Aeroacoustic formulation based on compressible flow data applying Helmholtz´s decomposition

Aeroacoustic analogies, in combination with a hybrid approach, represent a computationally efficient way to predict sound radiation. The classical hybrid approach, of first performing an incompressible flow computation, evaluate the acoustic sources and finally compute the acoustic field does not consider any feedback of the acoustic field on the flow. Therefore, we propose the following adapted approach: (1) Perform a compressible flow simulation on a restricted domain, which incorporates two-way coupling of flow and acoustics; (2) Filter the flow data by Helmholtz´s decomposition, such that we obtain a pure non-radiating field, which the acoustic sources are computed with; (3) Perform the acoustic propagation computation. In this work, we present the theoretical fundamentals of this adapted hybrid approach and in particular Helmholtz´s decomposition of the flow data using the finite element method.