Encapsulated formulation of the Selective Frequency Damping method

We present an alternative "encapsulated" formulation of the Selective Frequency Damping method for finding unstable equilibria of dynamical systems, which is particularly useful when analysing the stability of fluid flows. The formulation makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a "black box". The method is first applied to a scalar problem in order to analyse its stability and highlight the roles of the control coefficient $χ$ and the filter width $Δ$ in the convergence (or not) towards the steady-state. Then the steady-state of the incompressible flow past a two-dimensional cylinder at $Re=100$, obtained with a code which implements the spectral/hp element method, is presented.

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