**4. Conclusions**

The objective of the work presented was to establish the potential of staggered mesh finite volume models as a way to improve the description of the effect of simple duct junctions on an otherwise one-dimensional flow system, as the intake or exhaust of an internal combustion engine.

With that purpose, specific experiments were performed making use of a modified impulse method, in which two different junctions were characterized as a multi-port, and that provided precise and reliable results on the propagation of pressure pulses across junctions.

The results obtained were then compared to numerical results obtained from different methods, both in the time and the frequency domains. First, methods assuming a zero-dimensional description of the junction were assessed, including the staggered mesh finite volume method with different flux limiters and, as a reference for comparison, a more conventional pressure loss-based model. Then, the potential of using the staggered mesh finite volume method in order to produce a quasi-3D description of the junction, to be coupled with the one-dimensional description of the adjacent ducts, was explored.

As an overall conclusion of the results found, one may state that none of the modeling approaches considered is able to reproduce totally the observed behavior. However, the performance of the different models is such that a suitable choice seems to be possible depending on which is the actual focus of the problem under study: situations in which a suitable time domain description may be sufficient may be addressed either with the conventional quasi-steady pressure loss model (most notably when the focus is on the reflection properties of the junction) or with the staggered mesh model with quasi-3D junction description (in this last case, when the main interest is on transmission, and given that the lengths involved in the problem will not be as long as to give rise to spurious oscillations due to the dispersive character of the method).

When the focus is on the frequency domain and on the dynamic behavior of the junction, it is the staggered mesh method the one that provides the most suitable results, at least from a qualitative point of view, as a consequence of the fact that momentum conservation across the junction is accounted for. However, due to spurious oscillation arising from the method used to couple a quasi-3D junction to the 1D ducts, suitable results with an acceptable computation time have been obtained only either with the zero-dimensional description of the junction or with a full quasi-3D description of the whole system, this last option being unacceptable in practice. It is thus clear that further work is needed in this case in order to find the optimal settings for the calculation, most notably in the connection between the quasi-3D and the 1D regions.

Finally, it should be recalled that no empirical information has been included in the staggered mesh method used; the incorporation of such information in terms of effective sections and characteristic lengths and the evaluation of their potential could be additional topics for further research.

**Acknowledgments:** Manuel Hernández is partially supported through contract FPI-S2-2015-1064 of Programa de Apoyo para la Investigación y Desarrollo (PAID) of Universitat Politècnica de València. The authors wish to thank Adolfo Guzmán for manufacturing the junctions and for his technical support during the tests.

**Author Contributions:** A.J. Torregrosa conceived the structure of the work, contributed to the analysis and wrote a large part of the article; A. Broatch supervised the experiments, wrote Appendix A and contributed to the discussion; L.M. García-Cuevas implemented the conventional model, ran the related simulations, wrote Appendix C and contributed to the discussion; M. Hernández implemented the staggered mesh method, ran the related simulations, wrote Appendix B and contributed largely to the discussion.

**Conflicts of Interest:** The authors declare no conflict of interest. The founding sponsors had no role in the design of the study; in the collection, analyses.
