I am into computational fluid dynamics and so far I've found that the most common approaches to solve for the governing equations are Eulerian and Lagrangian. The former samples the domain at fixed locations while the latter samples the domain using the particles moving freely across the domain.
Reading through some pdf's over the net someone mentioned about mesh-based methods but as far as I could see they were very close to what the Eulerian approach is (if not the same).
Could someone clarify is there is indeed a difference between what is called Grid-Based methods (like Finite differences) and Mesh-Based methods (like ???) ?