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

Jordi Casacuberta, Koen J. Groot, Henry J. Tol, Stefan Hickel*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

14 Citations (Scopus)
50 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)481-497
Number of pages17
JournalJournal of Computational Physics
Publication statusPublished - 15 Dec 2018


  • Computational fluid dynamics
  • Flow control
  • Flow stability analysis
  • Selective frequency damping


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