A localized relaxation scheme for the computation of steady flows

The computation of steady flow solutions in unstable settings is often the first step in studying the instability features. For this purpose, we present a method inspired by the Selective Frequency Damping of Akervik \emph{et al.} (2006). A low-pass temporal filter is applied at a small number of locations in the flow, and these values are used to relax the nonlinear system. If the relaxation points are properly selected, such a scheme may stabilize the dynamics. In this case, the steady flow can be computed using a regular time marching procedure with almost the same computational cost and memory requirements as a regular simulation. The relation between the optimal location of the relaxation points and the wavemaker region will be discussed.