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

Abstract

Listen

Translate article

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.