Significant research efforts have been conducted by many research groups in the last decades to circumvent the acoustic metamaterial concept limitations. Principally, the lack of a reliable methodology for the design of such metamaterial-based devices and their performance decay when they operate in a moving medium were the main topics of investigation that culminated in a number of possible approaches with a high potential of application in aeroacoustics. One of these approaches is based on the aeroacoustic spacetime reformulation of the problem to recast the governing equations in a generalized form, independent of the kinematic conditions of the supporting medium. In the present paper, the response of a spacetime-corrected metacontinuum is coupled with a high-fidelity aeroacoustic model of the hosting fluid to allow for the modelling of actual experimental realizations of a laser-generated sound source. The availability of a reliable model to couple the convective metacontinuum design with the heat-release source would make possible the systematic cross-validation of the numerical simulations with the experimental results obtained in the most advanced testing facilities, paving the way to an effective inclusion of metacontinuum-based devices in aeronautics and, finally, in a simulation-based, multidisciplinary design optimization framework. Although the method presented is valid for arbitrary acoustic responses, the numerical simulations presented in this work have been conducted using the classic Cummer-Schurig inertial cloaking as a reference application, which can now be considered a widely accepted benchmark for acoustic metamaterial applications.