Assessment of the performances and limitations of spacetime convective corrections for acoustic metacontinua design

The acoustic metamaterial extension to aeroacoustic applications is still an open issue principally due to the lack of a reliable methodology for the meta-devices design when they have to operate in a non-quiescent medium. One suitable strategy is to use spacetime coordinate transformations that include the background flow features to tune the meta-device design parameters analytically, and, therefore, the phenomenon must be reinterpreted into the spacetime. However, a change of coordinates capable of including all the convective effects is not known for general flow conditions and analytical approximations are inevitably introduced. This work validates the spacetime framework numerically, providing a better comprehension of the approximation effects on the spacetime-corrected acoustic metacontinuum and its cautious interpretation both from the mathematical and physical points of view.