| Summary: | To compute stability analysis numerically with high accuracy, it is crucial to carefully choose the base flow around which the governing equations will be linearised. The steady-state solution is mathematically appropriate because it is a genuine solution of the fluid motion equations. In this thesis we introduce an encapsulated formulation of the selective frequency damping (SFD) method. The SFD method is an alternative to Newton's method to obtain unstable equilibria of dynamical systems. In its encapsulated formulation, the SFD method makes use of splitting methods, which means that it can be wrapped around an existing time-stepping code as a 'black box'. This largely simplifies the implementation of a steady-state solver into an already existing unsteady code. However this method has two main limitations: it does not converge for arbitrary control parameters; and when it does, it may take a very long time to reach a steady-state solution. Hence we also present an adaptive algorithm to address these two issues. We show that by evaluating the dominant eigenvalue of a 'partially converged' steady flow, we can select SFD parameters that ensure an optimum convergence of the method. We apply this adaptive method to several classical two-dimensional test cases of computational fluid dynamics and we show that a steady-state solution can be obtained with a very limited (or without any) a priori knowledge of the flow stability properties. Eventually, we study the three-dimensional behaviour of the interaction between two identical co-rotating trailing vortices. We use the SFD method to obtain steady base flows and compute Tri-Global stability analysis. We show that there is a fundamental qualitative difference between the least stable eigenmode observed at Re = 250 and the most unstable eigenmode obtained at Re = 600.
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