A novel optimization algorithm for the selective frequency damping parameters

Abstract

Flow stability analysis is of great importance in flow physics and control. The solution of base flow, achieved as the steady state of the unsteady Navier–Stokes equation (UNSE), counts among keystones in the field of flow stability analysis. To obtain the numerical solution of base flow, the selective frequency damping (SFD) method has been widely used, with the numerical effectivity and computational efficiency being closely related to the selection of a pair of parameters (χ,Δ), where χ represents the control coefficient and Δ denotes the filter width. In the present work, a novel method for calculating the base flow of the unsteady Navier–Stokes equation (UNSE) has been established, by combining the SFD method with the immersed boundary method. Detailed analysis of the influences of the SFD parameters is presented, attempting to establish the relationships between the parameters and eigenvalues for the Jacobian matrix of UNSE. The dynamic mode decomposition method is introduced to calculate the eigenvalues for the velocity field, and several techniques and strategies are applied for improving the solving accuracy. Further, an optimization method of the parameter pair is developed to accelerate the convergence to the steady state, trying to minimize the spectral radius of the Jacobian matrix in the parameter space of (χ,Δ). Two test simulations, that is, flow past a cylinder and flow past two side-by-side cylinders at Re=100, are conducted by applying the optimization method. A faster convergence rate and higher efficiency are demonstrated compared to the results using the previous methods.