The study focuses on characterizing the whistling ability of an axisymmetric orifice in a confined flow, using numerical simulation. A single hole orifice in a duct can generate whistling when it is submitted to a low Mach number flow. Whistling is a consequence of an acoustic amplification by the shear flow downstream of the orifice, coupled to an external acoustic resonator. The feedback of the resonator coupled to the acoustic amplification leads to whistling by linear instability. Recently a whistling criterion was experimentally validated, based on the acoustic scattering matrix of an orifice. Balancing the incoming and the scattered acoustic powers, the frequencies at which acoustic amplification occurs can be determined. The present study deals with the acoustic amplification mechanism. A Large Eddy Simulation (LES) is performed for an orifice submitted to a $0.026$ Mach number flow with a Reynolds number around $10^4$. Broadband acoustic signals are applied in the inlet and outlet of the computational domain. The times series of the LES are finally post-processed with a Wiener-Hopf Inversion technique to obtain the coefficients of the scattering matrix in the linear regime. The whistling criterion is then computed from this scattering matrix. Comparison with the experimental data are provided.