The prediction of dynamic phenomena in compressible fluids, such as the air path systems of Internal Combustion Engines (ICEs) has seen an enormous growth in the past years. Striving to improve engine performance, fuel economy and emissions has led to the understanding that significant gains can only be achieved if improvements in engine design can be matched by the ability to closely control engine breathing and combustion performance. The current state of the art in the modeling of ICEs air path systems presents two main approaches, namely the high-fidelity, computationally intensive numerical methods and the low-fidelity, calibration intensive lumped-parameter models. This paper introduces a novel approach for modeling unsteady phenomena in compressible fluids that combines the advantages of numerical methods (high accuracy and low calibration effort) with the limited computation time of lumped-parameter models based on ordinary differential equations (ODEs). The approach is here presented for the one-dimensional nonlinear Euler equations for compressible fluid flow systems, which are particularly relevant for modeling the air path systems of internal combustion engines.