This 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.
|Translated title of the contribution||Stabilisation of Reduced Order Models via Restarting|
|Number of pages||22|
|Journal||International Journal for Numerical Methods in Fluids|
|Early online date||12 Jun 2013|
|Publication status||Published - 2013|