Computations of linear and nonlinear ship waves by higher-order boundary element method

Abstract

A practical method for computing ship waves accurately and efficiently is favorable for hull form optimization in early stage of ship design. In the present study, Rankine source method incorporated with high-order boundary element (HOBEM) discretization is applied to solve linear ship waves at first. Numerical implementation is described in detail. An incomplete LU factorization preconditioned Generalized Minimal Residual method (GMRES) is employed to solve the resulting boundary integral equation in order to improve efficiency. A corresponding Fortran program is developed for the validation study. It is applied to solve ship waves of different hulls, including slender Wigley hull, KRISO Container Ship (KCS) with relatively full form and a fishery patrol boat. Ship wave drag, sinkage, trim and wave pattern over a wide range of Froude numbers are all well predicted.In order to further investigate nonlinear effects on ship waves, a fully nonlinear potential flow method based on stationary iteration is proposed. The same numerical approach of HOBEM is employed. The combined nonlinear free surface condition is solved in each iteration to evaluate the free surface. Numerical investigation for Wigley and KCS hull shows the present nonlinear method are accurate. Comparison study with linear and partial nonlinear solution are also carried out and nonlinear effects on ship waves are detailedly discussed.