efficiency of TEBEM.And the interior boundary value problem and the frequency domain second order hydrodynamic problem of KVLCC2 ship in deep water depth have been studied in this paper;At the same time,the Gauss-Laguerre integration combined with infinite water depth Green's function and exponential integral function is used to illustrate the numerical integration of finite water depth Green's function,and the second order hydrodynamic problem of floating cylinder in finite water depth is analyzed and studied.First,by analyzing of the integral equation,geometric characteristics and meshing strategy corresponding to the non-smooth boundary,an automatic solution of non-smooth boundary panels marking is introduced in the PTEBEM method,which can accurately capture the first layer non-smooth boundary panels of the model.And multi-layer expansion is also very easy.The study of the interior boundary value problem shows that by marking non-smooth boundary panels and only retaining the Taylor expansion terms corresponding to the panels,the numerical accuracy almost equivalent to the TEBEM method can be obtained,and a smaller linear algebraic equation system is formed by PTEBEM method,which effectively reduces the complexity,and the computational efficiency has been significantly improved.For the key parameters in the PTEBEM method,this article also presented recommended values.Then,the PTEBEM method and SM are used to study the irregular frequency phenomenon of KVLCC2 ship in deep water depth,and the extended boundary integral method(EBIM)is used to eliminate the irregular frequency.The results show that,the large error of velocity potentials at waterline calculated by SM occurs,both in trend and in value.And the maximum of velocity is concentrated.And using EBIM,the irregular frequency phenomenon is effectively eliminated,the maximum of velocity are no longer concentrated,and the distribution is more smooth.And compared to the SM,the PTEBEM method can give more accurate results,which is in good agreement with the far-field formula,and the PTEBEM method is more efficient than the TEBEM method.Totally 80%of the elapsed time of solving linear algebraic equations by TEBEM is saved.Finally,the integral method of Green's function and its high order directives in the frequency domain of finite water depth is studied in this paper,and it is applied to the study of the diffraction problem of a floating cylinder in finite water depth.The Gauss-Laguerre integral combined with infinite water depth Green's function and exponential integral function is used in numerical integral method of Green's function.In the diffraction problem of a floating cylinder in finite water depth,the semi-analytical solution is used as a reference value.Numerical results show that the PTEBEM method can guarantee at least one to two significant digits when calculating the pure second order diffraction force,which can meet the needs of engineering analysis;In addition,the PTEBEM method is better than the TEBEM method in efficiency,and its advantages are more obvious in actual analysis.