Parametrically rich nonlinear reduced-order modeling: An application in viscous incompressible flow
In this work, we seek parametrically rich modes that can be used to analyze nonlinear systems for a continuous variation of operating conditions. Towards this end, based on the Modally Equivalent Perturbed System (MEPS) and the Degenerate Transformation (DT) methods, a new and linear perturbed system is formulated and the basis vectors that span a rich nonlinear solution space are obtained from the resulting system of equations. These basis vectors, which obey the principle of linear superposition, lead to a new approach to nonlinear analysis that has the potential for a significant reduction in the complexity of the analysis as well as in computing time. The new scheme is demonstrated using a computational model of a two-dimensional incompressible, viscous flow in which the basis modes are obtained conveniently from snapshots of time responses of the unsteady flow field. It is shown that when used in conjunction with nonlinear reduced-order modeling they produce very accurate results for a wide range of Reynolds numbers and boundary conditions.
