Researching method of building flow field of initial development stage of low Reynolds number flow past a circular cylinder

POD-Galerkin method is an effective way to build low-dimensional models for unsteady flows. However, studies have shown that low-dimensional models, based on snapshots of periodic oscillations and the time averaged solutions, can only rebuild the flow field of saturated periodic oscillating state, but iftcannot rebuild the divergence process of the flow from unstable steady solution to final unsteady saturated oscillation state. So it is inconvenient for stability analysis of the flow and for the controller design in future research. In this paper, we attempt to found low-dimensional dynamics modelsby using the snapshots of the fluid before entering the cyclical movement. And then we use this model to rebuild the flow field of the initial development stage with small oscillating amplitude. We take the flow past a circular cylinder at a low Reynolds number of 100 as an example to build a low-dimensional model for the initial instable stage of Karman vortex street. It is shown that, by choosing appropriate snapshots, the reduced-order model can rebuild some characteristics of the initial divergence regime of the flow, such as frequency and damping characteristics. This study, we believe, establishes a good foundation for the fluid-structure coupling analysis and flow instability control in future research.