Numerical assessment of the correction defect induced by spacetime coordinate transformations in the design of a convective meta-device

The use of analytical corrections for the convective adaptation of statically-designed acoustic meta-devices revealed themselves to be a promising strategy for the development of metamaterials expected to operate in the presence of a flow. This method relies on the identification of a suitable spacetime coordinate transformation capable of embedding the convective terms in a formally invariant governing equation. However, a change of coordinates capable of exactly including all the convective effects is not known for general flow conditions and analytical approximations are inevitably introduced. Here, two spacetime coordinate transformations are tested on a cylindrical inertial cloaking device that surrounds a sound-hard cylindrical obstacle. These regions are embedded in a domain where a uniform background flow and an acoustic monopole source live. A sensitivity analysis of the meta-device performance to the variation of relevant aeronautical parameters is performed. Specifically, the location of the source and the free-stream Mach number are varied to numerically assess the correction defect in terms of intensity and directivity. The numerical simulations are performed in the frequency domain through a commercial FEM solver.