Static/Dynamic Correction Approach for Reduced-Order Modeling of Unsteady Aerodynamics

Abstract

Presented is a newly devised static/dynamic correction approach for eigenvector expansion based reduced-order modeling (ROM). When compared to the fundamental Ritz ROM formulation, along with the static and multiple static correction ROM approaches, the technique is demonstrated to have much better performance in modeling unsteady linearized frequency-domain aerodynamics in regions of the complex frequency plane near the imaginary axis, and up to a prescribed frequency of interest. As with the static and multiple static correction approaches, the method requires a directly computed solution at zero frequency. The method then requires one additional direct solution to be computed at some nonzero frequency, which typically is the maximum frequency of interest. When compared to the multiple static corrections method, the method circumvents the necessity of having to determine each of the multiple static corrections, which require a solution to an alternate set of equations that must be formulated and which can be costly to solve for large systems. We also consider the feasibility of using a proper orthogonal decomposition (POD) to determine approximations for the least damped fluid-dynamic eigenvectors. We demonstrate that in certain situations these approximate eigenvectors can be used in conjunction with the static/dynamic correction ROM approach to achieve an improvement in performance over the recently devised POD/ROM method where the POD shapes alone are used as ROM shape vectors. Finally, we illustrate how the method can be coupled with a structural model to compute the Mach-number flutter speed trend for a large computational-fluid-dynamics model of a three-dimensional transonic wing configuration.