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Direct Numerical Simulations of the incompressible Navier-Stokes equations have been performed with a parallel pseudo-spectral numerical method, to study the flow of an incompressible viscous fluid in a smooth pipe of radius R and length 30R. The fully developed flow is driven by a uniform and constant streamwise pressure gradient.
The numerical simulations have been performed by assigning the value of the friction Reynolds number, based on the pipe radius R and friction velocity, to three different values: Retau=200, 400 and 800. The main first- and second-order statitics are presented and discussed.
The method is based on a compact finite-differences scheme along the radial direction, and a Fourier expansion along the homogeneous directions. The undesired increase of the azimuthal spatial resolution as the pipe axis is approached is avoided by having the number of azimuthal modes vary with the radial coordinate. In particular they vary linearly, from a maximum at the wall to a minimum at the centerline.
The code is parallel with good efficiency on both distributed and shared memory architecctures. However, extending the parallel algorithm to a massively parallel message-passing approach will be key to achieve a further significant increase of Re.