Accelerating the convergence of steady adjoint equations by dynamic mode decomposition

To improve the efficiency of adjoint-based optimization algorithms, dynamic mode decomposition (DMD) technology is used to accelerate the convergence of steady adjoint equations in this paper. During pseudo-time marching, adjoint fields are projected onto the modal space and modal analysis is carried out by DMD. When only first zero frequency mode is reserved, the convergence speed of adjoint equations is significantly enhanced. Through two examples of flow past airfoils in subsonic and transonic flows and a transonic optimization example, the validity of the proposed methodology is verified. Results indicate that the proposed methodology can improve optimization efficiency remarkably, and the iteration step number of adjoint equations is reduced by almost 60%.