## 4 Conclusions  
This study evaluates the computational effort and simulation output results among three engine models with different levels of detail. For this purpose, starting from a validated high-fidelity 1D model, two simplified models were proposed: a Simplified  
Figure 11: RT comparison.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model Type** & **Simulation Run-Time** & **RT** \\ \hline Detailed 1D & 285,522 & 230 \\ Simplified 1D & 59,312 & \(\approx\)50 \\ Map-based & 1161 & 0.9 \\ Map-based 10x & 115 & 0.09 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Real-Time factors of the proposed engine models.  
1D model and a non-dimensional one, built through operative maps to simulate engine behavior. To assess the differences among the listed models, numerical simulations were carried out, performing the NRTC standard after the cycle denormalization procedure.  
The numerical results reported in this work have highlighted several key points and conclusions:  
* To estimate the accuracy of the engine models running NRTC, the instantaneous errors and the average errors compared with the NRTC target BMEP were assessed. For all of the considered models, the average errors over the transient cycle are within 6%.
* The simplified 1D model, after the calibration procedure, loses some details due to the lumped volumes. Nevertheless, it maintains a good accuracy compared to the more detailed model. In particular, in terms of fuel consumption, the error is within 1%. The simplified 1D model is less computational-time expensive than the detailed one, due to its lower RT \(\approx\) 50.
* A qualitative analysis of the NOx emission was carried out. The simplest approach, with no chemical kinetic equations implemented into it, achieved a good result in cumulative NOx prediction compared to the more complex models; the simulation results show a difference among the models, ranging in the interval 0-10%.
* In terms of the cumulative fuel consumption prediction, the map-based model shows comparable results with the other models listed, with a maximum difference of about 3% with the high fidelity 1D model.
* By comparing the three models in terms of computational speed, the map-based model is 250 times and 50 times faster compared to the detailed and Simplified 1D model, respectively.  
Based on the results above, since the predictive combustion model is unchanged, in order for the Simplified 1D Model to be adopted for HiL applications, the improvement of the calibration process by using an advanced optimization tool must be considered, ensuring multiple parameter variations to achieve the given target. The map-based model, notwithstanding its lower accuracy, shows good predictive results through numerical simulation in terms of the cumulative fuel consumption and NOx emissions performing a transient cycle. Moreover, it can be considered inexpensive in terms of computational demand due to its low RT factor. Thus, it is suitable in applications where computational speed is the priority, such as numerical simulations of complex hybrid architectures or HiL applications. In this regard, future activities will be oriented in using the most adequate approach by evaluating the differences for Hybrid, Diesel-Electric and powertrain applications.  
Writing-original draft, methodology, G.D.L.; Writing-review and editing, G.D.L. and M.M.; Software, G.D.L. and G.G.; Conceptualization, G.D.B.; Supervision, A.G. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors would like to thank [PERSON] and [PERSON], who contributed to this study with their thesis works, and [PERSON], for the technical informatic contribution.  
The authors declare no conflict of interest.