Model reduction of systems with traveling waves using projection methods

Proper Orthogonal Decomposition (POD) based projection methods are an impor- tant tool for the reduction of complex nonlinear models. Large reductions in model order can be frequently be obtained due to the exploitation of correlations between model states that exist for representative behavior of the model. However, when this model behavior includes traveling waves or shock fronts these methods perform less well as a large number of modes is required to capture this type of behavior. This paper investigates the use of correlation to pre-process simulation data such that bi-orthogonal projection can subsequently be applied to obtain a reduced model that is of low order.