An investigation on HOBEM in evaluating ship wave of high speed displacement ship

Abstract

A practical numerical tool is developed to evaluate ship waves of high speed displacement ships on the basis of potential flow theory, in which high order boundary element method (HOBEM) based on biquadratic shape functions is applied to solve the boundary value problem. Since the sinkage and trim of ship at high speeds are notable, influences of ship attitude on wave drag are investigated and three kinds of models are used to evaluate them. To make the numerical approach highly efficient, an incomplete LU factorization preconditioner is adopted and incorporated with the restarted generalized minimal residual method GMRES (m) to solve the boundary integral equation. A corresponding Fortran code is developed and applied to evaluate ship waves of the Wigley hull and 4a model, a transom stern ship. Computations are performed for both monohulls and catamarans over a wide range of Froude numbers (Fr = 0.10 - 1.00) . Numerical issues including mesh convergence and computational efficiency are investigated at first. Computed results of the wave drag, sinkage and trim show generally good agreement with experimental data. Reasonable wave patterns are obtained and physical phenomena that wake angle φmax, where the largest waves occur, would become narrow at high speeds is also captured by the present computations. Numerical results indicate the proposed method would be accurate and efficient to evaluate resistance for hull design of high speed displacement ship.