A multigrid method for three-dimensional steady and time-resolved viscous free surface flows

In the present work, a robust and efficient algorithm for the computation of steady and time-dependent viscous fluid flow about advancing ships is developed.; The baseline numerical algorithm couples the method of artificial compressibility with a finite volume cell-center discretization of the Reynolds Averaged Navier-Stokes equations. A very efficient multigrid time-stepping scheme with residual smoothing and local time-stepping is implemented, resulting in an algorithm with fast convergence rates. A multiblock grid strategy is chosen to provide flexibility in mesh topologies which enables accurate resolution of complex hull shapes. Fully nonlinear treatment of the wave field is provided by conforming the grid to the free surface shape. Enhanced resolution of the waves is supported by the utilization of a local extrema diminishing (LED) discretization of the kinematic equation which is fully coupled to the multigrid cycles of the bulk flow solver. This core scheme is implemented for solution on parallel computers using the method of domain decomposition. Speedup curves demonstrate high parallel scalability. The resulting computational tool is highly efficient and provides fast and accurate solutions of fluid flow about general hull shapes.; The steady state method is validated using experimental data for the Series60 C_b = .6 hullform. Accurate numerical results for ship resistance, wavefield, and boundary layers are shown. The time-dependent method is validated with several model problems in addition to a comparison with experimental data for the Wigley hullform in regular headwaves.