i am confuse / is it true that a time dependent navier-stokes eqn. can simulate a full turbulent flow which called Directed Numerical Simulation(DNS) ?

then what is" Large Eddy Simulation:LES" , and Is turbulent model such as k-epsilon the subset of LES ?

thank all

It may confuse you that it is TURE a time-dependent NS code can simmulate a full turbulne flow. But the motion of any scale in the turbulent flow should be resolved spartially and temporally. It often requiers a large grid even in a simple flow and small time step. Basic criteria can be given by Kolmogorov theory. You can find them in many turbulence book like written by Pope.

The question about the LES is not for me to explain in single sentence. May you can find the suitable explanation of the review papers in annual review of fluid mechanics written by the P. Moin or Germano. I cannot remind the volume and page of the article but we can search them on the annual review homepage.

BDO

To do DNS one has to employ a grid that is capable of resolving the smallest eddy (a length scale where the the inertial forces ballances the viscous forces), This typically means a grid size of the order Re^(3/2). Hence there is no need to employ any turbulent model. Essentially in DNS one employ a laminar NS solver on very fine grid in time dependence manner.

LES is similar to DNS in the sense that the simulation is time dependent. Unlike DNS, the grid can be made much coarser as long as the grid size fall inside Kolmogorov inertial length scale. Hence LES requires a "turbulence model" to deal with eddies that are smaller than the grid size. (Normally called Sub-grid Sclae model). The governing equation is formed by filtering to separate the numerically resolve scales and the sub-grid scale. In practice filtering is often a function of the grid size. Thus LES is grid dependent!!! Theoretically LES should be a lot cheaper than DNS, but in prcatice for a simple wall bounded flow (e.g. flow between two parallel wall) a good LES would cost 1 order of magnitude lower than DNS.

K-epsilon is normally used for RANS or URANS, both employs grid that is coarser than LES. RANS is normally a time-independent turbulent simulation. URANS is also called very Large Eddy Simulation. K-epsilon is normally used in this class of turbulent flow simulation. This method is a lot cheaper than either LES or DNS.