Coupled Newton–Krylov Time-Spectral Solver for Flutter and Limit Cycle Oscillation Prediction

Abstract

Flutter and limit cycle oscillation (LCO) are important phenomena that need to be considered in aircraft design. Previous harmonic-balance-based flutter and LCO prediction methods either have low linear convergence rates or require expensive Newton steps to achieve quadratic convergence. In this paper, we propose a preconditioned, Jacobian-free, coupled Newton–Krylov (CNK) method for the time-spectral aeroelastic equations. By solving the coupled system directly, the method reduces the computational cost of each Newton step, making quadratic convergence affordable. The proposed Jacobian-free method is easier to implement and requires less memory relative to previous methods. We demonstrate the capability of the CNK solver by verifying the results against a time-accurate solver and by comparing them to other harmonic-balance-based results reported in the literature. We observe that the proposed method is more efficient than the time-accurate method in LCO response simulations. And the LCO velocities and frequencies predicted by the proposed method and the time-accurate method are within 1% of relative difference when the same mesh is used. This method can be potentially used in aircraft design.