Multiphase flows imply interface interactions. Two approaches to describe the interface evolution in space and time: Lagrangian (interface tracking) and Eulerian (interface capture).
The Lagrangian methods are based on the use of markers. For this type of approach, the interface can be tracked either by markers indicating the presence/absence of fluid, or by markers defined only on the interface, for which the motion is tracked.
Eulerian methods use a fixed mesh to solve the fluid’s and interface’s progression equations. For this kind of method, the interface is marked though the amount of scalar quantity transported by the local velocity field. Among these methods, one can distinguish the Level Set tracking methods and the Volume Of Fluid (VOF) methods and alike (VOF‐PLIC, VOF‐TVD).
The literature is rich in documentation related to this subject.
Both Euler and Lagrangian models are available in CFD codes (Fluent Ansys, Star CCM+, OF, etc...).
In most of cases we use 2 fluids Euler model. It is less exepensive in terms of calculation time.
VOF is quite expensive. We use it when it is important to capture interfaces (gas jets in liquids for example). There is a paper on my profil published in CES journal (2017) about such modeling using OpenFoam.