Stabilisation of reduced order models via restarting

SUMMARYThis paper describes the development, implementation and validation of an explicit restarting scheme to stabilise reduced order models produced using the Eigensystem Realisation Algorithm. Here, the method is applied to a continuous time fluid dynamics model that is actually solved in discrete time space using a CFD approach. However, the methods described are generic and could be applied to any other similar dynamically linear system. The basic restarting approach successfully stabilises ROMs in the majority of cases. However, there are cases where this approach breaks down. The reasons for this breakdown in the basic restarting scheme are discussed, and the strategies for overcoming this problem are described. These include creating ROMs restricted to a range of time step sizes for a specific finite difference scheme and a more general approach using inexact shifts that overcome the problems associated with closely located eigenvalues. Copyright © 2013 John Wiley & Sons, Ltd. Reduced order models of continuous high order systems are usually produced in the discrete time domain for a fixed time step. When using an ROM as a surrogate for the high order system for continuation, an equivalent continuous ROM that can be used for any time step is required. A discrete ROM may work for the time step used in construction, but leads to an unstable continuous ROM. This problem is overcome by the restarting approach presented in this study.