| Viscous free-surface flow phenomena near a surface-piercing body are of significant interest in naval architecture and offshore engineering. However, because of their complexity, these flow phenomena are not fully understood. Accurate and efficient methods to analyze them are lacking.;A pseudo-spectral method is developed for solving three-dimensional, unsteady viscous free-surface flows near a vertical circular cylinder. The Navier-Stokes equations governing such flow problems are treated using Chorin's projection method. The resulting Poisson equation for pressure is solved using a spectral collocation method in conjunction with a diagonalization technique. The momentum equations are solved using an ADI scheme, followed by a spectral collocation method. Extensive validations of this solution method are carried out. The Poisson equation solver is applied to solve Laplace equation for several inviscid free-surface flow problems of practical interest. Accurate numerical results are obtained with low computational efforts, establishing the accuracy and efficiency of this approach.;For the purpose validation, several viscous flow problems without free surface are first studied. Among them, high-resolution results for flows past an impulsively started cylinder are found to agree excellently with experimental data, at Reynolds number as large as 10... |
