Assessment of the convective correction defect of metacontinua using spurious sources in the aeroacoustic spacetime

The analytical convective adaptation of statically-design acoustic meta materials could be a suitable strategy to achieve their implementation in the aeronautical context preserving their performances. The adaptation process follows from the application of analytical correction based on coordinate transformation. Their introduction is possible by exploiting the formal invariance of the governing equation when it is rewritten in the space time domain. In the present paper, two analytical corrections based on Taylor’s and Prandtl-Glauert’s coordinate transformation are considered, and the effect of the analytical approximation introduced is investigated for several Mach numbers up to 0.3. The test case considers a cylindrical sound-hard obstacle surrounded by an in viscid fluid model adapted through the corrections, embedded in a conventional medium domain characterized by a uniform background flow where a simple monopole source emits acoustic perturbations. The numerical setup is chosen to make the effect of the spurious terms evident and hence to quantify their influence on the corrections’ goodness. The scattered fields are evaluated in the frequency domain through the commercial FEM solver COMSOL Multi physics.