A Spectral Element Method for Fluid Dynamics: Laminar Flow in a Channel Expansion
Abstract
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible NavierStokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a highorder Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a onedimensional inflowoutflow advectiondiffusion equation, and the method is then applied to laminar twodimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
 Publication:

Journal of Computational Physics
 Pub Date:
 June 1984
 DOI:
 10.1016/00219991(84)901281
 Bibcode:
 1984JCoPh..54..468P
 Keywords:

 Channel Flow;
 Computational Fluid Dynamics;
 Finite Element Method;
 NavierStokes Equation;
 Separated Flow;
 Spectral Methods;
 Advection;
 Backward Facing Steps;
 Diffusion Theory;
 Expansion;
 Incompressible Flow;
 Laminar Flow;
 Poisson Equation;
 Reattached Flow;
 Fluid Mechanics and Heat Transfer