Spectral element - Fourier methods applied to simulation of turbulent pipe flow

Abstract

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 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 that employ Fourier expansions for each of these two directions in turn. For the case with Fourier expansions in the azimuthal direction, a cylindrical coordinate system is used.