摘要
The computational cost of unsteady adjoint equations remains high in adjoint-based unsteady aerodynamic op-timization.In this letter,the solution of unsteady adjoint equations is accelerated by dynamic mode decomposi-tion(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.
基金
the Natural Science Foundation of Jiangsu Province(Grants No.BK20230202)
Basic Science(Natural Science)Re-search Project of Colleges and Universities in Jiangsu Province(Grant No.22KJB130005)
Changzhou Science and Technology Project(Grant No.CJ20220242)for financial support
Jiaqing Kou would like to thank the support of the Alexander von Humboldt Foundation(Ref 3.5-CHN-1227287-HFST-P)
Wenkai Yang would like to thank the support of the National Natural Science Foundation of China(Grant No.52205335)
supported by Changzhou Sci&Tech Pro-gram(Grant No.CM20223013).
