Low Dimensional Modeling of Laminar Wake Behind a Square Cylinder

Abstract

Proper Orthogonal Decomposition(POD) and Dynamic Mode Decomposition (DMD) are widely used techniques for model order reduction of fluid flows. In this work velocity data from Full order simulation of Laminar flow over a square cylinder is used to construct a reduced order model via POD Galerkin technique and DMD. Proper Orthogonal Decomposition is used to reveal the most energetic modes influencing the behaviour of the system. A dynamical system of equations is obtained by projecting Navier stokes equation on to the obtained energetic spatial modes. Solution of Dynamical system shows presence of a limit cycle corresponding to unsteady vortex shedding. Bifurcation phenomena occurring in the vicinity of critical Reynolds Number is analyzed and validity of reduced order model away from the simulated parametric value is studied. Similarly, DMD algorithm is applied to the snapshot velocity matrix to obtain DMD modes and their respective frequencies and growth rates. Finally both the techniques are compared for their numerical accuracy and robustness.