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

Theoretical and Applied Mechanics Letters, vol. 13, pp. 100472

Abstract

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. Results 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.

Authors 3

1. Wengang Chen

   Changzhou Institute of Technology

   Affiliation as printed

   Changzhou Institute of Technology, Changzhou 213032, China

2. Jiaqing Kou corresponding Aachen Institute of Aerodynamics

   RWTH Aachen University

   Affiliation as printed

   Institute of Aerodynamics, RWTH Aachen University, Wüllnerstraße 5a, 52062 Aachen, Germany

3. Wenkai Yang

   Changzhou Institute of Technology

   Affiliation as printed

   Changzhou Institute of Technology, Changzhou 213032, China