A set of Compact Disturbance Equations (CDE) is developed for high-accuracy and efficient jet flow and noise simulations. The CDE in their complete form are an exact rearrangement of the Navier-Stokes (NS) equations, but incorporate various linear and nonlinear disturbance equations such as the Linearized Euler Equations (LEE) and Linearized Navier-Stokes (LNS) equations. Their attractive mathematical properties facilitate the implementation of the CDE in existing CFD solvers. The reduced equations can be implemented in essentially the same form with minor modifications, and thus can be coupled seamlessly to solve problems that include viscous and nonlinear effects as well as situations where these effects are unimportant. The CDE have been implemented as another hybrid RANS/LES method. A high-resolution Large Eddy Simulation (LES) in a reduced domain can be embedded inside a less expensive Reynolds-averaged Navier-Stokes (RANS) solution of flow in a larger, possibly very complex, configuration. This results in reduced meshing difficulty and computational cost for complex configurations, an optimal grid design for the unsteady turbulent flow and noise simulations, and a more accurate non-reflecting boundary treatment. Two benchmark tests are simulated to show the computational efficiency and accuracy. Excellent agreement with analytical solutions or the experimental measurements is obtained.