An Efficient Proper Orthogonal Decomposition based Reduced-Order Model

This paper presents a novel, more efficient proper orthogonal decomposition (POD) based reduced-order model (ROM) for compressible flows. In this POD model the governing equations, i.e., the conservation of mass, momentum, and energy equations were written using specific volume instead of density. This substitution allowed for the pre-computation of the coefficients of the system of ODEs that make up the reduced-order model. Several methods were employed to enhance the stability of the ODE solver: the penalty method to enforce boundary conditions, artificial dissipation, and a method that modifies the number of modes used in the POD approximation. This new POD-based reduced-order model was validated for four cases at both on- and off-reference conditions: a quasi-one-dimensional nozzle, a two-dimensional channel, a three-dimensional axisymmetric nozzle, and a transonic fan. The speedup obtained by using the POD-based ROM vs. the full-order model exceeded four orders of magnitude in all cases tested.