A Body-Exact Strip Theory Approach to Ship Motion Computations.

Abstract

A body-exact strip theory is developed to solve nonlinear ship motion problems in the time-domain. The hydrodynamic model uses linearized free surface conditions for computational efficiency and stability, and exact body boundary conditions to capture events such as slamming and submergence. The strip theory approach is used to speed up computations and reduce the difficulty in modeling complex geometries. A nonlinear rigid body equation of motion solver is coupled to the hydrodynamic model to predict ship responses in large waves.

Constant source strength flat panels are used to model the body and desingularized sources are used on the free surface. At each time-step, a mixed boundary value problem is solved. The free surface and rigid body motions are evolved using a fourth-order Adams-Bashforth time-stepping technique. The acceleration potential is used to increase numerical accuracy and highlight the coupling between the hydrodynamic and rigid body motion problems, improving stability.

The problem formulation is comprehensive, and details of numerical techniques are included. Two-dimensional problems are used to study the accuracy and convergence of the method. Strip theory results include a variety of hull forms: two Wigley models (I and III), a Series-60 hull, the ITTC standard S-175 containership, and two naval vessels. This emphasizes the robust capabilities of the method and presents a variety of analyses for discussion. The two-dimensional and strip theory results include small and large amplitude motions. Comparisons to experiments and other numerical methods are shown and discussed, when possible. In several cases, a variety of alternative solution techniques are shown to highlight improvements or differences in problem formulation.

The results obtained show good agreement with previous computational and experimental results. The method developed is accurate, robust, very computationally efficient, and can predict nonlinear ship motions. It is well suited to be used as a tool in ship design or as part of a path optimization model.