Temporal information sharing-based multivariate dynamic mode decomposition

This paper introduces temporal information shared multi-variable dynamic mode decomposition (TIMDMD), a novel data-driven algorithm for multi-variable modal decomposition. TIMDMD leverages joint singular value decomposition to share temporal information across variables, resulting in multi-variable rather than single-variable optimization. The algorithm effectively addresses several common issues with traditional DMD approaches, such as inconsistent physical interpretations, a lack of phase consistency between variables, and the mixing of frequency components in the reconstructed flow field. To demonstrate its efficacy, TIMDMD is applied to the analysis of wake flows behind a circular cylinder and a pitching airfoil. The results highlight TIMDMD's ability to align modal indices across variables, correct phase relationships, reduce prediction errors, and improve the clarity of frequency components in the reconstructed flow field.