Ship motions using single-phase level set with dynamic overset grids

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor–corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.