I am building a 3D finite-element solver for NS turbulent equations (k-eps model). Should I use a fully coupled approch or traet k and eps as separeted problems ? Thanks !

(1). I think, it is all right to treat the turbulence model (equations) separtely in the loop. (2). This is because you may have to treat these equations in a different way. (different from that for the momentum and energy equations)

Treating the k and epsilon equations as loosely coupled (i.e. solved separately) is probably the way to go, especially to start with. The loosely coupled formulation works well for most problems and allows some flexibility in how you treat the k and epsilon equations.

Be aware, however, that some applications (flows with strong pressure gradients, shock interactions, or chemical reactions) may require a fully coupled (simultaneous solution) method to get a solution. This occurs because the solutions can become very numerically stiff.

Lastly, if you do use k-epsilon for such applications, make sure you understand the limitations of the model for such flows. David Wilcox's book "Turbulence Modeling for CFD" is a good place to start looking for this type of information.

"a fully coupled (simultaneous solution) method" means to solve each equation in the same iteration, is it right?

Fully coupled (as I mean it) is a simultaneous solution of ALL the equations (i.e. if you have a 3-D problem and are solving continuity, 3 momentum equations, an energy equation, and the k-epsilon equations, you would be solving a block matrix with each block having a size of 7x7).

The applications I'm thinking of relate to compressible flows. Hope that helps.