Hello Dr. George, please allow me to answer.

Second moment turbulence models belong to RANS methodologies. Reynolds stress or stress transport models lie with in this category.

Thank you for your reply.

http://onlinelibrary.wiley.com/doi/10.1002/fld.1650090806/abstract

solution method is pressure velocity coupling,

solver - pressure-based, SIMPLE (semi-implicit method pressure linked Eqs.)

method of a discretization is second order upwind;

Reynolds Stress Models are a direct consequence from the RANS philosophy. In that equations a  Third Moment is generated, and closures must be applied.  If the 3rd moments are solved, a 4th moment is generated ( and 27 new variables), as so on. It is called the closure problem of turbulence.  LES is another thought, you solve some scales and model the subgrid  scales. The mesh is projected to capture a specific frequency. 

Thank you for your answer. I think I understand now. For RSM (or second moment closure) we solve additional partial differential equations for the Reynolds stresses but there is still the closure problem. I am wondering if the results with RMS will be better than the eddy viscosity approach in order to justify the additional computational time that we will need to solve the new diferrential equations.

Very difficult to say that this way you get better results....RANS is a formulation strongly depending on the type of problem you solve thus you can have some problems where simple closure is good enough.

Definitely you will get better results in comparison to EVM's. Through RSM you can get complete turbulence structure, since we are solving six additional transport equations for each independent components of Reynold stress. but computational cost will be high.

I have concluded that for basic research in high Reynolds number problems (where computational time is not a problem) it is better to use LES and then RSM. For practical problems (where computational time is crucial) it is better to use RANS.

Reynolds average navier stokes equation   and large eddy simulations models could be used for your problem .