The acceleration potential in fluid-body interaction problems

The velocity potential phi is commonly used when solving fluid-body interaction problems. The acceleration potential d phi/dt is a supplementary concept that offers several advantages. It increases temporal accuracy when solving large-amplitude motions numerically. It also results in better time-stepping stability when solving body equations of motion in the time-domain. The acceleration-potential formulation requires solving the velocity-potential problem first, and in many interesting cases increases accuracy and stability while improving overall computational efficiency. This paper reviews various formulations of the acceleration potential found in potential-flow hydrodynamics. For brevity, only the radiation-problem is considered where waves are due to the motion of the body. First, the velocity-potential problem is stated, including conventions and coordinate systems. The form of the rigid-body equations of motions is briefly discussed, as well as the coupling to the hydrodynamic problem. The various acceleration-potential formulations are reviewed and compared mathematically. Analytic and numerical solutions are also evaluated and analyzed. The computer simulations include convergence studies and large-amplitude motions. Finally, conclusions are presented discussing the applicability and advantages of the methods described, as well as the general use of the acceleration potential.