Numerical Method For The Simulation Of Viscous Flow Of Fluid With Moving Interface

A numerical method for the solutions to two-phase viscous incompressible flow of fluid with moving interface is presented. The moving surface is supposed to be the interface of water and air and is described as the zero level set of a smooth function. The density and the viscosity of air and water are used in the two phase respectively and are smoothed at the interface properly. The Navier-Stokes(N-S) equations in the two phase are solved simultaneously to obtain the velocity. The N-S equations are solved by Level Set method which can be used to capture the interface implicitly and based on fixed grid,the second order projection method,the second order ENO (Essentially Non-Oscillatory) scheme and high-order upwind difference scheme. The Level Set equation is solved by CIP (Cubic-Interpolated Pseudoparticle) method. Adams-Bashform method is used for discreting the N-S equations in time. A treatment of the Level Set method allows us to include large density and viscosity ratios as well as surface tension. The motions of dam-break and air bubble in water are considered. The evolution of the moving interface and the contour of the velocity are given. The interface existing and the flow field characteristic are thought simultaneously. This method is used to capture the breaking,the merging and the other changes of the interface efficiently. Numerical results are presented to demonstrate the effectiveness of this method for simulating the viscous flow of fluid with the moving interface.