  In this work we present a reduced basis Smagorinsky turbulence model for
steady flows. We approximate the non-linear eddy diffusion term using the
Empirical Interpolation Method, and the velocity-pressure unknowns by an
independent reduced-basis procedure. This model is based upon an a posteriori
error estimation for Smagorinsky turbulence model. The theoretical development
of the a posteriori error estimation is based on previous works, according to
the Brezzi-Rappaz-Raviart stability theory, and adapted for the non-linear eddy
diffusion term. We present some numerical tests, programmed in FreeFem++, in
which we show an speedup on the computation by factor larger than 1000 in
benchmark 2D flows.
