Level Set Based Finite Element Method of Bubble-in-Liquid Simulation

As far as the author knows, few papers have been reported for the level set simulation of a two-phase (bubble-in-liquid or liquid droplet-in-gas) flow based on unstructured background mesh. Almost all existing studies are based on structured mesh using finite difference or finite volume method as spatial discretization. Therefore, the application of existing various level set methods based on structured mesh to a bubble-in-liquid flow problem in a complex geometry is not straightforward. In the present study, a level set based two-phase flow code has been developed using finite element discretization, which can be utilized for the analysis of a bubble-in-liquid flow problem in a complex geometry. Since the finite element method has been employed for the spatial discretization of governing equations, unstructured mesh can be naturally adopted for the level set simulation of a bubble-in-liquid flow without an additional load for the code development except that solution methods of the hyperbolic type redistancing and advection equations of the level set function should be devised in order to give a bounded solution on unstructured mesh. In this study, some issues of the level set simulation based on finite element method for a bubble-in-liquid flow problem are discussed including the discretization of the hyperbolic type equations using SUPG type formulation and a three-dimensional benchmark problem of a bubble-in-liquid motion have been solved and compared with the existing results. It has been shown that the present bubble-in-liquid simulation method based on FEM gives a satisfactory solution with the level set method alone while the other researches based on finite difference/volume method use a combined level-set/volume-of-fluid method (CLSVOF) or solve another equation of the volume conservation constraint in order to circumvent a volume loss/gain problem in a level set simulation.