an:03850665
Zbl 0535.76035
Patera, Anthony T.
A spectral element method for fluid dynamics: Laminar flow in a channel expansion
EN
J. Comput. Phys. 54, 468-488 (1984).
00148907
1984
j
76D05 76M99
spectral element method; high-order Lagrangian interpolant; Chebyshev collocation points; pressure; viscous contributions; variational principle; one-dimensional inflow-outflow advection-diffusion equation; laminar two-dimensional (separated) flow; channel expansion
Summary: 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 Navier-Stokes 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 high-order 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 one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.