Partial proper orthogonal decomposition: Numerical applications and comparisons

Isolating localized phenomena in complex, multi-scale, and multi-physics flow fields, such as those encountered in scramjet engines or combustion enhancement studies, remains a significant challenge due to the dominance of global modes and the limitations of traditional decomposition methods. To address this, we propose a partial proper orthogonal decomposition (partial-POD) method based on spatial partitioning, which selectively decomposes submatrices of regions of interest to extract localized features. Theoretical validation using a synthetic dataset confirms the method's ability to precisely separate time-evolution coefficients and spatial distributions of individual modes. Practical applications in fluid dynamics, including multiscale cylindrical bypassing and dynamic injection boundary conditions, demonstrate its effectiveness in revealing localized flow characteristics and providing physically meaningful modal decompositions. Additionally, the method serves as a computationally efficient low-order approximation of standard POD, significantly reducing computational costs while maintaining accuracy. These results underscore the potential of the partial-POD method as a practical tool for analyzing localized phenomena in complex flow fields, offering insight for engineering and research applications.