NUMERICAL STABILITY ANALYSIS FOR TIME-DOMAIN SHIP MOTION SIMULATIONS

This paper studies the numerical stability of Newton's rigid-body equa tions of motion for a ship advancing in waves in the time domain. The strong memory effects associated with the free-surface flow and the de pendence of the fluid force upon the ship displacement, velocity, and acceleration introduce a degree of complexity not encountered in ordin ary differential equations free of strong memory effects. Drawing upon the physics of the continuous problem, a rational stability theory is developed that permits the development of stable and efficient integr ation methods of the multi-step or Runge-Kutta variety. Upper bounds f or the time step are derived and the resulting performance of various integration schemes is demonstrated in motion simulations for realisti c ships.