Capacitance matrix technique for avoiding spurious eigenmodes in the solution of hydrodynamic stability problems by Chebyshev collocation method

Journal of Computational Physics

Volumn 238, Issue , 2013, Pages 210-216

  Hagan, Jonathan ^a   Priede, Janis ^a  

^a Faculty of Engineering and Computing   (United Kingdom)

Author keywords

Chebyshev collocation method; Hydrodynamic stability; Spurious eigenvalue

Indexed keywords

BOUNDARY CONDITIONS; CAPACITANCE; EIGENVALUES AND EIGENFUNCTIONS; HYDRODYNAMICS;

CAPACITANCE MATRIX; CHEBYSHEV COLLOCATION METHOD; EIGEN MODES; HYDRODYNAMIC STABILITY; MATRIX TECHNIQUE; ORR-SOMMERFELD EQUATIONS; PLANE POISEUILLE FLOW; SIMPLE++; SPURIOUS EIGENVALUE; STABILITY PROBLEM;

VORTICITY;

EID: 84873279470     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2012.12.012     Document Type: Article

References (16)

1. Anderson E., Bai Z., Bischof C., Blackford S., Demmel J., Dongarra J., Du Croz J., Greenbaum A., Hammarling S., McKenney A., Sorensen D. LAPACK Users' Guide 1999, SIAM, Philadelphia. third ed.
2. Boyd J.P. Chebyshev and Fourier Spectral Methods 2001, Dover, New York, pp. 139-142.
3. Canuto C., Hussaini M.Y., Quarteroni A., Zang T.A. Spectral Methods in Fluid Dynamics 1988, Springer, Berlin.
4. Dawkins P.T., Dunbar S.R., Douglass R.W. The origin and nature of spurious eigenvalues in the spectral tau method. J. Comput. Phys. 1998, 147:441-462.
5. Drazin P.G., Reid W.H. Hydrodynamic Stability 1981, Cambridge University Press, Cambridge, p. 141.
6. Gardner D.R., Trogdon S.A., Douglass R.W. A modified tau spectral method that eliminates spurious eigenvalues. J. Comput. Phys. 1989, 80:137-167.
7. Gottlieb D., Orszag S.A. Numerical Analysis of Spectral Methods: Theory and Applications 1977, SIAM, Philadelphia, pp. 143-148.
8. Huang W., Sloan D.M. The pseudospectral method for solving differential eigenvalue problems. J. Comput. Phys. 1994, 111:399-409.
9. Lindsay K.A., Ogden R.R. A practical implementation of spectral methods resistant to the generation of spurious eigenvalues. J. Numer. Methods Fluids 1992, 15:1277-1294.
10. McFadden G.B., Murray B.T., Boisvert R.F. Elimination of spurious eigenvalues in the Chebyshev tau spectral method. J. Comput. Phys. 1990, 91:228-239.
11. Orszag S.A. Accurate solution of the Orr-Sommerfeld problem. J. Fluid Mech. 1971, 50:689-703.
12. Peyret R. Spectral Methods for Incompressible Viscous Flow 1982, Springer, Berlin.
13. Priede J., Aleksandrova S., Molokov S. Linear stability of Hunt's flow. J. Fluid Mech. 2010, 649:115-134.
14. Weideman J.A.C., Reddy S.C. A MATLAB differentiation matrix suite. ACM Trans. Math. Softw. 2000, 26:465-519.
15. Zebib A. A Chebyshev method for the solution of boundary value problems. J. Comput. Phys. 1984, 53:443-455.
16. Zebib A. Removal of spurious modes encountered in solving stability problems by spectral methods. J. Comput. Phys. 1987, 70:521-525.