Two extensions to Lighthill’s aeroacoustic analogy are presented. First, equivalent sources due to initial conditions are derived that supplement those due to boundary conditions, as given by Ffowcs Williams & Hawkings. The resulting exact inhomogeneous wave equation is then reformulated with pressure rather than density as the wave variable, and the right-hand side is rearranged using the energy equation with no additional assumptions. Applications to computational aeroacoustics are discussed, and illustrated with examples based on 2D and 3D simulations
