A Tutorial on the Proper Orthogonal Decomposition

This tutorial introduces the Proper Orthogonal Decomposition (POD) to engineering students and researchers interested in its use in fluid dynamics and aerodynamics. The objectives are firstly to give an intuitive feel for the method and secondly to provide example MATLAB codes of common POD algorithms. The discussion is limited to the finite-dimensional case and only requires knowledge of basic statistics and matrix algebra. The POD is first introduced with a two-dimensional example in order to illustrate the different projections that take place in the decomposition. The n-dimensional case is then developed using experimental data obtained in a turbulent separation-bubble flow and numerical results from simulations of a cylinder wake flow