Application of spectral collocation techniques to the stability of swirling flows

Abstract A Chebyshev spectral collocation method for the temporal and spatial stability of swirling flows is presented. The linearized stability equations in cylindrical coordinates are solved using the method and eigenvalues obtained by employing the QZ routine. The developed algorithm is found to be robust and easily adaptable to various flow configurations, including internal and external flows, with only minor changes in the application of the boundary conditions. The accuracy and efficiency of the spectral method is tested for plane Poiseuille flow, annular flow, rotating pipe flow, and a trailing line vortex.