A FAST MULTIGRID METHOD FOR SOLVING THE NONLINEAR SHIP WAVE PROBLEM WITH A FREE SURFACE

This paper presents a finite volume method for the solution of the three dimensional, nonlinear ship wave problem. The method can be used to obtain both Euler and Navier-Stokes solutions of the flow field and then a prior unknown free surface location by coupling the free surface kinematic and dynamic equations with the equations of motion for the bulk flow. The evolution of the free surface boundary condition is linked to the evolution of the bulk flow via a novel iteration strategy that allows temporary leakage of mass through the surface before the solution is converged. The method of artificial compressibility is used to enforce the incompressibility constraint for the bulk flow. A multigrid algorithm is used to accelerate convergence to a steady state. The two-layer eddy viscosity formulation of Baldwin and Lomax is used to model turbulence. The scheme is validated by comparing the numerical results with experimental results for the Wigley parabolic hull and the Series 60, Cb=0.6 hull. Waterline profiles from bow to stern are in excellent agreement with experiments. The computed wave drag compares favourably with experiments.