Sohail R. Reddy, Brian A. Freno, Paul G.A. Cizmas, Seckin Gokaltun, Dwayne McDaniel, George S. Dulikravich, Constrained reduced-order models based on proper orthogonal decomposition, Computer Methods in Applied Mechanics and Engineering, Volume 321, 1 July 2017, Pages 18-34, ISSN 0045-7825, https://doi.org/10.1016/j.cma.2017.03.038.
Abstract: A novel approach is presented to constrain reduced-order models (ROM) based on proper orthogonal decomposition (POD). The Karush–Kuhn–Tucker (KKT) conditions were applied to the traditional reduced-order model to constrain the solution to user-defined bounds. The constrained reduced-order model (C-ROM) was applied and validated against the analytical solution to the first-order wave equation. C-ROM was also applied to the analysis of fluidized beds. It was shown that the ROM and C-ROM produced accurate results and that C-ROM was less sensitive to error propagation through time than the ROM.
Keywords: Proper orthogonal decomposition; Reduced-order modeling; Karush–Kuhn–Tucker; Multiphase flows; Computational fluid dynamics; Fluidized beds