Space-Time Mapping Analysis of Airfoil Response to Impinging Gust

A new numerical approach first presented in Ref. [1], is applied to the nonlinear analysis of the unsteady gust-airfoil interaction problem (Problem 1 in Category 3). The Space-Time Mapping Analysis (STMA) method has been developed to effectively treat any two- or three-dimensional unsteady problems as a steady-state one in the three- or four-dimensional space. Such approach essentially paves the way for extending high-accuracy discretization schemes developed in Computational Aeroacoustics (CAA) for spatial derivatives, to the time derivative, thus achieving highly time-accurate computations with absolute stability. It appears to provide additional flexibility of clustering space-time grid in regions of rapid solution changes, and is well-suited for the distributed-memory parallel processing. The numerical formulation used in the current study employs a high-order discretization scheme to achieve time-accurate predictions of both unsteady aerodynamic and aeroacoustic airfoil responses.