3D Dual Basis Proper Orthogonal Decomposition*

Conventional implementations of the proper orthogonal decomposition (POD) produce a basis spanning the velocity field optimally with respect to its kinetic energy content, allowing formulation of reduced order models (ROMs) by projecting transport equations onto the truncated basis. The truncation may leave out dynamically relevant modes, leading to less accurate models. This issue is important to turbulent flows where a decisive role is played by interactions between multiple scales potentially associated with different mode orders.

Lee and Dowell [1] showed that supplementing an energy-optimized POD basis with a POD basis optimized with respect to the velocity gradient norm enhances the accuracy of ROMs at high Reynolds numbers in 2D. Given the different dynamics governing turbulence in 2D vs 3D it is not given that similar results would apply in 3D. We analyze the effect of using a dual-basis ROM for a 3D flow. This facilitates quantification of the dynamical importance of different modes and their interactions, yielding insight to the fundamental dynamics of the flow.

References:

[1] M.W. Lee and E.H.Dowell. "Improving the predictable accuracy of fluid Galerkin reduced-order models using two POD bases". In: Nonlinear Dynamics 101.2 (2020), pp. 1457-1471.