Aeroelastic Reduced-Order Model Differential Equations in Transonic Buffeting Flow

Numerical simulation of the transonic shock buffet phenomenon remains a formidable challenge due to its inherent nonlinear and unsteady characteristics. These difficulties are further compounded in three-dimensional configurations and when aeroelastic coupling is considered. Consequently, computational studies of aeroelastic shock buffet interactions have largely been confined to two-dimensional systems. This limitation underscores the need for reduced-order models (ROMs) capable of efficiently and accurately capturing the aeroelastic response of structures subjected to shock buffet oscillations. This paper presents a novel nonlinear unsteady aerodynamic ROM that integrates nonlinear oscillator dynamics with Volterra theory to model aeroelastic shock buffet phenomena. The coefficients and terms of the resulting Integro-Differential Equation ROM (IDE-ROM) are identified using the Orthogonal Matching Pursuit (OMP) algorithm. Application of the IDE-ROM to an OAT15A airfoil demonstrates that the compact and computationally efficient formulation can reproduce key nonlinear behaviors, including aeroelastic lock-in, with a high degree of accuracy. The limitations and potential extensions of the proposed approach are also critically examined.