The short answer is: the mathematical description. To be clear, Fluent has three multiphase models that are based on an Eulerian framework, also called an Euler-Euler approach: Volume of Fluid (VOF), Mixture, and Eulerian models. In this context, the term “Eulerian” is used for the mathematical description used, but also for one specific model. In general, “Eulerian” means that you are representing some field quantity as a continuous variable that exists on a computational mesh. In contrast, “Lagrangian” is a different framework in which discrete objects (like particles) are followed/tracked through a domain by solving F = ma at their location, rather than solving a governing equation on a background mesh. This is why the Discrete Particle Model in Fluent is referred to as an “Eulerian-Lagrangian approach”: the carrier fluid is solved on an Eulerian mesh, while the discrete particles are tracked in Lagrangian fashion. Now back to VOF versus the Eulerian model in Fluent: even though both models fall within the Eulerian class of models, they are very different in terms of the way the governing equations are solved. VOF is suitable for flows that have a clearly defined phase interface, with a radius of curvature that is everywhere much larger than the mesh size. It is formulated in a way that this interface is explicitly captured in the domain, so the two phases are not interpenetrating and cannot mix. The Eulerian model has a very different formulation that does not explicit capture the interface, thus you do not need to have the interface exist on length scales much larger than the mesh. The two continuous phases are assumed to be interpenetrating continua (e.g., Eulerian could be used to simulate a bubbly flow with bubbles that are smaller than the mesh size, while VOF could not).