Some numerical studies of interface advection properties of level set method

In this paper, we discuss the results of a series of tests carried out to assess the level set methodology for capturing interfaces between two immiscible fluids. The tests are designed to investigate the accuracy of convection process, the preservation of interface shape, and the mass conservation properties of individual fluids. These test cases involve the advection of interfaces of different shapes exposed to translation, rotation, deformation, and shear flow. Prescribed solenoidal velocity fields are used and no attempt is made to couple the advection of the level set function with the momentum equations. For the solution of level set equation we have employed first-order upwind scheme, MacCormack method, second-order ENO scheme, and fifth-order WENO scheme. Our studies show that the level set method perform well when higher-order schemes are used for the solution of advection equation. However, for certain type of shearing and vortical velocity fields mass conservation is an issue on coarser meshes even with higher order schemes. Finer mesh must be used in such situations to reduce numerical diffusion.