A spectral element method applied to unsteady flows at moderate Reynolds number
The spectral element method is a high-order technique for solution of the incompressible Navier-Stokes equations which combines spectral expansions with finite element methodology to give high accuracy in general geometries. In the spectral element discretization, the computational domain is broken up into macro-elements, and the velocity and pressure in each element are represented as high-order Lagrangian inter polants. The nonlinear terms in the equation are then treated with explicit collocation, while the pressure and viscous contributions are handled implicitly with variational projection operators. Parallel static condensation applied to the implicit equations gives an operation count commensurate with that for low-order sub-structure techniques at the same resolution. A time-splitting technique is presented for solution of the Navier-Stokes equations, and results are given for linear and (three dimensional) secondary spatial stability of plane Poiseuille flow, and for steady and unsteady separated channel flows at Reynolds numbers of several thousand.
KeywordsReynolds Number Spectral Element Spectral Element Method Plane Poiseuille Flow Spanwise Wavenumber
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