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

• Published in: Journal of computational physics 1991-12, Vol.97 (2), p.398-413
• Main Authors: Mahajan, Aparajit J, Dowell, Earl H, Bliss, Donald B
• Format: Article
• Language: English
• Subjects: Aerodynamics
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/0021-9991(91)90006-7

A Lanczos procedure is applied to a Navier-Stokes solver for computing eigenvalues and eigenvectors. These eigenvalues and eigenvectors are associated with small perturbation analysis of a finite difference representation of the Navier-Stokes equations for flows over airfoils. A combination of block tridiagonal matrices is converted into a two-dimensional matrix for this eigensystem calculation. This matrix is very large, sparse, real, and nonsymmetric. A separate procedure, based on lopsided iteration, is also used to determine the eigensystem. The results from these two procedures are compared. The Lanczos procedure provides complete spectral information about the eigenvalues, whereas the lopsided iteration provides only a few of the eigenvalues which are largest in magnitude and the corresponding eigenvectors. Such eigensystem information is central to transient stability analysis of Navier-Stokes solvers, for determining the modal behavior of fluid in a fluid-structure interaction problem and for development of reduced order models based on variational principles for Navier-Stokes solvers.