Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils

Abstract

A Lanczos procedure is presently applied to a Navier-Stokes (N-S) solver for eigenvalues and eigenvectors associated with the small-perturbation analysis of the N-S equations' finite-difference representation for airfoil flows; the matrix used is very large, sparse, real, and nonsymmetric. The Lanczos procedure is shown to furnish complete spectral information for the eigenvalues, as required for transient-stability analysis of N-S solvers.