Mathematical modeling and numerical simulation of two-phase flows using Fourier pseudospectral and front-tracking methods: The proposition of a new method

In the present work, an extension of the Fourier Pseudospectral Method coupled with the Immersed Boudary Method for non-periodic problems (IMERSPEC) applied to numerical simulation of two-phase flow was developed. The proposed method was originally developed for single-phase, incompressible flow. Here, the method is extended to two-phase flows using the front-tracking method (IMERSPEC-FT) to model fluid-fluid interfaces. The proposed method was verified and validated through results involving spurious currents, mass conservation and numerical experiments analysis for rising bubbles. IMERSPEC-FT is shown to be a promising scheme for the two-phase computational fluid dynamics (CFD).