Unsteady physics-based reduced order modeling for large-scale compressible aerodynamic applications

Abstract

A physics-based reduced order model is presented as a viable approach to accurately predict unsteady flowfield solutions at a fraction of the computational time that is required by high fidelity computational fluid dynamics solvers. Such a model could be useful during the preliminary phases of the aircraft design process when an accurate prediction of unsteady loads is crucial to reduce the uncertainty of design choices. This paper extends the formulation of a previously defined technique to unsteady aerodynamic problems involving motion excitation in both subsonic and transonic conditions. In particular, the proposed unsteady-residual-based model defines a reduced solution space by applying proper orthogonal decomposition to a set of snapshots collected from the unsteady high fidelity simulations. Approximate flow solutions for unseen motion signals is then obtained in a time-marching fashion where, at each time step, the prediction coefficients are computed via L2-norm minimization of the unsteady residual vector as provided from the underlying flow solver. As suggested by previous studies, a further reduction of computational complexity is attempted by including a hyperreduction node selection, specifically the missing point estimation routine, in the prediction framework. Different model reduction and hyperreduction levels for the flowfield prediction of harmonic pitching motion of a 2D airfoil and a 3D aircraft in both subsonic and transonic conditions are investigated to determine their influence on the solution accuracy as well as on the required computational cost. Results show that the proposed technique accurately predicts unsteady solutions (maximum prediction error of about 3%) with a computational cost that is around 10% of the time needed to perform the equivalent high fidelity simulations. This performance achievement substantiates the idea that a reduced order model based on unsteady residual minimization is viable replacement for expensive flow solver evaluations in various applications where the computational budget is constrained.