Efficient computation of quasiperiodic oscillations in nonlinear systems with fast rotating parts

We present a numerical method for the investigation of quasiperiodic oscillations in applications modeled by systems of ordinary differential equations. We focus on systems with parts that have a significant rotational speed. An important element of our approach is that it allows us to verify whether one can neglect gravitational forces after a change of coordinates into a corotating frame. Specifically, we show that this leads to a dramatic reduction of computational effort. As a practical example, we study a turbocharger model for which we give a thorough comparison of results for a F. Schilder ( ) · H. M. Osinga · B. Krauskopf Bristol Center for Applied Nonlinear Mathematics, Department of Engineering Mathematics, University of Bristol, Queen’s Building, University Walk, Bristol BS8 1TR, UK e-mail: [email protected] J. Rübel Interdisciplinary Center for Scientific Computing (IWR) and Institute of Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, D-69120 Heidelberg, Germany J. Starke Department of Mathematics, Technical University of Denmark, Matematiktorvet, Building 303, DK-2800 Kongens Lyngby, Denmark M. Inagaki Toyota Central Research and Development Laboratories, Inc., Nagakute, Aichi 480-1192, Japan model with and without the inclusion of gravitational forces.