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

作　　者：Wengang Chen Jiaqing Kou Wenkai Yang 

机构地区：[1]Changzhou Institute of Technology,Changzhou 213032,China [2]Institute of Aerodynamics,RWTH Aachen University,Wüllnerstraße 5a,52062 Aachen,Germany

出　　处：《Theoretical & Applied Mechanics Letters》2023年第5期353-356,共4页力学快报（英文版）

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).

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.

关 键 词：Acceleration method Unsteady adjoint Dynamic mode decomposition Optimization efficiency 

分 类 号：O175[理学—数学]