A step towards reduced order modelling of flow characterized by wakes using Proper Orthogonal Decomposition

Abstract

High fidelity simulations of flow can be quite demanding, involving up to O(106) to O(109) degrees of freedom, and several hours or days of computational time, even on powerful parllel architectures. These techniques become prohibitive when expected to deal quickly and efficiently with repetitive solutions of partial differential equations. One set of PDE encountered on a regular basis is the Navier Stokes equation, used to simulate flow around complex geometries, e.g. sub-sea structures. To address the issues associated with computational efficiency, the field of Reduced Order Modelling (ROM) is evolving quickly. In this paper, we investigate the use of Proper Orthogonal Decomposition (POD) as a potential method for constructing reduced bases for such ROMs. In the case of flow around cylindrical bodies and the NACA 0015 airfoil we found that only a few modes were sufficient to represent the dominant flow structures and their associated energies. This makes POD an attractive candidate for constructing such bases.