Removal of spurious modes encountered in solving stability problems by spectral methods
Journal of Computational Physics
A modified tau spectral method that eliminated spurious eigenvalues
Journal of Computational Physics
Elimination of spurious eigenvalues in the Chebyshev Tau spectral method
Journal of Computational Physics
The pseudospectral method for solving differential eigenvalue problems
Journal of Computational Physics
The origin and nature of spurious eigenvalues in the spectral tau method
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A MATLAB differentiation matrix suite
ACM Transactions on Mathematical Software (TOMS)
Hi-index | 31.45 |
We present a simple technique for avoiding physically spurious eigenmodes that often occur in the solution of hydrodynamic stability problems by the Chebyshev collocation method. The method is demonstrated on the solution of the Orr-Sommerfeld equation for plane Poiseuille flow. Following the standard approach, the original fourth-order differential equation is factorised into two second-order equations using a vorticity-type auxiliary variable with unknown boundary values which are then eliminated by a capacitance matrix approach. However the elimination is constrained by the conservation of the structure of matrix eigenvalue problem, it can be done in two basically different ways. A straightforward application of the method results in a couple of physically spurious eigenvalues which are either huge or close to zero depending on the way the vorticity boundary conditions are eliminated. The zero eigenvalues can be shifted to any prescribed value and thus removed by a slight modification of the second approach.