Transonic Buffet Modeling via Invariant Manifolds

Abstract: In transonic flow over aircraft wings, shock-boundary-layer interactions can give rise to transonic buffet, which degrades maneuverability through unsteady aerodynamic loads. Beyond its practical importance, two-dimensional transonic buffet represents a canonical example of a global instability for which reduced-order modeling remains challenging due to nonlinearity, sharp spatial gradients, and the coexistence of an unstable equilibrium with an attracting limit cycle. Commonly, reduced-order models of such phenomena capture nonlinear dynamics only in aerodynamic observables, while prediction of the full flow state is achieved through linear representations valid only near the unstable equilibrium or on the limit cycle. In this work, we present a reduced-order model that predicts the nonlinear evolution of the full flow field by exploiting the existence of an attracting two-dimensional invariant manifold. We adapt an existing data-driven framework for identifying invariant manifolds and the associated reduced dynamics, making it suitable for scaling to large-scale CFD applications. The invariant manifold is identified as a graph over its tangent space using an iterative encoder-update and the reduced dynamics are obtained via least-squares regression. A subsequent extended normal-form transformation enables physical interpretability of the model through a modal decomposition of the flow. The reduced-order model is identified for transonic buffet over the OAT15A supercritical airfoil, showing that it is possible to achieve this accurately using just a single training trajectory. Validation against independent simulations demonstrates accurate prediction of nonlinear behavior, together with reliable reconstruction of the full flow field, particularly in the late-transient and limit-cycle regimes.