Pseudo-spectral methods for homogeneous or inhomogeneous flows

Pseudo-spectral formulations are implemented for the resolution of unsteady Navier-Stokes equations. A finite difference scheme and a pseudo-spectral scheme are used and compared for the calculation of time derivatives for cubic domain or square pipe inhomogeneous flows. The Navier-Stokes unsteady equations are solved by expanding the unknown functions for each space or time direction on Fourier series on the basis of first kind Chebyshev polynomials. An exact Taylor-Green solution is compared with the results of the pseudo-spectral space-time calculations, and differences between theoretical and computed values are found to be less than 0.00001.