Stability Analysis of Flow Pattern in Flow around Body by POD

Abstract

A method is presented for the numerical analysis of instabilities and bifurcations of the complex flows around body. First, the formations, developments and evolvements of the complicated flow pattern in flow around a cylinder are numerically simulated using finite element method combined with explicit characteristic based split scheme (CBS) method, and the flow patterns are classified tentatively by streamline topology, in comparison with the existing results. The results show streamline topology method is powerful to investigate the instability and nature of the streamline patterns, especially, the vortex shedding. Further, the model reduction of fluid dynamics based on proper orthogonal decomposition (POD) and the stability analysis are given. Following POD, a low-dimensional dynamic system is derived to study numerically the stability and bifurcation of pattern. As an example, the stability analysis of flow around a circular cylinder is carried out, and is verified by the existing results. As a conclusion, the results show that the numerical method presented is powerful for the stability and bifurcation analysis of the complicated flows around body, and some nonlinear phenomena can be captured by the method.