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Fast multigrid method for solving incompressible hydrodynamic problems with free surfaces

James Farmer, Luigi Martinelli, A. Jameson

Abstract

We develop 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 flow 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

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Key concepts: Multigrid method, Free surface, Compressibility, Euler equations, Nonlinear system, Finite volume method, Flow (mathematics), Convergence (economics)