Numerical Imitation For Unsteay Fluid Flow With Free Surface

The problem of the free-surface flows is being one of focus and difficulty in hydrodynamics. The key to discover the character of the free-surface flows depends on developing and perfecting methods and instruments. In this paper kinds of methods to solve problem of the free-surface flows were reviewed firstly, especially those methods of numerical calculation, and their advantage and also the disadvantage were analyzed respectively, and then the VOF method which is applied in this paper to track the flowing of free-surface is introduced in detail.Has generalized the basic character of 2-D unsteady fluid flow with multiple free boundaries, this paper established the numerical model on it, including continuity equation and momentum equation (N-S equation) as control equations of key flow field and using the volume of fluid function as assistant equation.Considering the character of the problem to solve, finite-difference method is used to approximate the predicting equations, and the difference schemes are listed as follows:(1) Momentum equation approximation is received by a linear combination of one order upwind difference scheme andcentered difference scheme with a parameter a that controls therelative amount of each one. When a=0 , this approximation reduces to a second order accurate, centered-difference approximation. When a=1, the first order upwind differenceform is recovered. And the basic procedure for advancing a solution through one increment in time is implemented by a pressure iteration method;(2) The finite-difference approximation used for the continuity equation is an implicit relation.(3) The VOF method is adopted in tracking the free-surface. The governing equation for the Volume of Fluid is solved by Donor-Acceptor method. The calculation results show that it can predict the surface transformation of wave.Additionally, at each step the F function defining fluid regions must be updated to give the new fluid configuration, this is a very important content in tracking the free-surface. In thispaper, the location and orientation of free-surface within surface cells are related to the F values of these surface cells and the Fvalues in the neighbor cells. And because we consider that the orientation of free-surface in those surface cells is only one, it is assumed that the boundary can be approximated by a straight-line cutting through the cell.The transmittal of the 2-D breaking bore in elevation and the tidal movement in factual seas are simulated by the model. And the results are compared with theoretical and experimental values respectively. It shows that the calculation results agree reasonably with the theoretical and experimental values.