Multigrid optimization for DNS-based optimal control in turbulent channel flows

JOURNAL OF COMPUTATIONAL PHYSICS

卷:366

Article

Nita, C.^1,2  Vandewalle, S.²  Meyers, J.¹ 

[1] Katholieke Univ Leuven, Dept Mech Engn, Celestijnenlaan 300A, B-3001 Leuven, Belgium

[2] Katholieke Univ Leuven, Dept Comp Sci, Celestijnenlaan 200A Box 2402, B-3001 Leuven, Belgium

关键词: DNS-based optimization;    Multigrid methods;    Damped L-BFGS;    Adjoint method;    Turbulent flow;   

DOI  :  10.1016/j.jcp.2018.03.044

来源: Elsevier

【 摘 要 】

The use of PDE-constrained optimization techniques in combination with transient three-dimensional turbulent flow simulations such as Direct Numerical Simulation (DNS) or Large-Eddy Simulation (LES) involves large computational cost and memory resources. To date, the minimization of a DNS-based cost functional is typically achieved by applying classical single-grid gradient-based iterative methods of quasi-Newton or non-linear conjugate gradient type. In the current study, a multigrid optimization (MG/OPT) strategy is investigated in order to speed up gradient-based algorithms designed for large scale optimization problems. The method employs a hierarchy of optimization problems defined on different representation levels. It aims to reduce the computational resources associated with the cost functional improvement on the finest level. We apply the MG/OPT method in the context of direct numerical simulations of a fully developed channel flow problem. The performance of the multi-grid optimization technique is compared against the single-grid optimization method in terms of equivalent function and gradient evaluations. Also the influence of the optimization problem properties and algorithmic parameters are investigated. It is found that, in some cases, the MG/OPT method accelerates the single-grid damped L-BFGS method by a factor of four. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free