Adjoint-based optimization of sound reinforcement including non-uniform flow

The determination of optimal geometric arrangements and electronic drives of loudspeaker arrays in sound reinforcement applications is an ill-posed inverse problem. This paper introduces an innovative method to determine complex driving functions, also considering complex environmental conditions. As an alternative to common frequency domain methods, the authors present an adjoint-based approach in the time domain: Acoustic sources are optimized in order to generate a given target sound field. Instead of the Helmholtz equation, the full non-linear Euler equations are considered. This enables an easier treatment of non-uniform flow and boundary conditions. As proof of concept, a circular and a linear monopole array are examined. For the latter, the environmental conditions include wind and thermal stratification. For all examples, the method is able to provide appropriate driving functions.