Ewert, R. and W. Schröder, Acoustic perturbation equations based on flow decomposition via source filtering. Journal of Computational Physics, 2003. 188(2): p. 365-398.
idea
It is derived by rewriting the governing flow equations such that the left-hand side is given by the APE-1 system while the right-hand source side is defined by the remaining terms. The variant of the acoustic perturbation equations demonstrated in the figure below is APE-1.
The purpose is to find sources qc and qm of the APE-1 system and that can be easily computed from a compressible flow simulation without solving a Poisson equation. The figure below shows the APE-4.
As usual whenever acoustic analogies are applied, the viscous terms in the source are assumed to be of negligible importance. Furthermore, as evidenced in Section 4.4 the non-linear and entropy terms are of minor importance considering vortex sound problems. Then, the major vortex source term is the Lambvector.