Stability and accuracy of periodic flow solutions obtained by a POD-penalty method

We develop a new penalty method to derive low-dimensional Galerkin models for fluid flows with time-dependent boundary conditions. We then outline a procedure based on bifurcation analysis in selecting the proper values of the penalty parameter(s) that yield asymptotically stable periodic solutions of the highest possible accuracy. We illustrate this new approach by studying flow past a circular cylinder using direct numerical simulation (DNS) data, and a wave-structure interaction problem using particle image velocimetry (PIV) data.