Abstract
The paper presents some new numerical investigations of the free-surface viscous flow around a submerged NACA 0012 hydrofoil based on the 2-D laminar incompressible Navier-Stokes equations by using the finite difference method where a composite grid system is applied.
A composite grid technique is proposed for the free-surface flow which has two parameters that describe the phenomenon: Reynolds number around the body and the Froude number. Because the latter is equivalent to the wave number or the wave length, the grid generation must meet the two different requirements according to these parameters. The physical domain is divided into several subdomains that are covered by different grids according to the main flow characteristics. Since the boundary condition is a Dirichlet-type one for all the component grids, the grids must overlap and the communication between them is realised by interpolation. The proposed numerical method is based on a Schwartz iterative procedure. The paper presents considerations concerning both interpolation and iteration processes. The results obtained by the present numerical scheme are compared with those obtained by the monoblock grid and show a good agreement.
The finite difference scheme is based on the use of the Euler-type kinematic boundary condition at the free-surface. The third order upwind difference scheme with the third derivative of the wave elevation is employed. The formulation is of a higher order of accuracy than those usually used where the position of the particle is determined locally. It takes into account the influence of the neighbouring particle movements, thus preserving the characteristics of the wavy motion. As a result, a faster elevation is obtained.
The flow still oscillates at the downstream and the zero-extrapolation is only valid for the viscous diffusion. Therefore an added dissipation zone is introduced as boundary condition at the downstream. Inside it waves are numerically damped within a certain range. As a result, instabilities determined by the numerical wave reflection are avoided.
