## 3 Results and Discussion
### Simplified 1D Model Calibration Results and Accuracy Check  
The Simplified 1D model was calibrated into the same steady points in which the detailed model was validated. The calibration process was composed of several steps. At each timestep, the matching was verified with the original simulation result. The main results are shown below.  
During the conversion process, especially where the volumes are joined (intake and exhaust plenums), it is necessary to identify the components which can restrict the timestep, especially the exhaust manifold due to the high gas velocities that occur in it. To ensure the right accuracy in comparison to the detailed model, both in terms of pressure and temperature, a recalibration of the duct diameters or heat transfer multiplier must be varied, respectively. An example of the recalibrated heat transfer multiplier of the turbine inlet and outlet is reported in Figure 6.  
Figure 6: Exhaust manifold: Inlet (**a**) and Outlet (**b**) temperature.  
As seen, despite slight deviations between the trends, the results can be considered satisfactory. After the calibration process to assess the accuracy of the simplified 1D model, some key parameters have been considered and compared with those of the detailed model. Indeed, in terms of \"performance\", as can be seen in Figure 7, power, IMEP and fuel consumption can be considered comparable.  
Figure 8 shows the comparison in terms of the timesteps in the crank angle units (a) and in time (b). As expected, the simulation run-time of the Simplified 1D Model was lower than that of the more detailed model, due to an increased value of the timestep. This can be related to the reduced number of sub-volumes that enable a larger timestep.  
In particular, to have stable solver operations, the timestep and discretization length must meet the Courant condition:  
\[\frac{\Delta t}{\Delta x}(|u|+c)\leq 0.8\times m \tag{6}\]  
The user-imposed maximum timestep for the detailed model is 0.2 crank angle degree (CAD), while for the Simplified 1D Model, the timestep has been set to a \"def\" value, which means, for the solver used (explicit method), that the maximum timestep allowed is 1 CAD. With this constraint, in the Simplified 1D model, performing the NRTC simulation, the timestep is dynamically restricted according to condition (6). Following the Courant criteria, as the explicit solver is used, higher local velocities imply a smaller crank angle  
Figure 8: (**a**) Timestep comparison in crank angle resolution; (**b**) Timestep comparison in time.  
Figure 7: (**a**) Power, (**b**) IMEP, (**c**) bsFC Comparison.  
timestep for numerical stability. As the local velocity \(\Delta x/\Delta t\) increases and the discretization length \(\Delta x\) is the same, the crank angle timestep \(\Delta t\) needs to be refined in order to meet the Courant condition. Thus, the maximum value reached is 0.42 CAD as shown in Figure 8. Nevertheless, the timestep in each case is 50% larger than for the detailed model. Further to this point, the Simplified 1D Model is characterized by a lower computational requirement, ensuring good predictability since the predictive combustion model is unchanged. A further computational time reduction can be obtained, for example, for real-time application, by superimposing the combustion evolution traces.