On the use of reduced order models in bifurcation analysis of distributed parameter systems

Bifurcation theory provides a powerful tool for analyzing the nonlinear dynamic behavior of process systems. However, although the theory in principle applies to lumped as well as distributed parameter processes, it is in practice necessary to reduce the order of distributed (PDE) models prior to application of the theory. In this paper we consider the problem of determining an appropriate model reduction method for this task. We first show that simply applying some ad hoc discretization method, such as finite differences or finite elements, can result in spurious bifurcations and erroneous predictions of stability. To avoid this problem we propose a method for estimating the error introduced by the model reduction. Apart from simply providing a label of confidence in the obtained results, the estimated error can be used to improve the model reduction. We here propose a method based on moving the discretization mesh such as to spatially equidistribute the total error. The method is ap...

• Type: Journal
• Year: 2004
• Where: CCE
• Authors: Yi Liu, Elling W. Jacobsen
• Keywords: CCE 2004, CCE 2007, Model Reduction, Model Reduction Method, Nonlinear Dynamic Behavior