- Mahajan, A.J. and Dowell, E.H. and Bliss, D.B., Eigenvalue calculation procedure for an Euler/Navier-Stokes solver with application to flows over airfoils,
J. Comput. Phys. (USA), vol. 97 no. 2
pp. 398 - 413 [0021-9991(91)90006-7] .
(last updated on 2007/04/09)
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 air-foils. 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
difference equations;eigenvalues and eigenfunctions;external flows;flow simulation;iterative methods;matrix algebra;Navier-Stokes equations;perturbation theory;