Distributed-parallel proper orthogonal/dynamic mode decompositions of large flow data

High-fidelity computational fluid dynamics (CFD) simulations produce large databases, which are typically stored on either centralized or distributed machines. Eigen/Singular value decompositions are some of the early-stage and most useful decompositions. The more popular proper orthogonal decomposition (POD) and dynamics mode decomposition (DMD) of fluid flows are essentially based on the eigen/singular value decomposition algorithms. Although there exist very efficient and parallel eigen/singular value solvers, most of them perform poorly when handling large data particularly in distributed settings, and often resort to a partial estimation of eigen/singular value spectra. In this paper, we present a memory-efficient and highly-scalable POD and DMD procedures in distributed-parallel settings, where the parallel DMD algorithm is an improved tall-and-skinny QR (TSQR) DMD algorithm. A Large Eddy Simulations (LES) database of a fully turbulent Shock Wave Boundary Layer Interaction (SBLI) at Mach 2.7 and Reynolds number of $54,600$ based on the inflow boundary layer thickness is employed, first, to evaluate the performance and accuracy of the algorithms, and second, to elucidate some of the three-dimensional coherent flow features of the SBLI pertaining to POD/DMD. The selected POD/DMD modes of the LES flowfields exhibit full 3D flow features, such as, the streamwise-elongated Görtler-like vortices and high-frequency acoustic packets that are physically relevant to the SBLI dynamics.