Using reduced hydrodynamic models to accelerate the predictor–corrector convergence of implicit 6-DOF URANS submarine manoeuvring simulations

Abstract

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.