A dynamic-mode-decomposition-based acceleration method for unsteady adjoint equations at low Reynolds numbers

The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic optimization. In this letter, the solution of unsteady adjoint equations is accelerated by dynamic mode decomposition (DMD). The pseudo-time marching of every real-time step is approximated as an infinite-dimensional linear dynamical system. Thereafter, DMD is utilized to analyze the adjoint vectors sampled from these pseudo-time marching. First-order zero frequency mode is selected to accelerate the pseudo-time marching of unsteady adjoint equations in every real-time step. Through flow past a stationary circular cylinder and an unsteady aerodynamic shape optimization example, the efficiency of solving unsteady adjoint equations is significantly improved. Re-sults show that one hundred adjoint vectors contains enough information about the pseudo-time dynamics, and the adjoint dominant mode can be precisely predicted only by five snapshots produced from the adjoint vectors, which indicates DMD analysis for pseudo-time marching of unsteady adjoint equations is efficient.

Automated summary

In this letter, the authors propose a method to accelerate the solution of unsteady adjoint equations using dynamic mode decomposition (DMD). By approximating the pseudo-time marching as an infinite-dimensional linear dynamical system and analyzing the adjoint vectors using DMD, the efficiency of solving unsteady adjoint equations is significantly improved.