One dimensional linear acoustics network models are commonly used for the acoustic design of intake and exhaust systems. These models are advantageous since they allow the characterization of the scattering matrices for individual elements, independent of the upstream or downstream components. For an intake or exhaust assembly, the individual elements can be combined by a simple multiplication of the individual matrices to assess the propagation characteristics of the whole system under consideration. The determination of the scattering matrix coefficients can be carried out in an analytical, numerical or experimental way. Since the analytical methodologies are limited to uniform or simplified mean flow representation and the experimental two-port determination is expensive and time-consuming, a numerical method using the time domain Linearized Euler Equations is proposed in this paper. These equations allow studying the aeroacoustic transmission characteristics in a non-uniform mean flow, determined by RANS calculations. The performance of this numerical technique is evaluated for a simple three-dimensional rectangular expansion chamber where different mean flow representations are used to gain more insight in the influence of non-uniform mean flow effects on the aeroacoustic noise propagation. In order to reduce the computational time, different computational strategies including the multiple source, multiple load and Wiener Hopf inversion techniques, incorporating different types of excitation signals, are compared. In this way, an accurate and efficient numerical methodology is proposed for the aeroacoustic characterization of intake and exhaust systems carrying a non-uniform mean flow.