Effectivity and efficiency of selective frequency damping for the computation of unstable steady-state solutions

JOURNAL OF COMPUTATIONAL PHYSICS

卷:375

Article

Casacuberta, Jordi¹  Groot, Koen J.¹  Tol, Henry J.¹  Hickel, Stefan¹ 

[1] Delft Univ Technol, Aerodynam Grp, Fac Aerosp Engn, Kluyverweg 1, NL-2629 HS Delft, Netherlands

关键词: Computational fluid dynamics;    Flow stability analysis;    Flow control;    Selective frequency damping;   

DOI  :  10.1016/j.jcp.2018.08.056

来源: Elsevier

【 摘 要 】

Selective Frequency Damping (SFD) is a popular method for the computation of globally unstable steady-state solutions in fluid dynamics. The approach has two model parameters whose selection is generally unclear. In this article, a detailed analysis of the influence of these parameters is presented, answering several open questions with regard to the effectiveness, optimum efficiency and limitations of the method. In particular, we show that SFD is always capable of stabilising a globally unstable systems ruled by one unsteady unstable eigenmode and derive analytical formulas for optimum parameter values. We show that the numerical feasibility of the approach depends on the complex phase angle of the most unstable eigenvalue. A numerical technique for characterising the pertinent eigenmodes is presented. In combination with analytical expressions, this technique allows finding optimal parameters that minimise the spectral radius of a simulation, without having to perform an independent stability analysis. An extension to multiple unstable eigenmodes is derived. As computational example, a two-dimensional cylinder flow case is optimally stabilised using this method. We provide a physical interpretation of the stabilisation mechanism based on, but not limited to, this Navier-Stokes example. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free