A formulation to introduce acoustic waves from a control surface using volumetric source terms is proposed for numerical simulations. A general expression of the source terms is derived from the non-linear Euler equations. The method is validated through three academic configurations: the injection of oblique plane waves and the radiation of a monopole source in two and three dimensions, in uniform flow. The governing equations are solved in a Cartesian grid using a low-dispersion and low-dissipation high order finite-difference numerical scheme. However, the control surface has an arbitrary shape, as demonstrated here with the use of a cylindrical surface. Numerical results show good agreement with analytical solutions in both phase and amplitude. The method is then applied to an open-fan aircraft engine configuration. The source terms are computed from a cylindrical control surface enclosing the rotor, based on data extracted from a previous fluid mechanics simulation. The radiated acoustic field is compared with the one obtained using the Ffowcs Williams–Hawkings integral formulation. The two solutions are again found in good agreement for this more realistic configuration.
Coco et al. (2026) studied this question.