Spectral Element Fourier Methods Applied to Simulation of Turbulent Pipe Flow
by
D. McIver
Department of Mechanical Engineering, University of Adelaide
Coauthors: H.M. Blackburn (CSIRO Building Construction and Engineering), G. Nathan (Department of Mechanical Engineering, University of Adelaide)

We present results from direct numerical simulations of turbulent pipe flow at a Reynolds number of 5000. The spatial discretisation employs Fourier expansions in one geometrically homogeneous direction coupled with tensor products of two-dimensional spectral elements in the remaining two coordinates. The geometry under study has two geometrically homogeneous directions, axial and azimuthal, and we compare statistics from two sets of simulations which employ Fourier expansions for each of these two choices in turn. For the case with Fourier expansions in the azimuthal direction, a cylindrical coordinate system is used. Previous applications using similar methods in cylindrical coordinates have employed special basis functions in elements that touch the axis; we demonstrate that exponential convergence is retained even when standard basis functions are used.

Date received: July 29, 1999