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Two schemes for the numerical solution of the Navier-Stokes equations at moderate Reynolds number are discussed. The essential ingredient of the present methods is the use of the fast Fourier transform. In one scheme, discrete Fourier transformation is used to compute the convolution sums appearing in the formally Fourier-transformed Navier-Stokes equations. This results in an aliasing-free, energetically conservative (when ν = 0) scheme that can be used convincingly as a model on which to test turbulence theories. The second scheme calculates in real space. Fast Fourier transform is used to solve Poisson's equation for the pressure. The latter scheme offers the advantages of speed and flexibility. The schemes are critically compared and a survey of applications is made.
Steven A. Orszag (Mon,) studied this question.