Vertical integral method incoporated with multi-domain HOBEM for time domain calculation of hydrodynamics of forward speed SHIP

Abstract

A vertical integral method incorporated with multi-domain higher-order boundary element method (MDHOBEM_VI) is proposed for time domain calculation of hydrodynamics of ship advancing in waves. To solve the initial boundary value problem of hydrodynamics, the fluid domain is decomposed by an imaginary vertical control surface into the inner and the outer domain, in which the Rankine panel method (RPM) and transient Green's function (TGF) method are used, respectively. By present method, the defects of RPM and TGF are avoided and the advantages of them are inherited. The range of discretization is reduced and the radiation condition is satisfied analytically by TGF, while stable and convergent calculation is obtained near waterline and more exact forms of linearization of free surface condition can be imposed by RPM. Due to the imaginary vertical control surface hired in this multi-domain method, the double integral of Green's function over vertical rectangular panel can be easily transformed into single integral of vertical lines. During the calculations, the kernel functions of both Green's function and its derivatives on vertical lines are conducted by ordinary differential equations (ODEs) method previously, which is more stable and of high efficiency.FORTRAN programs are coded originally to fulfill this method. To validate the accuracy of such vertical integral method, simple cases for integral on line and panel are calculated, and results agree well with Gaussian point integral on line and panel. By MDHOBEM_VI, hydrodynamics and motions of three types of ship including math model Wigley-III, ship with flare S175 and full form ship 50500T are investigated in regular waves, as well as ship added resistance. Results show good agreement with experiment data and the advantage in efficiency is significant. Long time simulation for ship motions and added resistance of S175 in irregular waves are studied. Time series of average value of added resistance are plotted and the envelope shows convergence along with time. The mean value is coincident with results in other literature. It indicates that MDHOBEM_VI is a method with enough accuracy and high efficiency, which is suitable for long time simulation of ship motions and added resistance in both regular and irregular waves.