3.3.1. Time Domain Assessment

In Figure 15 the results obtained with the quasi-3D description of the junction (labeled MDT Q3D) are compared with those previously shown in Figure 7 corresponding to the MDT with 0D description of the junction. Again the plots on top represent the raw results, whereas the bottom plots show the differences with respect to the experimental values. It can be seen that, in all the cases, a certain improvement is achieved when using the quasi-3D junction, improvement which is more apparent when the junction is excited at port 3, this is, at the side branch, which is intuitively reasonable.

**Figure 15.** Influence of the description of the junction in the time domain, MDT method: raw data (top) and differences with measurement (bottom). (**a**) Excitation at port 1; (**b**) excitation at port 3. Ports are denoted as in Figure 1.

Again, the mean quadratic errors were computed, as shown in Table 3.

These results indicate that, while the reflection coefficients exhibit a similar mean error, there is a substantial improvement in the transmission coefficients, thus confirming the previous analysis.

However, the improvement achieved is not sufficient to produce results comparable to those shown in Figure 8 for the conventional model in the case of the reflection coefficient, and the differences in the transmission coefficients are clearly significant only when the junction is excited at the side branch. Therefore, while it appears that further refinement of the mesh at the junction should improve further the quality of the results, this might produce in turn an unacceptable increase in the computation time.


**Table 3.** Values of the mean quadratic error: T-junction.

Abbreviations: MDT Q3D: momentum diffusion term with quasi-3D description of the junction.
