## A Chebyshev Matrix Method for Spatial Modes of the Orr-Sommerfeld Equation, Volume 4247National Aeronautics and Space Administration, Office of Management, Scientific and Technical Information Division, 1989 - Boundary layer - 13 pages |

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adapted to problems Aerospace Engineering Sciences basic state velocity Biringen Blausius boundary layer boundary conditions requiring boundary layer flows Bridges and Morris6 calculations channel and boundary channel flow Chebyshev collocation matrix Chebyshev domain Chebyshev matrix collocation Chebyshev Matrix Method Chebyshev polynomials Chebyshev-tau method collocation matrix method collocation points companion matrix method companion matrix technique complex wave number conditions requiring different Danabasoglu Department of Aerospace derivative eigenfunction eigenvalue spectrum eigenvector equation 12 equation for Poiseuille free stream velocity i i i i I i i i i Jordinson1 Khorrami Langley Research Center last four rows least damped eigenvalue mapping transformation matrix collocation method Method for Spatial NASA nonlinear eigenvalue problem number of collocation obtain the spatial Orr-Sommerfeld equation parallel shear flows Performing Organization Poiseuille flow problem is linearized problems with different QZ algorithm requiring different transformations Reynolds stress semi-infinite domain solve the temporal Spatial Modes stability University of Colorado VAX/VMS velocity profile viscosity