Zero-frequency added mass of submerged bodies with near-surface effects

The added mass of ships, submarines, and marine platforms is a primary quantity of interest to understand vessel dynamics and motion. For low-frequency maneuvers at low forward speed, the water surface acts as a wall and the added-mass depends on the proximity to the free-surface. In this paper a method for efficiently determining the full six-degree-of-freedom zero-speed added-mass tensor is presented for bodies that are on or near a wall boundary. The method is based on solving the unsteady Euler equations from rest for one time step to find the generalized added-mass force. The method is based on the work of el Moctar (2022) but in this paper it is simplified to use a static grid, and thereby extended for general six degree-of-freedom motion. The method is validated for a series of canonical problems with analytical solutions that include a circular cylinder that is both deeply submerged and near a wall, and a spheroid that extends from a wall. The method is further validated by computing the added mass for a very-large-crude carrier that is in finite-depth water. Finally the method is used to compute the full six degree-of-freedom added-mass tensor for the Joubert BB2 Submarine for deep submergence and near the water surface.