Steady state simulations in Computational Fluid Dynamics (CFD), which rely on implicit time integration, are not experiencing great accelerations on GPUs. Moreover, most of the reported acceleration effort concerns solving the linear system of equations while neglecting the acceleration potential of running the entire simulation on the GPU. In this paper, we present the software implementation of an implicit RANS CFD solver, which is fully running on GPU. We use the GMRES linear solver of the Paralution package combined with the incomplete LU factorization for the preconditioning. We propose also a control mechanism -on-demand factorization - capable of reducing the number of times an incomplete LU factorization is performed. The on-demand factorization accelerates the linear solver without altering the flow convergence. The GPU implementation achieved a speedups of 9.2x compared to a single-core CPU and 3.5x compared to a 4-cores CPU for 3-D flow predictions in turbine applications.