LES, DNS and RANS

Sas

Would anyone please explain the basic discrete difference among the above three. What I understant is, in LES the smaller scale (smaller than the grid) are modeled using some turbulence model like Smagorinsky model or dynamic model, DMM etc and NS equations are directly solved on the grid level. In DNS, these models are not used and the NS equations are directly solved with any turbulence closure. To resolve the smallest eddy, one needs a fine mesh. What about RANS ??? What is the meaning of time average NS equations..? Any type of comments will be appreicated. Sas.......