LevelSet Methods For Moving Interfaces

There are essentially two techniques for approximating the interface: interface tracking methods and interface capturing methods. The main difference between the two methods is that interface tracking methods are Lagrangian, while interface capturing methods are Eulerian. Volume of fluid methods (VOF) and LevelSet methods are the two most important techniques of interface capturing. This paper is to research the application of LevelSet Methods in simulating the moving interfaces.In this paper, VOF methods and LevelSet methods are described in details, and the Taylor-Galerkin finite elements methods is used to discrete the LevelSet equation. Furthermore, both TG-LevelSet methods and WENO-LevelSet methods are used to solve the LevelSet equation by C++ language. This paper compares the results by TG-LevelSet methods, WENO-LevelSet methods and Youngs-VOF methods in the constant, revolving as well as shear flow fields, and shows that both TG-LevelSet and WENO-LevelSet methods are better than Youngs-VOF methods in capturing interfaces. Especially, WENO-LevelSet methods are good at simulating for stability in the revolving flow fields, while TG-LevelSet methods for reducibility in shear flow fields.On most physical phenomena (such as flame interfaces, shock wave interfaces), physical variables will jump across the interfaces, so solving the the jump conditions correctly plays an important role in simulation. Since the direct methods for solving the derivative of physical variables near interfaces will cause unconvergence, numerical smearing, ambiguous interfaces and even faulty physical computational results, Ghost techniques are used to obtain the derivative of physical variables near interfaces reasonably in this paper. Based on Rankine-Hugoniot jump conditions across interfaces, flame interfaces jump conditions are deduced. SMAC, a kind of original variable MAC methods, is a better method to solve unsteady Navier-Stokes equations. It is proved that the program of SMAC by the writer is valid in solving classical cavity driven flow. This paper uses SMAC method for Navier-Stokes equations, Ghost technique for jump condition and LevelSet Methods for capturing interfaces to simulate merging problems of flame interfaces in one and two dimensions. All of these methods are prove to be available in this paper.Continuum surface force (CSF) modal essentially is used to handle surface tension and Ghost technique for solving surface tension by jump pressure across interfaces are introduced in detail. Fluent, commercial CFD software, uses VOF method and CSF modal to simulate interfaces affected by surface tension, while LwFlow program uses LevelSet method and Ghost technique. It is shown that LwFlow program combined SMAC method, Ghost technique and LevelSet methods can get the same results as the Fluent, besides, conservativeness of LevelSet methods is better than VOF in mass changing rates, so the idea of this paper is reasonable.At the last part of this paper, schemes and algorithm involved in LwFlow program are described briefly.