Publication

Abstract : This paper presents a stabilized finite element method for the solution of incom-pressible two-phase flow problems in three dimensions using a level set method. The interface between the two phases is resolved using the level set approach de-veloped by Sethian [1], Sussman, Smereka and Osher [2], and Sussman et al. [3]. In this approach the interface is represented as a zero level set of a smooth function. The stabilized upwind Petrov-Galerkin method was used to discretize the governing flow and level set equations. The continuum surface force (CSF) model proposed by Brackbill et al. [4] was applied in order to account for surface tension effects. To restrict the interface from moving while re-distancing, an improved re-distancing scheme proposed in the finite difference context [3] is adapted for finite element discretization. This enables us to accurately compute the flows with large density and viscosity differences, as well as surface tension. The capability of the resultant algorithm is demonstrated with two and three dimensional numerical examples of a single bubble rising through a quiescent liquid, and two bubble coalescence.