  We use density functional theory plus dynamical mean-field theory (DFT+DMFT)
to study multiple control parameters for tuning the metal-insulator transition
(MIT) in CaVO$_3$ thin films. We focus on separating the effects resulting from
substrate-induced epitaxial strain from those related to the reduced thickness
of the film. We show that tensile epitaxial strain of around 3-4% is sufficient
to induce a transition to a paramagnetic Mott-insulating phase. This
corresponds to the level of strain that could be achieved on a SrTiO$_3$
substrate. Using free-standing slab models, we then demonstrate that reduced
film thickness can also cause a MIT in CaVO$_3$, however, only for thicknesses
of less than 4 perovskite units. Our calculations indicate that the MIT in such
ultra-thin films results mainly from a surface-induced crystal-field splitting
between the $t_{2g}$-orbitals, favoring the formation of an orbitally-polarized
Mott insulator. This surface-induced crystal-field splitting is of the same
type as the one resulting from tensile epitaxial strain, and thus the two
effects can also cooperate. Furthermore, our calculations confirm an
enhancement of correlation effects at the film surface, resulting in a reduced
quasiparticle spectral weight in the outermost layer, whereas bulk-like
properties are recovered within only a few layers away from the surface.
