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A numerical procedure is developed for the simultaneous implicit numerical solution of the coupled A>£ and Navier-Stokes equations for compressible viscous flows. The numerical algorithm is based on the approximate factorization scheme of Beam and Warming for the strongly coupled set of equations. The scheme incorporates a new second-order Jameson type damping model that enhances the stability and relieves the stiffness associated with the solution to the A>e equations. The model, which is based on the changes in both pressure and turbulent kinetic energy, eliminates the need to use subiteration techniques. Unsteady calculations were performed for supersonic flow over an open cavity at a freestream Mach number of 1.5 and Reynolds number of 1.09 X 10 6 . The computed results are compared with experiments and predictions from computations using uncoupled A>E and Navier-Stokes equations.Nomenclature E = total energy / = Jacobian of coordinate transformation k = turbulent kinetic energy P = static pressure t = time u, v = Cartesian velocities jc, y = Cartesian coordinates 8 = turbulent dissipation rate £, rj = curvilinear coordinates p = density

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