Local-in-time adjoint-based method for design optimization of unsteady flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:229

Article

Yamaleev, Nail K.¹  Diskin, Boris^2,3  Nielsen, Eric J.⁴ 

[1] N Carolina Agr & Tech State Univ, Dept Math, Greensboro, NC 27411 USA

[2] Natl Inst Aerosp, Hampton, VA 23666 USA

[3] Univ Virginia, Dept Mech & Aerosp Engn, Charlottesville, VA 22904 USA

[4] NASA, Computat AeroSci Branch, Langley Res Ctr, Hampton, VA 23681 USA

关键词: Time-dependent optimization;    Discrete adjoint equations;    Gradient methods;    Design optimization;    Euler equations;   

DOI  :  10.1016/j.jcp.2010.03.045

来源: Elsevier

【 摘 要 】

We present a new local-in-time discrete adjoint-based methodology for solving design optimization problems arising in unsteady aerodynamic applications. The new methodology circumvents storage requirements associated with the straightforward implementation of a global adjoint-based optimization method that stores the entire flow solution history for all time levels. This storage cost may quickly become prohibitive for large-scale applications. The key idea of the local-in-time method is to divide the entire time interval into several subintervals and to approximate the solution of the unsteady adjoint equations and the sensitivity derivative as a combination of the corresponding local quantities computed on each time subinterval. Since each subinterval contains relatively few time levels, the storage cost of the local-in-time method is much lower than that of the global methods, thus making the time-dependent adjoint optimization feasible for practical applications. Another attractive feature of the new technique is that the converged solution obtained with the local-in-time method is a local extremum of the original optimization problem. The new method carries no computational overhead as compared with the global implementation of adjoint-based methods. The paper presents a detailed comparison of the global- and local-in-time adjoint-based methods for design optimization problems governed by the unsteady compressible 2-D Euler equations. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free