A Localized Finite-Element Method for the Nonlinear Steady Waves Due to a Two-Dimensional Hydrofoil

An application is described of the localized finite-element method to a steady nonlinear free-surface flow past a submerged two-dimensional hydrofoil at an arbitrary angle of attack. The earlier investigations with the linear free-surface boundary condition have shown some disagreement between the computed results and the experimental measurements for the cases of shallow submergence. The aim of this paper is to investigate the effect of the nonlinear free-surface condition for the cases where the linear results show disagreement with the experimental measurements. The computational method of solution is the localized finite-element method based on the classical Hamilton's principle. In the present study, a notable step is introduced in the matching procedure between the fully nonlinear and the linear subdomains. The numerical results of wave resistance, lift force, and circulation strength are presented. The computed pressure distributions on the hydrofoil and wave profiles are shown and compared with the experimental measurements and also with the linear computational results. The present computed results show better agreement with the experimental results. In some cases, however, a difficulty in the convergence of the iterative solution procedure was experienced. This difficulty in the convergence may be due to the limit of the range of the existence of the true solution in potential-flow formulation.