Buoy relay method for instantaneous fluid flow with free surface

Several methods have been used to approximate free surface boundaries in finite difference numerical simulations. Each of these methods has its advantages and disadvantages. This paper presents a new technique for the numerical solution of transient incompressible free surface fluid flows, This powerful method, which is based on the concepts of “Buoy positioning” and “Buoy relaying”, successfully represents the free surface using a Lagrangian method on a Eulerian grid by directly solving the free surface evolution equation. The Eulerian finite difference forms of the full Navier Stokes equations are solved by the Successive over Relaxation (SOR) method with a set of buoys to keep track of the free surface. The capabilities of the analysis procedure are demonstrated through viscous free surface fluid flow examples. The method is simpler and more efficient than other methods especially in treating complicated free boundary configurations.