Green's Function Discretization Scheme for Sound Propagation in Nonuniform Flows

Abstract

A new frequency-domain discretization technique that permits the numerical solution of the equation governing the propagation of small disturbances within nonuniform potential flows is described. The method can be applied successfully to the numerical solution of aeroacoustic problems because a good accuracy is preserved up to 3-4 points per period for three-dimensional unstructured meshes. The discretization scheme is based on a local interpolation formula that is strictly joined to the physics of wave propagation because It is constructed with the superimposition of elementary sources that are local solutions of the local convective wave equation. The method presents aspects in common with both finite difference and finite element methods, with the peculiarity that the local interpolation formula can be interpreted as a specific shape function introduced to take advantage of the physics of the problem. The method is applied to the potential equation linearized around an arbitrary aerodynamic mean flow, and several comparisons with theoretical results, as well as several convergence tests, are conducted to show that a good accuracy is preserved up to 3-4 points per period also for irregular meshes with both random and Systematic distortions. Numerical calculations are presented for three-dimensional problems with both uniform and nonuniform flow, and comparisons are made with theoretical and other available numerical results. With the appropriate generalizations, the method can be regarded as a new, efficient general approach for the discretization of generic partial differential equations.