Abstract: A numerical method is developed for the simulation of three dimensional viscous rotor stator interactions in turbomachinery.The governing equations are three dimensional unsteady Navier Stokes equations in absolute frame of reference with velocity components relative to blade fixed rotating coordinates.The simple Baldwin Lomax two layer algebraic model is adopted to account for the turbulence effects.Central type finite volume method with anisotropic artificial viscosity is used for the spatial discretization of the governing equations.An efficient implicit time marching scheme is proposed in terms of dual time stepping technique.This time marching scheme is in similar form to Runge Kutta method with residual smoothing but it does not need any free parameter and runs faster than traditional four stage Runge Kutta scheme.At the interfaces of rotor grids and stator grids,a conservative method is developed for the evaluation of numerical flux.The proposed method has been applied to simulating the three dimensional viscous rotor/stator interactions in a subsonic turbine stage under different rotational speed and rotor/stator distance.The numerical results agree favorably with the experimental data.