The steadily increasing demands on vehicle fuel economy, emissions, and performance are a major driving force in developing and optimising future powertrains. In order to meet customers' and legislative requirements it is of particular importance not only to simulate and optimise different powertrain elements, but also to develop simulation models capable of modeling the performance of the powertrain system as a whole. The latter is of particular importance for developing and testing components in a virtual environment, as well as for accompanying the conventional development steps from design phases in the office to the application and validation phases on the test bed. Test bed validation, development and calibration of components in the hardware-in-the-loop (HiL) environment and modelbased engine controlling require real-time capable simulation models. Moreover, computational speed is also of considerable importance when simulating complete emission test cycles where engine and vehicle dynamics are simulated on time scales of 10 3 s.Recently, 0-dimensional (0-D) crank-angle (CA) resolved engine simulation models, e.g. [1] to [4], have emerged as a promising approach for real-time engine simulations of internal combustion engines (ICE) and hybrid powertrain of heavy-duty engines [5]. Unlike higher resolution 1-D, e.g.[6] to [9], and 3-D models, e.g.[10] and [11], 0-D models can comply with realtime constraints and provide a higher level of detail compared to mean-value engine models, e.g. [12] and [13]. The latter models reach their limits when future control functions need to be taken into account, which incorporate CA resolved events such as cylinder pressure based control functions, electronic control unit controlled fuel injections, and variable valve timing. Mean-value engine models are not able to model these phenomena predictably since they rely on experimental data that are used to tune or train the model as presented in [14] for camshaft variability.Besides computational speed, the convergence and stability of numerical solution algorithms are the prerequisites for the successful application of 0-D CA resolved engine simulation models. This topic has not yet been systematically analysed in the literature and therefore the presented paper aims to provide a study of the convergence, stability, and computational speed of different explicit and implicit integration schemes.The cylinder model represents the crucial element to attaining high computational speed and accuracy of results, since the time variation of the thermodynamic variables is most pronounced in the cylinder due to piston kinematics and combustion. It is common practice to validate the accuracy of simulation models by comparing numerical and experimental results. This indeed gives an indication of the consistency
On the Convergence, Stability, and Computational Speed of Numerical Schemes for 0-D IC Engine Cylinder Modelling