Compact disturbance equations for aeroacoustic simulations

A set of compact disturbance equations is developed for high-accuracy and efficient aeroacoustic simulations. The compact disturbance equations in their complete form are an exact rearrangement of the Navier-Stokes equations, but incorporate various linear and nonlinear disturbance equations such as the linearized Euler equations and the linearized Navier-Stokes equations. Their attractive mathematical properties facilitate the implementations of the full compact disturbance equations and the reduced equations in essentially the same form as in existing computational fluid dynamics solvers with minor modifications. A high-resolution unsteady simulation in a reduced domain can be embedded inside a less-expensive Reynolds-averaged Navier-Stokes solution of flow in a larger, possibly very complex, configuration. This results in a hybrid Reynolds-averaged Navier-Stokes/large-eddy simulation method with reduced meshing difficulties and computational costs, but improved grid qualities and more accurate boundary treatments for complex configurations. Furthermore, a seamless switch can be made between the embedded governing equations. This enables a novel closely coupled computational fluid dynamics/computational aeroacoustics approach for complex aeroacoustic applications, where the full Navier-Stokes equations can be recovered in the source region to capture the turbulent noise sources and the linearized Euler equations can be applied to simulate the noise propagation and possible reflection more accurately and efficiently. These benefits are demonstrated with three benchmark tests and excellent results are obtained.