The DAE-aspect of the charge cycle in a combustion engine

The gas exchange in the cylinders is essential for the overall performance of an internal combustion engine. A CAE approach leads to technically improved and less polluting engines. Its base is a network formulation of the engine. The mathematical model describes the gas flow in the various parts of the engine. A system of ordinary differential equations in time represents conservation of mass and energy in the chambers. Considering the gas flow in the pipes yields an hyperbolic system of partial differential equations, the unsteady one-dimensional Euler equations. In contrast to classical difference schemes the numerical treatment with an ENO scheme prevents spurious numerical oscillations. The coupling of the pipes with the cylinders and other elements of the network leads to differential-algebraic equations (DAEs), which are solved by a predictor-corrector method. The implementation in an industrial simulation package shows that even large-scale problems can be solved with a very good congruence of measured and computed data.