Projection based reduced order models for fluid structure interaction problems

In this study, projection based reduced order models for compressible viscous fluid and elastic structure interaction problems are constructed. To obtain low dimensional basis, Proper Orthogonal Decomposition(POD) modes are calculated using snapshots obtained by finite element analysis. The governing equations for fluid and structure motion are formulated on a reference domain, and inner product and POD modes are defined on this domain to enable projections. New energy inner product for compressible flow and elastic structures are defined to acheve stabiization. The energy inner product is based on total energy of the system of the fluid structure interaction problems, and defined ver fluid and structure domains with primitive variables of density, velocity and temperature. The proposed method was validaded by solving sveral benchmark problems, and it is shown that the proposed method constructs fast, stable and acculate reduced order models. Speedup of two to three orders of magnitude to the full order model by finite element method is achieved at relative error of 1%.

This POD modes and reduced order models not only allows for fast calculations, but is also used to analyze the relationship between fluid and structure motion.