An implicit predictor–corrector method is presented for the simultaneous integration of the six degrees of-freedom
(DOF) equations of motion for a manoeuvring submarine and the unsteady Reynolds-Averaged
Navier Stokes (URANS) equations describing the vehicle hydrodynamics. The novel method uses
coefficient-based hydrodynamic models for estimating the Jacobian matrix for Newton iteration. The
method is applied to emergency rising and horizontal plane zig-zag manoeuvres. It is shown to converge
faster at each timestep than under-relaxed fixed-point iteration with an optimum relaxation parameter.
A simple model containing only primary linear hydrodynamic coefficients that are relatively easy to estimate
or measure was found to be adequate for modelling the Jacobian matrix in these simulations.
2014 Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence,
2014. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license