Noise generation and propagation through mechanical ventilation and air conditioning (MVAC) ducts have been increasingly investigated since commercial solutions allow sensible noise attenuation while reducing the duct section. So, a commercial silencer forces the MVAC power to rise to overcome the flow resistance, increasing the noise source. For this reason, this study focuses on soundproofing ventilation ducts through acoustic metamaterials with no inner duct section decreasing. A crucial part of this study falls into the multiphysical interaction between acoustics and fluid dynamics, which is a phenomenon that may result in a challenging analytical model. In conditions of flowing motion, the wave vector has been modelled according to the Lighthill model: the component of the velocity rotor potential becomes significant, influencing the soundproofing performance due to the metamaterial placed at the edge of the inner surface of the duct. FEM analysis helped design a series of samples which then have been tested experimentally in static conditions. Once the numerical method is calibrated, further multiphysical numerical analysis are used to implement the sound insulation properties of the metamaterial-based filter through dynamic flow conditions. Guidelines for multiphysical setup for wave-based simulation are drawn, and preliminary experimental results are presented.