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 acous-
tic 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 ob-
tain a pure non-radiating field, which the acous-
tic 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 Helm-
holtz´s decomposition of the flow data using the
finite element method.