The present work addresses the coupling of a flamelet database that can accurately represent the flame structure in composition space with a low-Mach approximation of the Navier-Stokes equations. An advancement of the CFI combustion model, which is currently based on laminar premixed flamelets, is used for chemistry tabulation. This model can be applied to different combustion regimes from premixed to non-premixed combustion, although this work is concentrated on turbulent premixed flames for Reynolds-averaged Navier-Stokes (RANS) and large-eddy simulations (LES). A premixed confined jet flame, which has been investigated experimentally at the German Aerospace Center (DLR) is used for validation in adiabatic conditions showing satisfactory agreement.