Improving the predictable accuracy of fluid Galerkin reduced-order models using two POD bases

A fundamental limitation of fluid flow reduced-order models (ROMs) which utilize the proper orthogonal decomposition is that there is little capability to determine one's confidence in the fidelity of the ROM a priori. One reason why fluid ROMs are plagued by this issue is that nonlinear fluid flows are fundamentally multi-scale, often chaotic dynamical systems and a single linear spatial basis, however carefully selected, is incapable of ensuring that these characteristics are captured. In this paper, the velocity and the velocity gradient were decomposed using differently optimized linear bases. This enabled an optimization for several dynamically significant flow characteristics within the modal bases. This was accomplished while still ensuring the resulting model is accurate and without iterative methods for constructing the modal bases.