An adaptive selective frequency damping method

TL;DR

This paper introduces an adaptive selective frequency damping method that dynamically adjusts parameters to efficiently find unstable steady states in dynamical systems, overcoming previous limitations of convergence and long computation times.

Contribution

It proposes an adaptive algorithm that automatically selects optimal control parameters for the SFD method based on eigenvalue evaluation, improving convergence and efficiency.

Findings

Successfully applied to classical CFD test cases

Achieves steady-state solutions without prior stability knowledge

Reduces convergence time compared to traditional SFD

Abstract

The selective frequency damping (SFD) method is an alternative to classical Newton's method to obtain unstable steady-state solutions of dynamical systems. However this method has two main limitations: it does not converge for arbitrary control parameters; and when it does converge, the time necessary to reach the steady-state solution may be very long. In this paper we 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 a control coefficient and a filter width that ensure an optimum convergence of the SFD method. We apply this adaptive method to several classical test cases of computational fluid dynamics and we show that a steady-state solution can be obtained without any a priori knowledge of the flow stability properties.