Model order reduction using DMD modes and adjoint DMD modes

摘要

Dynamic mode decomposition (DMD) is known for its strength to capture frequency features of dynamic systems. However, without intrinsic orthogonality, it is not convenient to apply DMD in model order reduction. This work introduces adjoint DMD modes to combine with the original DMD modes for bi-orthogonal bases, and allows to construct a simple DMD-based Galerkin low-order model from a full-order Navier-Stokes equation system. The approach was applied on a benchmark case of the flow passing a fixed cylinder. Both the DMD modes and the adjoint DMD modes show well-organized paired structures. In a comparison of model results with the low-dimensional projection of the original simulation data, the DMD-based Galerkin model requires only 8 pairs of modes to represent all basic dynamics.