A Numerical Solution Of N-S Equation With Free Surface Flow

The free surface flow problems are commonly found out in the fields of chemical, metallurgy, aviation and aerospace and material science. In this process, the position of the free surface changes along with the movement of liquid, moreover, the movement of the free surface has a great influence on the system.it has become a great concern in the field of fluid dynamics.The task of this paper is to study the movement of the free surface associated flow of an incompressible viscous Navier-Stokes equations solution. For the free interface flow volume,we use the VOF (volume of fluid) to track the free interface motion changes,the basic idea of which is that a volume fluid function which satisfies convection function, is defined in whole flow flied. When the cell is empty, the function equals 0; when the cell is full, the function equals 1; when the cell contains interface, the function between 0 and 1. We compare with four kinds of methods to solve VOF function:Hirt & Nichols method, Integral mean type TVD scheme, FCT method and Youngs method. By comparison of four methods, detailed description of the four methods in dealing with free surface flow problems in accuracy, efficiency, good or bad. And gives numerical simulation resultsOf four ways to cut farm field and translation field.Through theoretical analysis,this paper deduceds two-dimensional incompressible vis-cous flow navier-stokes equations, and introduces four major numerical solution, including projection method, artificial compressibility method, pressure poisson equation method and pressure correction algorithm, solving the navier-stokes equations. Staggered grid in-troduced in the processing speed and pressure coupling process of the specific application, can effectively solve the speed and pressure on the same appear in a grid Chessboard prob-lem of unreasonable pressure field.Besides, we give the discrete form of the navier-stokes equations and the form of pressure correction equation in the staggered grid. Using time difference forwards and convection-dispersion central difference format. To speed up the convergence velocity and pressure, in particular the process of solving the corresponding amendments to the pressure and velocity relaxation techniques. In the last, we give an example of a driver of party cavity flow simulation results to verify the effectiveness of the algorithm.