FAST MULTIGRID METHOD FOR SOLVING INCOMPRESSIBLE HYDRODYNAMIC PROBLEMS WITH FREE SURFACES

The focus of this work is the development of a finite-volume multigrid Euler scheme for solving three-dimensional, fully nonlinear ship wave problems. The flowfield and the a priori unknown free surface location are calculated 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 now via a novel iteration strategy that allows temporary leakage 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 scheme is validated by comparing the numerical results with experimental results for the Wigley parabolic hull. Waterline profiles from bow to stern are in excellent agreement with the experimental results. The computed wave drag compares favorably with both theory and experiment for a wide range of Froude numbers. Overall, the present method proves to be accurate and efficient.