How to implemment numerically the k-epsilon model?
 

I've worked with the shallow water equations (depth averaged) but now I need to include a turbulence model. I've checking the k-epsilon model and I see that it solves a transport equation for the kinetic energy. If a want to add this model to my system, that means solving simultaneously for the velocity and all the variables involved in the turbulence model?
That also would mean that I need initial conditions for all those variables, right?
Is the solution for this new system also discretized in the same way as I have done it for the SWE without turbulence or should I use a specific discretization based on the turbulence model?
I'm working with finite volume method.