Feature-based modal decomposition of non-stationary flows

Linear model reduction methods are limited in providing accurate low-dimensional approximations of non-stationary flows featuring translation, rotation, scaling, etc., due to the Kolmogorov barrier. To mitigate this barrier, a Feature‐based Proper Orthogonal Decomposition (FPOD) method, which is a local registration approach inspired by image processing techniques, is proposed. This method captures the spatiotemporal evolution of fluid structures through local adaptive meshing, which aligns their positions and flow field variables in the storage space and subsequently eliminates convection–diffusion effects. In numerical tests of the advection–diffusion equation, Burgers' equation, a co-rotating vortex pair, and flow around a cylinder with and without acceleration, FPOD demonstrated superior performances in modal compression, reconstruction, and prediction over linear and nonlinear registration and quadratic manifold approaches, particularly in non-stationary scenarios. Code is available at https://github.com/leigq/FPOD.