FourierLegendre spectral methods for incompressible channel flow
Abstract
An iterative collocation technique is described for modeling implicit viscosity in threedimensional incompressible wall bounded shear flow. The viscosity can vary temporally and in the vertical direction. Channel flow is modeled with a FourierLegendre approximation and the mean streamwise advection is treated implicitly. Explicit terms are handled with an AdamsBashforth method to increase the allowable timestep for calculation of the implicit terms. The algorithm is applied to low amplitude unstable waves in a plane Poiseuille flow at an Re of 7500. Comparisons are made between results using the Legendre method and with Chebyshev polynomials. Comparable accuracy is obtained for the perturbation kinetic energy predicted using both discretizations.
 Publication:

NASA STI/Recon Technical Report A
 Pub Date:
 June 1984
 Bibcode:
 1984STIA...8439969Z
 Keywords:

 Channel Flow;
 Fourier Transformation;
 Incompressible Flow;
 Legendre Functions;
 Spectral Methods;
 Three Dimensional Flow;
 Chebyshev Approximation;
 Collocation;
 Computational Fluid Dynamics;
 Iterative Solution;
 Laminar Flow;
 Shear Flow;
 Viscous Flow;
 Wall Flow;
 Fluid Mechanics and Heat Transfer