Directional sound source modeling using the adjoint Euler equations in a finite-difference time-domain approach

An adjoint-based approach for synthesizing complex sound sources by discrete, grid-based monopoles in finite-difference time-domain simulations is presented. Previously, Stein, Straube, Sesterhenn, Weinzierl, and Lemke [(2019). J. Acoust. Soc. Am. 146(3), 1774-1785] demonstrated that the approach allows one to consider unsteady and non-uniform ambient conditions such as wind flow and thermal gradient in contrast to standard methods of numerical sound field simulation. In this work, it is proven that not only ideal monopoles but also realistic sound sources with complex directivity characteristics can be synthesized. In detail, an oscillating circular piston and a real two-way near-field monitor are modeled. The required number of monopoles in terms of the sound pressure level deviation between the directivity of the original and the synthesized source is analyzed. Since the computational effort is independent of the number of monopoles used for the synthesis, also more complex sources can be reproduced by increasing the number of monopoles utilized. In contrast to classical least-square problem solvers, this does not increase the computational effort, which makes the method attractive for predicting the effect of sound reinforcement systems with highly directional sources under difficult acoustic boundary conditions.